RELATED PATENT APPLICATION

[0001]
U.S. patent application Ser. No. 09/687,044, filed Oct. 11, 2000, and titled SATELLITE NAVIGATION RECEIVER AND METHOD is incorporated herein by reference.
FIELD OF THE INVENTION

[0002]
The present invention relates to satellitenavigation receivers and systems, and more particularly to minimalcost field devices that are assisted with information about precise time and frequency by a network to improve timetofirstfix, accuracy, and manufacturing costs of the field devices.
DESCRIPTION OF THE PRIOR ART

[0003]
Global positioning system (GPS) receivers use signals received from typically three or more earthorbiting satellites to determine navigational data such as position and velocity. GPS signals are available worldwide at no cost and are now being routinely used to determine the location of automobiles to within one city block, or better. Dualfrequency carrier GPS receivers typically track a pair of radio carriers, L1 and L2, associated with the GPS satellites to generate accumulated deltarange measurements (ADR) from Pcode modulation on those carrier frequencies and at the same time track L1 C/Acode to generate code phase measurements. Carrier frequency L1 is allocated to 1575.42 MHz and carrier frequency L2 is positioned at 1227.78 MHz. Less expensive receivers tune only one carrier frequency, and therefore do not have adequate information to compute the local troposheric and ionospheric signalpropagation delays that appear as position errors. At such frequencies, radio carrier signals travel by lineofsight. Thus buildings, mountains and the horizon can block reception, and multipath reflections can interfere with good reception.

[0004]
Each one of the constellation of GPS satellites in orbit about the earth transmits one of thirtytwo unique identifying codes in a codedivision multiple access (CDMA) arrangement. Such allows all of the many GPS satellites to transmit in spread spectrum mode at the same frequency, plus or minus a Doppler frequency shift of that frequency as results from the satellite's relative velocity. Particular satellites are sorted out of a resulting jumble of signals and noise by correlating a 1023 “chip” code to one of the thirtytwo pseudo random number (PRN) sequence codes that are preassigned to individual GPS satellites. These codes are not necessarily being transmitted in phase with one another. Therefore, “finding” a GPS satellite initially involves searching various carrier frequencies, to account for Doppler frequency shift and local crystal oscillator inaccuracies. The searching also needs to find a code match, using 1023 different code phases and twenty or more possible correlation code templates.

[0005]
The single largest uncertainty stems from the random frequencies possible from typical local oscillators at startup. Therefore, the apparentDoppler frequency is known only within wide search boundaries. Knowing the actual Doppler frequency is not much help, because the local oscillator can be so far off nominal on its own.

[0006]
From the user's standpoint, at least two operational characteristics of prior art GPS receivers interfere with complete satisfaction. Such conventional receivers often quit working indoors because the buildings reduce the local signal field level to less than the receiver's maximum sensitivity. And, most receivers take a very long time to produce a position solution from a cold start.

[0007]
Intensive calculations in GPS receivers have necessitated high clock speeds and lots of expensive storage memory. These, in turn, demand expensive and comprehensive hardware. Manufacturers and users alike would appreciate lighter and thinner navigation solutions that could use inexpensive platforms or share preexisting platforms for other applications.

[0008]
The Internet also represents a way for individual GPS receivers to monitor differential correction data in their areas and to offload calculationintensive tasks on regional webservers that have high performance processors.

[0009]
SnapTrack, Inc., (San Jose, Calif.) is a commercial supplier of wireless assisted GPS (WAG) systems. Time, frequency, and approximate location data are extracted from a wireless network to assist GPSsignal processing in a navigation receiver. Such technology is described in a number of United States Patents assigned to SnapTrack, including: U.S. Pat. Nos. 5,945,944; 5,663,734; 5,781,156; 5,825,327; 5,831,574; 5,841,396; 5,812,087; 5,874,914; 5,884,214; etc. Also see, U.S. Pat. No. 6,078,290.
SUMMARY OF THE INVENTION

[0010]
It is therefore an object of the present invention to provide a satellitenavigation receiver that can work indoors with extremely low signalstrength levels.

[0011]
It is another object of the present invention to provide a satellitenavigation receiver that produces position solutions rapidly after each cold start.

[0012]
It is a further object of the present invention to provide a satellitenavigation system that is inexpensive.

[0013]
It is a still further object of the present invention to provide a satellitenavigation system that interfaces with the Internet.

[0014]
Briefly, a system embodiment of the present invention comprises a cellphone, a base cellular telephone site, and a webserver. Each is paired with a GPS receiver. The GPS receiver associated with the cellphone is aided with information received from the cellsite and webserver that help reduce satellite search uncertainty. Time difference and/or frequency difference measurements are taken with data collected from what the cellphone and its GPS receiver assume to be accurate time and frequency. Correction information is used in postprocessing of the velocity solutions computed by the cellphone to arrive at more precise determinations for the system.

[0015]
An advantage of the present invention is that a system and method are provided that reduce the costs of user navigation equipment.

[0016]
Another advantage of the present invention is that a system and method are provided that improve sensitivity and timetofirstfix enough for urban canyon and indoor use.

[0017]
A further advantage of the present invention is that a system and method are provided that makes higher level database services to be offered on the Internet which are related to realtime and historical user position fixes.

[0018]
These and other objects and advantages of the present invention will no doubt become obvious to those of ordinary skill in the art after having read the following detailed description of the preferred embodiments which are illustrated in the various drawing figures.
IN THE DRAWINGS

[0019]
[0019]FIG. 1 is a functional block diagram of an infrastructureassisted navigation system embodiment of the present invention that includes a cellular telephone, a cellulartelephone base site, and a webserver;

[0020]
[0020]FIG. 2 is a diagram representing how the differences in two different clocks can be quantified as clock pulse accumulations in digital counters;

[0021]
[0021]FIG. 3 is a diagram representing a bias skew of a second event in the last onethousandth part of a 1PPS period;

[0022]
[0022]FIG. 4 is a diagram of the relationships between GPS events, cellsite events, and the various kinds of timing bias that are computed by embodiments of the present invention;

[0023]
[0023]FIG. 5 is a timing diagram representing the relationships between clocks and time periods in support of the mathematical equations presented herein;

[0024]
[0024]FIG. 6 is a diagram representing a quantization of external cellsite clocks in a freqDiff observation;

[0025]
[0025]FIG. 7 is a diagram representing the physical geometry of a GPS satellite, cellsite, and cellphone, and how timing/frequency biases can affect position information;

[0026]
[0026]FIG. 8 is a timing diagram that represents each clock with its own system time and a corresponding clock bias from this time, the sum of these two produce a reference time used for making observations in a receiver, and the timedifference observations are taken in between these timereferences;

[0027]
[0027]FIG. 9 is a chart of the frequency relationships amongst the cellsite, cellphone, and GPS receiver 1PPS outputs; and

[0028]
[0028]FIG. 10 is a functional block diagram of a second infrastructureassisted navigation system embodiment of the present invention wherein no political or economic opportunity existed to include a GPS receiver at a cellulartelephone base site, so a cellphone and GPS receiver combination was permanently parked at a stationary location to serve instead.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0029]
Three hardwarebased measurements can be used to synchronize the local clocks in two independent systems, e.g., (1) timedifference, (2) frequency difference, and (3) crystal temperatureversusfrequency models. Any or all three can be used to synchronize clocks. In a timeDiff observable, if the time difference between time events from two different time sources is known, the time of an event at one time source can be used to compute the time of the event at the other time source. In a freqDiff observable, if the frequency difference between two clocks is known, then finding the frequency of one can be used to predict the frequency of the other. In a tempMeas observable, a temperaturefrequency calibration model is used to predict the frequency of a local GPS clock by measuring the crystal temperature. If one of the time sources is a GPS receiver, other clocks can be related to GPS time. Such potentially allows devices all around the world to be time and frequency synchronized to a common and stable reference, for example, the GPS system atomic clocks.

[0030]
[0030]FIG. 1 illustrates a system 100, in an embodiment of the present invention, that includes a cellsite 102, at least one cellphone 104, and a network server 106. The cellsite 102 comprises a cellular transceiver 108, its reference clock 110, and a GPS receiver112. The cellphone 104 has a cellularphoneserviceband receiver 114 that is used to track the frequency and phase of signals it receives from the cellsite 102. The cellphone 104 also includes its own GPS receiver115. The network server 106 receives and distributes time information and other data from both the cellsite and cellphone GPS receivers over a data network 116. A database 118 of positions and their time and frequency offsets from GPS time is collected for later reference.

[0031]
Passive network synchronization embodiments of the present invention use the cellsite GPS receiver to synchronize the cellsite clocks to GPS time. Then both the cellphone GPS receiver clock and the cellphone clock can be synchronized to GPS time by the network server over a network infrastructure, e.g., the Internet. A typical GPS receiver generates a onepulsepersecond (1PPS) time reference that can be compared and related with timeDiff circuitry to a 1PPS clock derived from each of the cellsite and cellphone cellulartelephony radio carriers. Other observation intervals besides one second would also work the same way, but the mathematics are simpler when a one second time interval is used.

[0032]
Embodiments of the present invention can use three different communication links to transfer time and frequency data. One links the GPS reference receivers 112 at the cellsite 102 with the network server 106. A second carries softwareAPI or packetcommunication between the cellphone 114 and GPS receiver 115 in the cellphone, either directly in the cellphone or indirectly through the network server. Sharing data directly between the receivers helps improve system performance. A third connection links the network server 106 and cellphone to both the cellphone and GPS receiver. The network server 106 can also be located at the cellsite 102 and communicate via the cellular telephony system transceivers 108 and 114.

[0033]
Timedifferenceofarrival measurements (TDOA), e.g., from a cellsite to a cellphone, can be used for positioning inside a combined cellphone and GPS receiver to improve positioning availability and accuracy. Timestamps sent from the cellsite to the cellphone can be combined with a priori knowledge of the cellsite position, the cellsite clock bias and the cellsite drift from GPS time. Such timestamps can be used to transfer time information from the cellsite to the cellphone with an accuracy affected only by the radiosignal propagation distance between the cellphone and the cellsite.

[0034]
The corrective frequency offset of the cellphone carrierfrequency synthesizer loop can be used to estimate the GPS receiver frequency offset. Such estimate is used to reduce the frequency uncertainty and thus reduce the timetofirstfix, improve receiver sensitivity, and/or reduce the size and powerconsumption of the hardware. Digital numericcontrolled oscillator (NCO) and analog voltagecontrolled oscillator (VCO) are both commonly used in such carrierfrequency synthesizer loops.

[0035]
The tempmeas measurement can be used to further improve the frequencytransfer accuracy passing from a cellphone to a GPS receiver. The freqDiff observation can be used alone in frequency transfers without any timeDiff observation. The timeDiff observation can also be used without the freqDiff observation for combined time and frequency transfers. The time transfer accuracy is preferably improved by reducing the timeDiff hardware quantization noise with softwarebased filters. Cellphone observations of the cellsite frequency and phase can be used in dualmode positioning system alternative embodiments of the present invention.

[0036]
The term “passive synchronization” as used herein means the time and frequency offsets of the clocks in the cellsite and cellphone are only observed with respect to a GPS receiver clock. Calibrations are made later by sending the measured offsets through the communication layers, e.g., using transfer control protocol/Internet protocol (TCP/IP) packets on the Internet. The real clocks in the cellphone and cellsite are not controlled. The signals from these clocks are merely observed, and the corrective data obtained is not in any way fed back to the source to change the clocks. Rather, the data is used mathematically at the network server and in the GPS receiver software to assist in the GPSsatellite search and then in the position calculation.

[0037]
[0037]FIG. 2 diagrams the time relationships between a GPS 1PPS period 202, a cell 1PPS period 204, and an output counter value 206. A timeDiff observation can be made with a counter circuit that uses a GPS master clock for its input frequency. The number of internal clocks are counted between the two event sources, e.g., the internal 1PPS 202 and the external (or cell) 1PPS 204. The result is periodically output and the counter is restarted, such that for every second of time there will be two counter outputs.

[0038]
Both output count values can be combined to estimate a key parameter, the bias between the two clock sources. Each restart at the external 1PPS 204 produces a bias result. If the counter is instead restarted on the internal 1PPS 202, the result is one minus the bias. The external 1PPS (from the cellsite or cellphone) can be synchronized to the internal 1PPS (the GPS receiver) in one of at least two ways, e.g., with a smooth steered or an unsteered internal 1PPS.

[0039]
Referring now to FIG. 3, it is assumed that a GPS 1PPS timing edge is accurately slaved to GPS system time. In this way, the GPS 1PPS timing edge represents “true” GPS time. A 1PPS edge can be generated by a countdown circuit that is started by a 999thmillisecond interrupt derived from the GPSinteger second. An interrupt range of ±1 millisecond is preferred so that the 1PPS can be adjusted to occur anywhere between msec999 and msec1 in the GPSinteger second. A msecbias error is computed in the GPS receiver as the GPSmillisecond timer to “true” GPStime error. If the GPSreceiver oscillator drifts from GPS time, such msecbias error will change. The countdown value will also change to reflect the drift. When the bias integrates more than ±0.5 msec, the GPS millisecond counter is preferably adjusted to keep the circuit in range.

[0040]
The smoothsteered method embodiment of the present invention is used in GPS receivers at the cellsites since the msecbias error is known. Time is known in the GPS receiver and can be passively transferred to the cellsite by measuring any offset between GPS time and a cellsite time reference.

[0041]
The time associated with the cellsite 1PPS can be computed as, TimeCS equals timeGPS+biasCSG. Wherein, the variable biasCSG represents the time offset between the cellsite and GPS time. It is estimated using a function that uses either a snapshot or a filtered estimate using the timeseries of the measurements Ni1, Ni2, for all i.

[0042]
The unsteered internal 1PPS method embodiment of the present invention does not use the additional countdown circuit. The internal 1PPS is generated directly from the millisecond interrupt corresponding to the integer GPS second event. Such still requires that the millisecond interrupt that corresponds to the GPS integer second be periodically shifted when the msecbias error grows beyond a predetermined threshold. The time between internal PPS events can be greater or less than one second. The step shifts that occur are brief, and do not adversely affect the receiver. It knows when the event will occur, and the 1msec shift can be accounted for in the computed residual msecbias error.

[0043]
The unsteered reference can be used by a GPS receiver in a cellphone whenever the position is being requested from the cellphone user interface. Such GPS receiver is typically not tracking satellites at the moment, and so the GPS msecbias error will be unknown. The inverse problem exists in the cellphone. GPS time is not known, and time is being transferred from the cell network to the cellphone.

[0044]
In operation, the time and frequency offset of a particular cellsite is obtained from a network server. The position of the cellsite is also useful in the solution calculations. The offset between the cellphone clock and the GPS receiver clock is measured. An estimate of the GPS receiver time and frequency offset is computed from GPS time, and is used to reduce the GPS satellite search range.

[0045]
The timeDiff observation is used in both the cellphone and the cellsite to reduce the total number of unknowns in the system. The timeDiff measurement is defined herein as the difference in time between two time events generated by two different sources. Both clocks generate a signal with the same expected period based on the expected nominal frequency of each clock. The measurement is the number of clocks between consecutive events.

[0046]
Because all clocks have some frequency offset from the desired nominal frequency, the Bias is also constantly changing due to the effect of the frequency offset from nominal of both clocks.

[0047]
Suppose that “Freq” equals the actual physical frequency that is observed, it also equals baseFreq+drift (eq2). The “baseFreq” equals a desired frequency, e.g., the clock is designed to operate at this frequency but appears as “Freq” due to imperfections, aging, and temperature effects, the actual frequency appears. “Drift” equals frequency offset between the current frequency and the desired nominal frequency.

[0048]
Assume now that both clocks generate asynchronous onesecond time event signal pulses with a specific time interval between. A onesecond event can be generated with a counter that counts a specific number of reference clocks and then outputs a pulse when the desired count is reached. The onesecond count number is the nominal crystal frequency.

[0049]
The actual time produced is equal to the number of clocks times the “true” period of each clock. Assuming a constant drift, the “true” period of each clock is the “ClockPeriod” variable, which equals the inverse of the frequency in Hertz.

[0050]
The actual time period produced, DT, equals baseFreq/freq. Inserting equation2,
$\begin{array}{cc}\begin{array}{c}\mathrm{DT}=\text{\hspace{1em}}\ue89e\text{(}\ue89e\mathrm{freq}\mathrm{drift}\ue89e\text{)}\ue89e\text{/}\ue89e\mathrm{freq}\\ =\text{\hspace{1em}}\ue89e1\mathrm{drift}\ue89e\text{/}\ue89e\mathrm{freq}\\ =\text{\hspace{1em}}\ue89e1+\mathrm{deltaBias},\end{array}& \text{(}\ue89e\mathrm{equation}\ue89e\text{}\ue89e3\ue89e\text{)}\end{array}$

[0051]
where, deltaBias equals the change in the bias that occurs between the two events.

[0052]
The effect of equation3 is that with each onesecond event, accumulate an additional increment to the total bias.

[0053]
For the 1PPS made with a steering clock when GPS time is known, the offset can be estimated from GPS time and steer the clock to always be within one clock of the “true” time that was desired at the event.

[0054]
Alternatively, the 1PPS can be left unsteered. The total bias is maintained in software and accounted for without a loss of synchronization when all calibration is in software.

[0055]
Extending to two clocks, baseGRfreq equals the expected the frequency of clock used in the GPS receiver (Hz). “BaseCSfreq” equals the expected frequency of the clock used in the cellsite (Hz). “FreqGR” equals the actual observed frequency of the GPS receiver (Hz). “FreqCS” equals the actual observed frequency of the cellsite (Hz). “BiasGRi” equals the bias of a GPS receiver's 1PPS from “true” GPS time at time Ti. “BiasCSi” equals the bias of a cellsite's 1PPS from “true” GPS time at time Ti. “DeltaBiasGR12” equals the change in bias in the GPS receiver from t1 to t2. “DeltaBiasCS12” equals the change in bias in the cellsite from t1 to t2.

[0056]
A reference clock and an unknown clock are defined, then the GPS clock is chosen to be the reference. It can synchronized to GPS by tracking the satellites.

[0057]
The cellsite is defined to be the unknown clock that is to be synchronized to GPS time.

[0058]
The “true” time between the GPS and cellsite events is defined. TDij equals “true” time between two consecutive events in the ith time where the source of the newest event is the jth source. J=1 is the cellsite and j=2 equals the GPS receiver.

[0059]
[0059]FIG. 4 represents the relationships between the “true” GPS 1PPS events, the actual locations of the 1PPS events, and the “true” tDiff observations. These observations can be made,
$\begin{array}{c}\mathrm{BiasGR2}=\text{\hspace{1em}}\ue89e\mathrm{biasGR1}+\mathrm{deltaBiasGR12}\\ =\text{\hspace{1em}}\ue89e\mathrm{biasGR1}\mathrm{driftGR}/\mathrm{freqGR}\\ \mathrm{BiasCS2}=\text{\hspace{1em}}\ue89e\mathrm{biasCS1}+\mathrm{deltaBiasCS12}\\ =\text{\hspace{1em}}\ue89e\mathrm{biasCS1}\mathrm{driftCS}/\mathrm{freqCS},\\ \mathrm{TD11}=\text{\hspace{1em}}\ue89e\left(1+\mathrm{biasCS1}\right)\left(1+\mathrm{biasGR1}\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{biasCS1}\mathrm{biasGR1}\\ \mathrm{TD12}=\text{\hspace{1em}}\ue89e\text{(}\ue89e1+\mathrm{biasGR1}+\text{(}\ue89e1\mathrm{driftGR}\ue89e\text{/}\ue89e\mathrm{freqGR}\ue89e\text{)}\ue89e\text{)}\left(1+\mathrm{biasCS1}\right)\\ =\text{\hspace{1em}}\ue89e1+\mathrm{biasGR1}\mathrm{driftGR}/\mathrm{freqGR}\mathrm{biasCS1}\\ =\text{\hspace{1em}}\ue89e1+\mathrm{biasGR1}+\mathrm{deltaBiasGR12}\mathrm{biasCS1}\\ =\text{\hspace{1em}}\ue89e1+\mathrm{biasGR2}\mathrm{biasCS1}\\ =\text{\hspace{1em}}\ue89e1\left(\mathrm{biasCS1}\mathrm{biasGR2}\right)\\ \mathrm{TD21}=\text{\hspace{1em}}\ue89e\text{(}\ue89e1+\mathrm{biasCS1}+\text{(}\ue89e1\mathrm{driftCS}\ue89e\text{/}\ue89e\mathrm{freqCS}\ue89e\text{)}\ue89e\text{)}(1+\mathrm{biasGR1}+\\ \text{\hspace{1em}}\ue89e\text{(}\ue89e1\mathrm{driftGR}/\mathrm{freqGR}\ue89e\text{)}\ue89e\text{)}\\ =\text{\hspace{1em}}\ue89e\left(2+\mathrm{biasCS1}+\mathrm{deltaBiasCS12}\right)\\ \text{\hspace{1em}}\ue89e\left(2+\mathrm{biasGR1}+\mathrm{deltaBiasGR12}\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{biasCS2}\mathrm{biasGR2}\\ \mathrm{TD22}=\text{\hspace{1em}}\ue89e\text{(}\ue89e1+\mathrm{biasGR1}+\text{(}\ue89e1\mathrm{driftGR}/\mathrm{freqGR}\ue89e\text{)}+\\ \text{\hspace{1em}}\ue89e\text{(}\ue89e1\mathrm{driftGR}/\mathrm{freqGR}\ue89e\text{)}\ue89e\text{)}(1+\mathrm{biasCS1}+\\ \text{\hspace{1em}}\ue89e\text{(}\ue89e1\mathrm{driftCS}/\mathrm{freqCS}\ue89e\text{)}\ue89e\text{)}\\ =\text{\hspace{1em}}\ue89e1+\mathrm{biasGR1}\mathrm{driftGR}/\mathrm{freqGR}\mathrm{driftGR}\ue89e\text{/}\ue89e\mathrm{freqGR}\\ \text{\hspace{1em}}\ue89e\text{(}\ue89e\mathrm{biasCS1}\mathrm{driftCS}/\mathrm{freqCS}\ue89e\text{)}\\ =\text{\hspace{1em}}\ue89e1+\mathrm{biasGR1}+\mathrm{deltaBiasGR12}+\mathrm{deltaBiasGR23}\\ \text{\hspace{1em}}\ue89e\left(\mathrm{biasCS1}+\mathrm{deltaBiasCS12}\right)\\ =\text{\hspace{1em}}\ue89e1\left(\mathrm{biasCS2}\mathrm{biasGR3}\right).\end{array}$

[0060]
Summarizing, if cellsite is the source at time t=i, then j=1 and,

TDi 1=biasCS(t=i)−biasGR(t=i), (eq4)

[0061]
if GR is the source, at time t=I, then j=2 and

TDi 2=1−((biasCS(t=i)−biasGR(t=i+1)). (eq5)

[0062]
The quantization error is harder to remove when only the timeDiff observable is available, and this motivates gathering the freqDiff measurement. Such allows the quantization noise to be reduced by filtering, and higher frequency clocks are not needed. Avoiding higher frequency clocks allows a system operating power savings to be realized, and is very important in batteryoperated portable devices.

[0063]
Two important parameters can be estimated from the timeDiff observables, the bias from GPS time of the cellsite, and the frequency drift of the cellsite. The frequency drift estimate is then correlated with the bias estimate, and no new information is needed to filter the cellsite bias estimates.

[0064]
[0064]FIG. 5 represents a redrawing of the timeline and allows the effects of the quantization error to be seen. Ni1 equals three because the first cellsite PPS is reported on MCLK3 due to the clock synchronization. The “true” measurement TD11 is equal to the measured count (TD11m) minus the quantization Q1.

[0065]
The “true” time difference is the “true” number of clocks (integer plus fraction, which is the quantization) times the period of the clock. Assume the frequency was constant over the interval, then the period is the inverse of the “true” frequency. The “truth” model for the ideal measurement is shown below.

[0066]
The “true” time differences are defined as,

TD 11 equals (N 11−Q 1)/freqGR

TD 12 equals (N 12+Q 1)/freqGR

TD 21 equals (N 21−Q 2)/freqGR.

[0067]
The measured counts are integers. The exact frequency of the clock used to count is only an estimate. The measurement used is the observed number of counts, times the predicted period which is the inverse of the expected frequency.

[0068]
The measurements are defined by,

TD 11 m=N 11/freqGRhat=3/freqGRhat

TD 12 m=N 12/freqGRhat=1/freqGRhat

TD 21 m=N 21/freqGRhat=2/FreqGRhat.

[0069]
where,

[0070]
FreqGRhat=estimated GPS receiver frequency

[0071]
FreqGRhat=baseGRfreq+driftGRhat

[0072]
DriftGRhat=estimated frequency offset from nominal made by the GPS receiver.

[0073]
The “true” time difference model defines,

TD 11=biasCS 1−biasGR 1

TD 12=1−biasCS 1+biasGR 2

TD 21=biasCS 2−biasGR 2.

[0074]
The numeric index on the bias parameters represents their timetags. The first numeric indicator on the TD is the time, the second is the source used to trigger the observation.

[0075]
The first measurement to find the error model for the estimate of biasCS1 starts by defining the error to be the “true!” one minus the estimated parameter.

[0076]
The estimation error is defined as “errorBiasCS11”, and is the estimation error of the cellsite bias in the 1
^{st }second using the cellsite PPS as the trigger.
$\begin{array}{c}\mathrm{ErrorBiasCS11}=\text{\hspace{1em}}\ue89e\mathrm{biasCS1}\mathrm{biasCS1hat}\\ =\text{\hspace{1em}}\ue89e\left(\mathrm{TD11}+\mathrm{biasGR1}\right)\left(\mathrm{TD11m}+\mathrm{biasGR1hat}\right)\\ =\text{\hspace{1em}}\ue89e\text{(}\ue89e\left(\mathrm{N11}\mathrm{Q1}\right)\ue89e\text{/}\ue89e\mathrm{freqGR}+\mathrm{biasGR1}\ue89e\text{)}\\ \text{\hspace{1em}}\ue89e\left(\mathrm{N11}/\mathrm{freqGRhat}+\mathrm{biasGR1hat}\right)\end{array}$

[0077]
The auxiliaryt variables are defined,

ErrorBias
GR=bias
GR−bias
GRhat
$\begin{array}{c}\mathrm{ErrorDriftGR}=\text{\hspace{1em}}\ue89e\mathrm{freqGR}\mathrm{freqGRhat}\\ =\text{\hspace{1em}}\ue89e\left(\mathrm{baseGRfreq}+\mathrm{driftGR}\right)\\ \text{\hspace{1em}}\ue89e\left(\mathrm{baseGRfreq}+\mathrm{driftGRhat}\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{driftGR}\mathrm{driftGRhat}.\\ \mathrm{Continuing},\mathrm{errorBiasCS11}=\text{\hspace{1em}}\ue89e\mathrm{N11}*\text{(}\ue89e1/\mathrm{freqGR1}1/\mathrm{freqGR1hat}\ue89e\text{)}\\ \text{\hspace{1em}}\ue89e\mathrm{Q1}\ue89e\text{/}\ue89e\mathrm{freqGR1}+\mathrm{errorBiasGR1}\\ =\text{\hspace{1em}}\ue89e\mathrm{N11}*\left(\mathrm{freqGR1hat}\mathrm{freqGR1}\right)/\\ \text{\hspace{1em}}\ue89e\left(\mathrm{freqGR1}*\mathrm{freqGR1hat}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q1}\ue89e\text{/}\ue89e\mathrm{freqGR1}+\mathrm{errorBiasGR1}\\ =\text{\hspace{1em}}\ue89e\mathrm{N11}*\mathrm{errorDriftGR1}/(\mathrm{freqGR1}*\\ \text{\hspace{1em}}\ue89e\mathrm{freqGRhat1})\mathrm{Q1}/\mathrm{freqGR1}+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR1}.\end{array}$

[0078]
Assuming Q
1 equals 1, errorDriftGR equals 0.01, driftGR=0, and baseGRfreq=27.456 MHz, then the error is,
$\begin{array}{c}\mathrm{errorBiasCS11}=\text{\hspace{1em}}\ue89e\mathrm{TimeDiffTrue}*(36.42191142\ue89e\text{\hspace{1em}}\ue89e\mathrm{ns}\\ \text{\hspace{1em}}\ue89e36.42191142\ue89e\mathrm{ns})1*36.42191142\ue89e\text{\hspace{1em}}\ue89e\mathrm{ns}\\ =\text{\hspace{1em}}\ue89e36\ue89e\text{\hspace{1em}}\ue89e\mathrm{ns}\\ =\text{\hspace{1em}}\ue89e\mathrm{one}\ue89e\text{\hspace{1em}}\ue89e\mathrm{clock}\ue89e\text{\hspace{1em}}\ue89e\mathrm{of}\ue89e\text{\hspace{1em}}\ue89e\mathrm{the}\ue89e\text{\hspace{1em}}\ue89e\mathrm{master}\ue89e\text{\hspace{1em}}\ue89e\mathrm{clock}.\end{array}$

[0079]
This is the worstcase accuracy error, which is about 10.91 meters.

[0080]
The first term can be ignored because the GPS drift error is much less than the total frequency. In general, the GPS receiver can measure frequency to less than 1 Hz at L1. The error at the nominal frequency is 1/(1575.42/27.456), which equals 1/57.4 and 0.0174 Hz at baseGRfreq. Since N11 can be close to freqGR, this breaks down to 0.0174/freqGR which is 0.63 nanosecond equals 0.19 meter. Such term can be ignored when the drift error is small.

[0081]
The second term is the larger error source. Worst case, Q1 is close to one clock, and Q1/baseGRfreq equals 36 nanoseconds or 10.91 meters. If both edges of the master clock are used, an accuracy of eighteen nanoseconds can be realized. Both such edges of the reference clock are used to drive the counter between the consecutive 1PPS events. The resolution is improved and the worstcase quantization is _/baseGRfreq equals 18 ns equals 5.46 meters.

[0082]
The above example gives the theoretical worstcase accuracy for TDiff based on only the frequency of the reference clock, which is 27.456 MHz.

[0083]
A second measurement in the first interval provides a second estimate of the cellsite bias, but with a different GR bias,
$\begin{array}{c}\mathrm{ErrorBiasCS12}=\text{\hspace{1em}}\ue89e\mathrm{biasCS12}\mathrm{biasCS12hat}\\ =\text{\hspace{1em}}\ue89e\left(1\mathrm{TD12}+\mathrm{biasGR2}\right)\\ \text{\hspace{1em}}\ue89e\left(1\mathrm{TD12m}+\mathrm{biasGR2hat}\right)\\ =\text{\hspace{1em}}\ue89e\text{(}\left(\mathrm{N12}+\mathrm{Q1}\right)/\mathrm{freqGR2}+\mathrm{biasGR2}\ue89e\text{)}\\ \text{\hspace{1em}}\ue89e\text{(}\mathrm{N12}/\mathrm{freqGR2hat}+\mathrm{biasGR2hat}\ue89e\text{)}\\ =\text{\hspace{1em}}\ue89e\mathrm{N12}(1/\mathrm{freqGR2}1/\mathrm{freqGR2hat}\ue89e\text{)}\\ \text{\hspace{1em}}\ue89e\mathrm{Q1}/\mathrm{freqGR2}+\mathrm{errorBiasGR2})\\ =\text{\hspace{1em}}\ue89e\mathrm{N12}\ue8a0\left(\mathrm{freqGR2hat}\mathrm{freqGR2}\right)/\\ \text{\hspace{1em}}\ue89e\left(\mathrm{freqGR2}*\mathrm{freqGR2hat}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q1}/\mathrm{freqGR2}+\mathrm{errorBiasGR1}\\ =\text{\hspace{1em}}\ue89e\mathrm{N12}\ue8a0\left(\mathrm{errorDriftGR2}\right)/\\ \text{\hspace{1em}}\ue89e\left(\mathrm{freqGR2}*\mathrm{freqGR2hat}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q1}/\mathrm{freqGR2}+\mathrm{errorBiasGR2}.\end{array}$

[0084]
The GPS drift estimation error is small so the first term can be ignored. Two estimates are obtained for the cellsite bias in one second with different noise errors.

[0085]
The estimated measurement models are,

BiasCS 11hat=N 11/freqGR 1hat+biasGR 1hat

BiasCS 21hat=1−N 21/freqGR 2hat+biasGR 2hat

BiasCS 12hat=N 12/freqGR 2hat+biasGR 2hat

[0086]
Where N11, N21, and N12 are the counts from the hardware measurement and freqGRhat and biasGRhat are calculated using the GPS receiver.

[0087]
The error models of the cellsite clock biases are,

ErrorBiasCS 11=−Q 1/freqGR 1+errorBiasGR 1−N 11(errorDriftGR 1)/(freqGR 1*freqGR 1hat)

ErrorBiasCS 12=−Q 1/freqGR 2+errorBiasGR 2+N 12(errorDriftGR 2)/(freqGR 2*freqGR 2hat)

ErrorBiasCS 21=−Q 2/freqGR 2+errorBiasGR 2−N 21(errorDriftGR 2)/(freqGR 2*freqGR 2hat)

[0088]
Using both edges of the 27.456 MHz GPS clock, the quantization error is a uniform random variable with a maximum error of 1/(2^ 27.456e6), and equals 18 ns or 5.46 m.

[0089]
The GPS errors can also be modeled,

errorBiasGR=N(0, sigmaBias^ 2)

sigmabias=TDOP*sigmaPR

[0090]
[0090]
$\begin{array}{c}\mathrm{sigmaPR}=\text{\hspace{1em}}\ue89e\text{(}\ue89e1\ue89e\text{}\ue89e2\ue89e\text{\hspace{1em}}\ue89e\mathrm{meters}\ue89e\text{)}\ue89e\text{/}\ue89e\mathrm{speed}\ue89e\text{}\ue89e\mathrm{of}\ue89e\text{}\ue89e\mathrm{light}\\ =\text{\hspace{1em}}\ue89e3\ue89e\text{}\ue89e6\ue89e\text{\hspace{1em}}\ue89e\mathrm{nanoseconds},\end{array}$
errorDrift
GR=N(
0, sigmaDrift^
2)

sigmaDrift=TDOP*sigmaPRR

sigmaPRR=0.01 m/s=0.003 nanoseconds/second,

[0091]
where, N(mean,variance) is a Gaussian distribution. TDOP equals timedilutionofprecision from the leastsquares solution matrix. The numbers given above for the standard deviations for the pseudorange (PR) and pseudorangerate (PRR) are for conventional tracking with code and carrier tracking loops.

[0092]
An estimate of the cellsite clock drift can be formed using timeDiff data. Two timedifference measurements can be added together to span two external PPS events from a cellsite. The sum of these is an estimate of the time of the cellsite onesecond event,
$\begin{array}{c}\mathrm{TD12}+\mathrm{TD21}=\text{\hspace{1em}}\ue89e\left(1\mathrm{biasCS1}+\mathrm{biasGR2}\right)+\left(\mathrm{biasCS2}\mathrm{biasGR2}\right)\\ =\text{\hspace{1em}}\ue89e1+\mathrm{biasCS2}\mathrm{biasCS1}\\ =\text{\hspace{1em}}\ue89e1+\mathrm{biasCS1}+\mathrm{deltaBiasCS12}\mathrm{biasCS1}\\ =\text{\hspace{1em}}\ue89e1\mathrm{driftCS12}/\mathrm{freqCS},\end{array}$

[0093]
where, DriftCS12 equals drift in cellsite clock in the interval between the cellsite PPS events.

[0094]
The frequency can be assumed to be constant over the interval so that freqCS
1 equals freqCS
2,
$\begin{array}{c}\mathrm{Substituting},\mathrm{TD12}+\mathrm{TD21}=\text{\hspace{1em}}\ue89e1\mathrm{driftCS12}/\mathrm{freqCS}\\ =\text{\hspace{1em}}\ue89e1\mathrm{driftCS12}/(\mathrm{baseCSfreq}+\\ \text{\hspace{1em}}\ue89e\mathrm{driftCS12}).\end{array}$

[0095]
Simplifying the derivation, TD=1−d/(base+d)

TD*(base+d)=(base+d)−d

TD*(base+d)=base

TD*d=base(1−TD)

d=base(1/TD−1).

[0096]
Expanding back to the usual notation, DriftCS12 equals baseCSfreq*(1/(TD12−TD21)−1).

[0097]
Substituting the definitions of the timeDiff measurements uses the equation for the “true” driftCS, driftCS12 equals baseCSfreq*(freqGR2/(N12+N21+Q1−Q2)−1). To define the driftCS12 estimate, driftCS12hat equals baseCSfreq*(freqGR2hat/(N12+N21)−1).

[0098]
In order to simplify the error in the drift estimate, return to the format of the third equation in the simplified notation above. Also multiply both sides by freqGR

TD*(base+d)=base

[0099]
The “true” model,

((N 12+Q 1)+(N 21−Q 2))*(baseCSfreq+driftCS 1)=baseCSfreq*freqGR 2.

[0100]
Applying the same to the measurement model (except that multiply both sides by freqGR2hat),

(N 12+N 21)*(baseCSfreq+driftCS 1hat)=baseCSfreq*freqGR 2hat.

[0101]
Subtracting the measurement model from the “truth” model,

(Q 1−Q 2)*(baseCSfreq+driftCS 1)+(N 21+N 21)*(driftCS 1−driftCS 1hat)=baseCSfreq(freqGR 2−freqGR 2hat)

[0102]
Applying the following definitions,

[0103]
freqGR=baseGRfreq+driftGR

[0104]
freqGRhat=baseGRfreq+driftGRhat

[0105]
ErrorDriftCS=driftCS−driftCShat

[0106]
ErrorDriftGR=driftGR−driftGRhat,

(Q 1−Q 2)*(baseCSfreq+driftCS 1)+(N 21+N 21)*(driftCSdriftCShat)=baseCSfreq*(baseGRfreq+driftGR 2−baseGRfreq−driftGR 2hat)

(Q 1−Q 2)*(baseCSfreq+driftCS 1)+(N 21+N 21)*(errorDriftCS 1)=baseCSfreq*errorDriftGR 2

[0107]
Rearranging to isolate the errorDriftCS term,

(N 21+N 21)*errorDriftCS 1=baseCSfreq1*errorDriftGR 2−(Q 1−Q 2)*freqCS 1.

[0108]
The previous cellsite bias estimate is protected forward in time between the two cellsite PPS events.

[0109]
A new parameter is defined that is the projection of the previous biasCS estimate with the drift estimate to generate a reference trajectory to filter the new biasCS estimate against.

[0110]
The “truth” model,

BiasCS 2Minus=biasCS 12−driftCS 1/(baseCSfreq+driftCS 1).

[0111]
The measurement model,

BiasCS 2MinusHat=biasCS 12hat−driftCS 1hat/(baseCSfreq+driftCS 1hat).

[0112]
Multiplying both sides by their respective estimated cellsite total frequency,

BiasCS 2Minus*(baseCSfreq+driftCS 1)=biasCS 12*(baseCSfreq+driftCS 1)−driftCS 1

BiasCS 2MinusHat*(baseCSfreq+driftCS 1hat)=biasCS 12hat*(baseCSfreq+driftCS 1hat)−driftCS 1hat

[0113]
Forming the “true” minus the measured models,

(BiasCS 2Minus−BiasCS 2MinusHat)*baseCSfreq+BiasCS 2Minus*driftCS 1−BiasCS 2MinusHat*driftCS 1hat=(biasCS 12−biasCS 12hat)*baseCSfreq+biasCS 12*driftCS 1−biasCS 12hat*driftCS 1hat−(driftCS 1−driftCS 1hat).

[0114]
The projection error is defined as, ErrorBiasCS2minus equals biasCS2minus−BiasCS2MinusHat

[0115]
Using the convention that hat equals trutherror,

errorBiasCS 2minus*baseCSfreq+biasCS 2Minus*driftCS 1−(biasCS 2Minus−errorBiasCS 2minus)*(driftCS 1−errorDriftCS 1)=errorBiasCS 12*baseCSfreq+biasCS 12*driftCS 1−(biasCS 12−errorBiasCS 12)*(driftCS 1−errorDriftCS 1)−errorDriftCS 1,

errorBiasCS 2minus*baseCSfreq+errorBiasCS 2minus*driftCS 1+(biasCS 2Minus−errorBiasCS 2minus)* errorDriftCS 1=errorBiasCS 12*baseCSfreq+errorBiasCS 12*driftCS 1+(biasCS 12−errorBiasCS 12)*errorDriftCS 1−errorDriftCS 1.

[0116]
For the convention that error equals “truth”hat,

then trutherror equals hat errorBiasCS 2minus*(baseCSfreq+driftCS 1)+biasCS 2MinusHat*errorDriftCS 1=errorBiasCS 12*(baseCSfreq+driftCS 1)+biasSC 12hat*errorDriftCS 1−errorDriftCS 1

errorBiasCS 2minus*freqCS 1=errorBiasCS 12*freqCS 1+(biasSC 12hat−biasCS 2MinusHat)*errorDriftCS 1−errorDriftCS 1

[0117]
Dividing both sides by freqCS and rearranging,

ErrorBiasCS 2minus=errorBiasCS 12+(biasSC 12hat−biasCS 2MinusHat−1)*errorDriftCS 1/freqCS 1.

[0118]
Plugging in the definition,

BiasCS 2MinusHat equals biasCS 12hat−driftCS 1hat/(baseCSfreq+driftCS 1hat).

[0119]
And rearranging,

biasCS 12hat−BiasCS 2hatMinus equals driftCS 1hat/(baseCSfreq+driftCS 1hat)

ErrorBiasCS 2minus=errorBiasCS 12+(−1+driftCS 1hat/(baseCSfreq+driftCS 1hat))*errorDriftCS 1/freqCS 1.

[0120]
Simplifying the term in the brackets, Using more simple notation: −1+d/(b+d) equals (−b−d+d)/(b+d)=−b/(b+d)

errorBiasCS 2minus=errorBiasCS 12−(baseCSfreq/(baseCSfreq+driftCS 1hat))*errorDriftCS 1/freqCS 1.

[0121]
Substituting that:

baseCSfreq/(baseCSfreq+driftCS 1hat) equals (N 12+N 21)/freqGR 2hat, errorBiasCS 2minus=errorBiasCS 12−((N 12+N 21)/freqGR 2hat)*errorDriftCS 1/freqCS 1.

[0122]
Plugging in the definition of errorBiasCS12=−Q1/freqGR2+errorBiasGR2+N12(errorDriftGR2)/(freqGR2*freqR2hat).

[0123]
Using the result in deriving the error in the drift estimate after dividing both sides by freqGR2hat,

((N 21+N 21)/freqGR 2hat)*errorDriftCS=−(Q 1−Q 2)*freqCS 1/freqGR 2hat+baseCSfreq*errorDriftGR 2/freqGR 2hat.

[0124]
Inserting these two equations into the working equation, errorBiasCS
2minus=−Q
1/freqGR
2+errorBiasGR
2+N
12(errorDriftGR
2)/(freqGR
2*freqGR
2hat)+(Q
1−Q
2)/freqGR
2hat−baseCSfreq*errorDriftGR
2/(freqCS
1*freqGR
2hat), errorBiasCS
2minus=Q
1*(1/freqGR
2hat−1/freqGR
2)−Q
2/freqGRhat+errorBiasGR
2+(errorDriftGR
2/freqGR
2hat)*(N
12/freqGR
2−baseCSfreq/freqCS
1),
$\begin{array}{c}\mathrm{errorBiasCS2minus}=\text{\hspace{1em}}\ue89e\mathrm{Q1}*\left(\mathrm{freqGR2}\mathrm{freqGR2hat}\right)/\\ \text{\hspace{1em}}\ue89e\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q2}\ue89e\text{/}\ue89e\mathrm{freqGRhat}+\mathrm{errorBiasGR2}+\\ \text{\hspace{1em}}\ue89e\text{(}\ue89e\mathrm{errorDriftGR2}/\mathrm{freqGR2hat}\ue89e\text{)}*\\ \text{\hspace{1em}}\ue89e\text{(}\ue89e\mathrm{N12}/\mathrm{freqGR2}\mathrm{baseCSfreq}/\mathrm{freqCS1}\ue89e\text{)},\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ =\text{\hspace{1em}}\ue89e\mathrm{Q1}*\mathrm{errorFreqGR2}/\mathrm{freqGR2hat}*\\ \text{\hspace{1em}}\ue89e\mathrm{freqGR2})\mathrm{Q2}/\mathrm{freqGRhat}+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR2}+\text{(}\ue89e\mathrm{errorDriftGR2}/\\ \text{\hspace{1em}}\ue89e\mathrm{freqGR2hat})*\text{(}\ue89e\mathrm{N12}/\mathrm{freqGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{baseCSfreq}/\mathrm{freqCS1}\ue89e\text{)}.\end{array}$

[0125]
Remembering the definition that, baseCSfreq/freqCS1 equals (N12+N21)/freqGR2+(Q1−Q2)/freqGR2.

[0126]
Simplifying the last term in parenthesis as,
$\begin{array}{c}\text{\hspace{1em}}\ue89e\left(\mathrm{N12}/\mathrm{freqGR2}\mathrm{baseCSfreq}/\mathrm{freqCS1}\right)\\ \text{\hspace{1em}}\ue89e=\mathrm{N12}/\mathrm{freqGR2}\left(\left(\mathrm{N12}+\mathrm{N21}\right)/\mathrm{freqGR2}+\left(\mathrm{Q1}\mathrm{Q2}\right)/\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e=\mathrm{N21}/\mathrm{freqGR2}\left(\mathrm{Q1}\mathrm{Q2}\right)/\mathrm{freqGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q1}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q2}/\mathrm{freqGRhat}+\mathrm{errorBiasGR2}+\\ \text{\hspace{1em}}\ue89e\left(\mathrm{errorDriftGR2}/\mathrm{freqGR2hat}\right)*(\mathrm{N21}/\mathrm{freqGR2}.\\ \text{\hspace{1em}}\ue89e\left(\mathrm{Q1}\mathrm{Q2}\right)/\mathrm{freqGR2}).\end{array}$ $\begin{array}{c}\text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q1}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q2}/\mathrm{freqGRhat}+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{N21}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\left(\mathrm{Q1}\mathrm{Q2}\right)*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q1}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q2}/\mathrm{freqGRhat}+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{N21}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\left(\mathrm{Q1}\mathrm{Q2}\right)*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q2}/\mathrm{freqGR2hat}+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{N21}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{Q2}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q2}\ue8a0\left(\mathrm{freqGR2}+\mathrm{errorDriftGR2}\right)/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{N21}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q2}\ue8a0\left(\mathrm{freqGR2}\mathrm{errorDriftGR2}\right)/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{N21}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q2}\ue8a0\left(\mathrm{freqGR2hat}\right)/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)+\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasGR2}\\ \text{\hspace{1em}}\ue89e\mathrm{N21}*\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\\ \text{\hspace{1em}}\ue89e\mathrm{errorBiasCS2minus}\\ \text{\hspace{1em}}\ue89e=\mathrm{Q2}/\mathrm{freqGR2}+\mathrm{errorBiasGR2}\mathrm{N21}*\\ \text{\hspace{1em}}\ue89e\mathrm{errorDriftGR2}/\left(\mathrm{freqGR2hat}*\mathrm{freqGR2}\right)\end{array}$

[0127]
This equals the equation derived above for errorBiasCS21.

[0128]
Quantization and GPS receiver errors will appear in the final filtered estimate of the cellsite. A complimentary filter is used to combine the two estimates of the same parameter into a single filtered estimate. The complimentary filter has the form, FilteredEstimate equals (1−a)*previousFilteredEstimate+a*newUnfilteredMeasurement, where a<=1.0.

[0129]
If both the previous filtered estimate and the new unfiltered measurement are estimates of the same parameter, then the filtered estimate is unbiased,
$\begin{array}{c}\text{\hspace{1em}}\ue89e\mathrm{FilteredEstimate}\ue89e\text{\hspace{1em}}\ue89e\mathrm{equals}\ue89e\text{\hspace{1em}}\ue89e\left(1a\right)*\left(X+\mathrm{N1}\right)+a*\left(X+\mathrm{N2}\right)\\ \text{\hspace{1em}}\ue89e=\left(\left(1a+a\right)*X\right)+\left(a*\mathrm{N2}+\left(1a\right)*\mathrm{N1}\right))\\ \text{\hspace{1em}}\ue89e=X+\left(\left(1a\right)*\mathrm{N1}+a*\mathrm{N2}\right).\end{array}$

[0130]
If the gain parameter “a” is small, then the noise on the previous filtered estimate is preferably not filtered. If there is an error in the propagation from a previous time to a current time, the error is placed directly into the filtered estimate.

[0131]
An optimal filter has a gain of 0.5 when the propagation error is on the same order of magnitude as the noise in a new raw measurement. In this way, some attenuation of the propagation error is obtained.

[0132]
Applying the complimentary filter, BiasCS12filtered=(1−a)*biasCS12minusHat+a*biasCS12hat. The error then has the form, Error=(1−a)*(error in biasCS12minusHat)+a*(error in biasCS12hat).

[0133]
It is not possible to reduce any of the error sources because the predicted bias is equal to the measured quantity and the error in both terms is the same.

[0134]
An earlier estimate of the cellsite bias can be used other than that allowed by the GPS observation. Variable errorBiasCS11 is used instead of errorBiasCS12.

[0135]
Starting with the “truth” model, BiasCS2Minus=biasCS11−driftCS1/(baseCSfreq+driftCS1).

[0136]
The measurement model, BiasCS2MinusHat=biasCS11hat−driftCS1hat/(baseCSfreq+driftCS1hat).

[0137]
Arriving at, errorBiasCS2minus=errorBiasCS11−(baseCSfreq/(baseCSfreq+driftCS1hat))*errorDriftCS1/freqCS1.

[0138]
Substituting that,

baseCSfreq/(baseCSfreq+driftCS 1hat) equals (N 12+N 21)/freqGR 2hat, errorBiasCS 2minus=errorBiasCS 12−((N 12+N 21)/freqGR 2hat)*errorDriftCS/freqCS 1.

[0139]
Plugging in the result, errorBiasCS11=−Q1/freqGR1+errorBiasGR1−N11(errorDriftGR1)/(freqGR1*freqGR1hat).

[0140]
And using the result to derive the error in the drift estimate after dividing both sides by freqGR2hat, ((N21+N21)/freqGR2hat)*errorDriftCS=−(Q1−Q2)*freqCS1/freqGR2hat+baseCSfreq*errorDriftGR2/freqGR2hat.

[0141]
Inserting these two equations into the working equation, errorBiasCS2minus=−Q1/freqGR1+errorBiasGR1−N11(errorDriftGR1)/(freqGR1*freqGR1hat)+(Q1−Q2)/freqGR2hat−baseCSfreq*errorDriftGR2/(freqCS1*freqGR2hat),

errorBiasCS 2minus=Q 1*(1/freqGR 2hat−1/freqGR 1)−Q 2/freqGR 2hat+errorBiasGR 1−N 11(errorDriftGR 1)/(freqGR 1*freqGR 1hat)−baseCSfreq*errorDriftGR 2/(freqCS 1*freqGR 2hat),

errorBiasCS 2minus=Q 1*(freqGR 1−freqGR 2hat)/(freqGR 2hat*freqGR 1)−Q 2/freqGR 2hat+errorBiasGR 1−N 11(errorDriftGR 1)/(freqGR 1*freqGR 1hat)−baseCSfreq*errorDriftGR 2/(freqCS 1*freqGR 2hat),

errorBiasCS 2minus=Q 1*(freqGR 1−freqGR 2+errorDriftGR 2)/(freqGR 2hat*freqGR 1)−Q 2/freqGR 2hat+errorBiasGR 1−N 11(errorDriftGR 1)/(freqGR 1*freqGR 1hat)−baseCSfreq*errorDriftGR 2/(freqCS 1*freqGR 2hat).

[0142]
Thus, the difference of

biasCS 2hat−biasCS 2minusHat, ErrorBiasCS 21−errorBiasCS 2minus=−Q2/freqGR 2+errorBiasGR 2−N 21 (errorDriftGR 2)/(freqGR 2*freqGR 2hat)−Q 1*(freqGR 1−freqGR 2+errorDriftGR 2)/(freqGR 2hat*freqGR 1)+Q 2/freqGR 2hat−errorBiasGR 1+N 11(errorDriftGR 1)/(freqGR 1*freqGR 1hat)+baseCSfreq*errorDriftGR 2/(freqCS 1*freqGR 2hat))=Q 2*(1/freqGR 2hat−1/freqGR 2)−Q 1*(baseGRfreq+driftGR 1−baseGRfreq−driftGR 2+errorDriftGR 2)/(freqGR 2hat*freqGR 1)+errorBiasGR 2−errorBiasGR 1+N 11(errorDriftGR 1)/(freqGR 1*freqGR 1hat)−N 21 (errorDriftGR 2)/(freqGR 2*freqGR 2hat)+baseCSfreq*errorDriftGR 2/(freqCS 1*freqGR 2hat)=Q 2*errorDriftGR 2/(freqGR 2hat*freqGR 1)−Q 1*(driftGR 1−driftGR 2+errorDriftGR 2)/(freqGR 2hat*freqGR 1)+errorBiasGR 2−errorBiasGR 1+N 11(errorDriftGR 1)/(freqGR 1*freqGR 1hat)−N 21 (errorDriftGR 2)/(freqGR 2*freqGR 2hat)+baseCSfreq*errorDriftGR 2/(freqCS 1*freqGR 2hat).

[0143]
It appears that this may actually be smaller than the error derived earlier. However, this result is inconclusive and needs more investigation.

[0144]
Counting the number of clock pulses from the clock with unknown frequency error in a known time interval generated by the reference clock, forms the freqDiff observable. The frequency is computed as the number of clocks divided by the “true” time interval. Even though there is enough information to make this estimation with the timeDiff measurement data, it turns out that the error in the estimate is perfectly correlated with the bias estimates. The same observations, with their associated quantization sources, are used in estimating the bias and drift. Thus, freqDiff is used to form an estimate of drift that is statistically independent from the bias estimates.

[0145]
Embodiments of the present invention count the clock pulses with unknown frequency error directly. In contrast, the timeDiff circuits count pulses from the reference clock.

[0146]
The quantization error is a uniform random variable between (0, 1) and it is not zero mean. To reduce the parameter, the data must be prewhitened to produce a zeromean measurement error, and conventional techniques can be used in parameter estimating with a quantized noise souce.

[0147]
Once the noise souce becomes a zeromean process, it may be reduceable with good filtering. However, in estimating a parameter that has a nonconstant slope, the previous filtered bias must be propagated to the current time. This is needed to assimilate the new measurement with the previous data in an unbiased manner. The difference between the average bias and the new data is scaled and then added to the propagated estimate to finish the update.

[0148]
The 1^{st }order lowpass filter,

Bfiltered(K) equals PropagatedBias(K)+gain(K)*(biasMeas(K)−PropagatedBias(K)),

[0149]
where,

PropagatedBias(K) equals Bfiltered(K−1)−drift(K)*deltaTime(K)

[0150]
gain(K) equals 1/m, where

[0151]
m equals k if k<Kmax

[0152]
m equals Kmax if k>Kmax

[0153]
deltaTime(K) equals time between t=K and t=K−1.

[0154]
Note, if Kmax equals infinity, then the filter output is the average of all the data.

[0155]
The propagation error from the timeDiff baseddrift estimate has the same error as the new measurement. The propagation error is not filtered, and cannot use the timeDiff baseddrift estimate in the projection phase.

[0156]
Embodiments of the present invention directly count the unknown frequency error clock pulses. The timeDiff circuit count pulses from the reference clock.

[0157]
The freqDiff measurement is the number of external clocks counted in an interval defined with an integer number of internal clocks. An estimate of frequency offset of the internal clock can measure the frequency of the external clock.

[0158]
The “true” measurement is,

ClockCount equals freqCS*DeltaTimeTrue.

[0159]
The observed count will be in error by the effects of the quantization of the external clock against the internal master clock at the time the count is started and finished.

[0160]
The observation model can be derived from FIG. 6, in which the circuit counts four external clocks. However, the real number is a number that contains a fractional component equal to (Q1−Q2) where Q1 and Q2 have units of counts and are continuous random variables between 0 and 1 count.

[0161]
The “true” integer plus fractional number of counts, ClockCountTrue equals freqCS*DeltaTimeTrue=N+(Q1−Q2).

[0162]
The count observed by the circuit is only N counts.

[0163]
The “true” time difference is the number of internal master clocks in the interval times the “true” period of the clock.

DeltaTimeTrue equals M*trueperiod=M/freqGR.

[0164]
Thus have:

N+(Q 1−Q 2) equals freqCS*M/freqGR (eq A.).

[0165]
Rearranging,

(N/M)*(baseGR+driftGR) equals (Q 2−Q 1)*(baseGR+driftGR)/M+baseCS+driftCS.

(N/M)*baseGR−baseCS equals (1/M)*(Q 2−Q 1)*baseGR+driftCS−driftGR*(1/M)*(−(Q 2−Q 1)+N).

[0166]
The term in the brackets can be replaced by manipulating eqA.

(N+(Q 1−Q 2))/M equals freqCS/freqGR.

[0167]
Thus,
$\begin{array}{c}\left(N/M\right)*\text{\hspace{1em}}\ue89e\mathrm{baseGr}\mathrm{baseCS}\\ =\text{\hspace{1em}}\ue89e\left(1/M\right)*\left(\mathrm{Q2}\mathrm{Q1}\right)*\mathrm{baseGR}+\\ \text{\hspace{1em}}\ue89e\mathrm{driftCS}\mathrm{driftGR}*\left(\mathrm{freqCS}/\mathrm{freqGR}\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{driftCS}\mathrm{driftGR}*\left(\mathrm{freqCS}/\mathrm{freqGR}\right)+\left(1/M\right)*\\ \text{\hspace{1em}}\ue89e\left(\mathrm{Q2}\mathrm{Q1}\right)*\mathrm{baseGR}.\end{array}$

[0168]
The scale factor in the first term on the left side of the equation (baseGR/M) is the approximation of the deltaTime based on the nominal GPS receiver frequency. Thus, this term is the estimate of the total cellsite frequency. By subtracting the nominal cellsite frequency from the total frequency estimate, the difference represents the difference in the frequency offset of the two clocks. The left hand side represents the manipulation of the measurement data that produces the frequency difference wanted. The error in the frequency estimate is due to the lost fractional cycles over the time interval. The error is reduced by either increasing the cellsite frequency (increasing baseCS which decreases Q1 and Q2), or increasing the time interval (by increasing M). The scale factor on the GPS receiver drift term (freqCS/freqGR) produces the translation of the GPS receiver clock frequency from its reference frequency into the reference frequency of the cellsite.

[0169]
The freqDiff measurement N is defined as shown below, ΔF equals (N/M)*baseGR−baseCS (units are counts at baseCSfreq) error equals (1/M)*(Q2−Q1)*baseGR.

[0170]
Applying this change of variables,

DriftCS equals ΔF+driftGR*(baseCS+driftCS)/(baseGR+driftGR)−error.

[0171]
Expanding,

DriftCS*(1−driftGR/(baseGR+driftGR))=ΔF+driftGR*baseCS/(baseGR+driftGR)−error.

[0172]
Expanding of the left,

DriftCS*((baseGR+driftGR−driftGR)/(baseGR+driftGR))=ΔF−driftGR*baseCS/(baseGR+driftGR)−error.

[0173]
And reducing,

DriftCS*baseGR/(baseGR+driftGR)=ΔF−driftGR*baseCS/(baseGR+driftGR)−error.

[0174]
Finally, solve for the cellsite drift and reinsert the error term,

DriftCS equals ΔF*freqGR/baseGR+driftGR*baseCS/baseGR+(1/M)*(Q 1−Q 2)*freqGR

[0175]
Using known parameters, the final cellsite drift estimate,

DriftCShat equals ΔF*freqGRhat/baseGR+driftGRhat*baseCS/baseGR.

[0176]
Where ΔF equals (N/M)*baseGR−baseCS.

[0177]
In the cellsite drift estimate accuracy the difference between the “true” and measured cellsite drift is

errorDriftCS=errorDriftGR*ΔF/baseGR+errorDriftGR*baseCS/baseGR+(1/M)*(Q 1−Q 2)*freqGR.

[0178]
Inserting the definition of the ΔF,
$\begin{array}{c}\text{\hspace{1em}}\ue89e\mathrm{ErrorDriftCS}\\ \text{\hspace{1em}}\ue89e=\mathrm{errorDriftGR}*\left(1/\mathrm{baseGR}\right)*(N/M*\mathrm{baseGR}\mathrm{baseCS}+\\ \text{\hspace{1em}}\ue89e\mathrm{baseCS})+\left(1/M\right)*\left(\mathrm{Q1}\mathrm{Q2}\right)*\mathrm{freqGR}\\ \text{\hspace{1em}}\ue89e=\mathrm{errorDriftGR}*\left(1/\mathrm{baseGR}\right)*\left(N/M*\mathrm{baseGR}\right)+\\ \text{\hspace{1em}}\ue89e\left(1/M\right)*\left(\mathrm{Q1}\mathrm{Q2}\right))*\mathrm{freqGR}\\ \text{\hspace{1em}}\ue89e=\mathrm{errorDriftGR}*N/M+\left(\mathrm{Q1}\mathrm{Q2}\right)/M*\mathrm{freqGR}\\ \text{\hspace{1em}}\ue89e=\mathrm{errorDriftGR}*N/M+\left(\left(\mathrm{Q1}\mathrm{Q2}\right)/M\right)*\mathrm{freqGR}.\end{array}$

[0179]
Thus,

ErrorDriftCS equals ((Q 1−Q 2)/M)*freqGR+(N/M)*errorDriftGR.

[0180]
The longer the integration time, the more the error in estimating the “true” time interval grows because of integrating the GPS drift error term errorDriftGR. The quantization error is the sum of two uniform random variables.

[0181]
It is the period of the clock used to count the frequency difference that determines the worst case frequency error. The higher the frequency, the smaller the period and the quantization term. Alternatively, one can use a longer observation period. Such may be a problem if the clock operates in an environment of some observable temperature change. This may cause the clock to change frequency, and can lead to nonlinear changes. The average frequency will be less accurate than the quantized estimate.

[0182]
If the external clock frequency is lower that the internal clock frequency, the driftCS estimate from the timeDiff measurement is used to estimate the cellsite frequency offset. However, if the external frequency is higher than the internal clock frequency, then the freqDiff observation is used instead.

[0183]
In cases where only frequency synchronization is possible, because a system lPPS does not exist, then the freqDiff counter will be used to estimate the external clock frequency as the timeDiff will not provide any information about the external clock when the external PPS is not available.

[0184]
For a device that communicates with a network infrastructure and a GPS receiver, both receivers will track the carrier frequency of their respective transmitters. For GPS, the receiver also tracks the phase of the pseudorandom code allowing a pseudorange measurement to be produced. The measurement is a time difference of arrival measurement, as the time of transmission is known, and the receiver records the time of arrival with respect to its local clock.

[0185]
The GPS satellite (SV) has a time and frequency error from “true” GPS time and the “true” desired reference frequency of the spacecraft clock.

[0186]
FreqSV equals baseSVfreq+driftSV.

[0187]
TimeSV equals timeGPS+biasSV.

[0188]
The GPS receiver (GR) also has a time and frequency error from GPS time.

[0189]
FreqGR equals baseGRfreq+driftGR.

[0190]
TimeGR equals timeGPS+biasGR

[0191]
A cellsite system (CSS) with a reference time for all its cellsites uses cellsitesystem time or timeCSS. Such time reference is different from GPS time. It is also possible that the cellsites are not synchronized to a common time. Embodiments of the present invention do not require that any of the cellsites have the same time reference.

[0192]
“FreqCS” equals baseCSfreq+driftCS. “TimeCS” equals timeCSS+biasCSS (with respect to cellsite System time). It also equals timeCSG+biasCSG (with respect to GPS time).

[0193]
Each cellsite has an offset from timeCSS that is the biasCSS. We can also reference timeCSS to GPS time. The time error for the cellsite changes to biasCSG. The cellphone also has a frequency offset from its nominal frequency referred to as driftCP.

FreqCP=baseCPfreq+driftCP

[0194]
[0194]
$\begin{array}{c}\mathrm{FreqCP}=\text{\hspace{1em}}\ue89e\mathrm{baseCPfreq}+\mathrm{driftCP}\\ \mathrm{TimeCP}=\text{\hspace{1em}}\ue89e\mathrm{timeCPS}+\mathrm{biasCPS}\\ =\text{\hspace{1em}}\ue89e\mathrm{timeCPG}+\mathrm{biasCPG}.\end{array}$

[0195]
There are two cellphone methods for tracking the cellsite frequency, the NCO method or the VCO method. In an NCO method embodiment of the present invention, the cellphone reference frequency is held constant and the additional frequency required to track the cellsite is made in an additional oscillator or NCO. The circuit that produces this additional frequency will generally have a software counter that integrates all the frequency adjustments to produce a number that represents the offset from nominal frequency needed to track the cellsite frequency. Such frequency offset is the driven by three processes, (1) the cellphone offset from its nominal frequency, (2) the Doppler between the cellphone and the cellsite caused by the projection of the cellphone user dynamics along the lineofsight between the cellphone and the cellsite, and (3) the frequency offset of the cellsite from its nominal frequency.

[0196]
The cellphone outputs a message that contains a total frequency offset number and an associated time tag. Such number is used with the freqDiff and timeDiff observations to synchronize the cellphone to the GPS receiver clock.

[0197]
In the VCO method embodiment of the present invention, a cellsite carrier is tracked by adjusting the reference frequency directly with a VCO. The voltage is changed to the circuit that produces the different mixdown frequencies. The NCO is not needed. If the adjusted reference clock is directly observed with the timeDiff and freqDiff observations, then there is no need for the cellphone to send any additional information. Any cellphone bias is replaced by a cellsite range and bias, and any cellphone drift becomes the rangeRate and cellsite drift.

[0198]
The tempmeas observable is very similar to the freqDiff. The navigation digitalsignal processor preferably includes an oscillator whose frequency is determined by an RCtime constant in which the resistor is actually a thermistor. The tempMeas circuit counts the number of cycles of the oscillator in a predetermined interval and gets a measure of temperature from a thermistor calibration curve.

[0199]
The GPS clock naturally drifts with temperature. Thus, during a calibration phase when the temperature of the complete navigation digitalsignal processor based GPS receiver, observe that the count and the GPS receiver clock drift (driftGR2hat) is swept at the same time. A model is built that allows the GPS clock drift to be predicted from the tempMeas.

[0200]
The aging of the clock and the crystal imperfections will cause deviations of the crystal frequency from the model. And the intrinsic variations in the crystal act to limit the accuracy of the estimator.

[0201]
The hardware to implement the tempMeas is simply a counter that starts on a GPS predetermined millisecond and ends after a predetermined number of milliseconds later.

[0202]
While sweeping over the industrial temperature range in the factory (and in the field whenever obtain a reliable GPS fix), observe tempMeas and the driftGR2hat and build the model (and update model in the field) of the driftGR2hat verses the counter value. A tempMeas can then be performed at any time and using this model, an estimate of the GPS receiver clock drift can be obtained. This estimate is called driftGR2HatSCXO. The acronym SCXO comes from SoftwareCompensatedCrystalOscillator.

[0203]
In the cellphone, a tempMeas at startup to form driftCR2hat is made. Such estimate will be used during the time and frequency transfer (from the phone to the cellphone) to reduce the required GPS search range and thus, enable a superthin GPS client.

[0204]
The components of the dual mode system are a GPS satellite, the GPS receiver, the cellsite, and the cellphone.

[0205]
A GPS satellite is being tracked by a GPS receiver at the cellsite whose purpose is to observe the offset of the cellsite clock from GPS time and its frequency reference. This receiver and cellsite have known locations and are static. They are physically close enough to allow the physical connection needed to make the timeDiff and freqDiff observations.

[0206]
The second GPS receiver is at the cellphone location. The goal is to estimate the location (position and velocity) of the cellphone. All possible measurement sources to do this. The normal GPS pseudorange and pseudorangerate measurements are used to compute the position, time, and frequency of the GPS receiver at the cell site. Such allows the GPS receiver to synchronize to GPS time, and thus, by observing the relative offset between the cellsite and the GPS receiver time and frequency, can calculate the time and frequency offset of the cellsite from GPS time.

[0207]
In cellphone embodiments of the present invention, the inverse is done. The cellphone is assumed to be tracking the cellsite frequency and time. Pseudorange and pseudorangerate measurements can also be formed for the signal between the cellphone and the cellsite. Because the cellsite position is known, the cellsite can be used as a ranging source in the same way a GPS satellite is used.

[0208]
Since the cellphone is tracking the cellsite, and the frequency required to track is known, the use of freqDiff allows two things. The pseudorange and pseudorangerate between the cellphone and the cellsite can be used as estimates of the cellphone time and frequency error. Estimates can be made about the GPS receiver's time and frequency using the timeDiff and freqDiff observations, and greatly reduce the search range for the GPS satellites. It can also be used to improve acquisition time and/or acquisition sensitivity. The cell system aids the GPS to acquire satellites. After at least one GPS satellite is acquired, the pseudorange and pseudorangerate between the cellphone and the cellsite are used along with the GPS pseudoranges and pseudorangerates in the position calculation. Because of the timeDiff and freqDiff observations, the cellsite time and drift can be expressed in terms of the GPS bias and drift, and the number of unknowns is reduced to the normal unknown as in the standalone GPS case.

[0209]
[0209]FIG. 7 represents a dualmode system 700 with GPS receiver tracking a satellite vehicle (SV) 702 and a cellphone 704 tracking a cellsite 706. The clocks in the system with respect to the dualmode system are,

[0210]
SV clock*(numSatellites),

[0211]
GPS receiver1 clock in the cellsite,

[0212]
GPS receiver2 clock in the cellphone,

[0213]
Cellsite clock*(numCellSites),

[0214]
Cellphone clock

[0215]
For example, if there are five GPS satellites, and five cellsites, then the total number of clocks in the system, nmSatellites+numCellSites+3=5+5+3=13. For each cellsite and GPS satellite, a pseudorange (PR) and pseudorangerate measurement (PRR) can be formed.

[0216]
For a system with one GPS satellite 702 and one cellsite 706, the calibration begins by making a passive connection between a cellsite 706 and cellphone 704. A cellsite clock signal and its 1PPS can be observed by GPS receiver1 706. These signals are connected to the freqDiff and timeDiff circuits of a navigation digitalsignal processor respectively. The cellphone clock signal and its 1PPS can be observed by the GPS receiver2 704. Such also has a navigation digitalsignal processor chip and such signals are connected to the freqdiff and timeDiff circuits of navigation digitalsignal processor respectively.

[0217]
[0217]FIG. 8 represents each clock with its own system time and a corresponding clock bias from this time. The sum of these two, e.g., the system time plus the bias, produce the reference time used by the hardware for making observations in the receiver. The timedifference observations are taken between these timereferences. The first one, TD1, is between GPS receiver1 and the cellsite. The second one TD2 is between GPS receiver2 and the cellphone. The clock pulse signals represent a timing signal leaving the transmitter at a known time and arriving at the receiver later in time according to the range. However, the time bias errors cause the observed phase measurement to be affected, e.g., by the bias error of both the transmitter and receiver. Such observations become the pseudoranges.

[0218]
TD1 is the timeDiff measurement between the 1PPS of the GPS receiver1 and the 1PPS of the cellsite. Such produces the observation N12 and N21 in units of counts from the receiver1 and can be used to form timeDiff TD1 in units of seconds.

[0219]
TD2 is the timeDiff measurement between the 1PPS of the GPS receiver1 and the 1PPS of the cellsite. Such produces the observation N12 and N21 in units of counts from the receiver2 and can be used to form timeDiff TD1 in units of seconds.

[0220]
From FIG. 8, it can be seen that,

BiasGR 1+TD 1=biasCSS+Δ(CSS−GPS)=biasCSG, (units are seconds)

BiasGR 2+TD 2=biasCPS+Δ(CSS−GPS)=biasCPG.

[0221]
The units of measure for the pseudorange measurements are preferably maintained in units of seconds rather meters, in order to simplify things in terms of the timeDiff and freqDiff. But the units in meters can be used too.

[0222]
Two measurements are obtained from the timeDiff circuit each second. They are Ni1 and Ni2, where 1=time marker, and “1” is the measurement from the external PPS and “2” is the measurement from the internal PPS.

[0223]
The phase measurement that was produced to make the local phase of the signalgenerated in the cellphone track the received phase of the signal transmitted by the cellsite can be accessed.

[0224]
From FIG. 8, the observed phase measurement is such that,

BiasCS+rangeCP=BiasCP+φcp. (units are seconds)

[0225]
Rearranging this yields,

φcp=rangeCP+BiasCS−BiasCP.

TD 1=biasCSG−BiasGR 1,

TD 2=biasCPG−BiasGR 2

[0226]
The analogous measurement from the GPS receiver is such that,

biasSV+rangeGR 2=biasGR 2+φGR 2,

biasSV+rangeGR 1=biasGR 1+φGR 1.

[0227]
Rearranging gives,

φGR 1=rangeGR 1+biasSV−biasGR 1,

φGR 2=rangeGR 2+biasSV−biasGR 2.

[0228]
The “true” positions can then be found. A threedimensional earthcenteredearthfixed (ECEF) Cartesian coordinate, e.g., WGS84, is used. A cellsite position and velocity is considered to be known,

PosCS (in meters)=(xCS, yCS, zCS),

VelCS (in m/s)=(xVelCS, yVelCS, zVelCS)=0.

[0229]
The GPS receiver1 at the cellsite has a known position that is near the cellsite position, but does not need to be identical to it. Thus, posGPS1=(x1, y1, z1), and velGPS1=(xVel1, yVel1, zVel1)=0.

[0230]
The GPS satellite position is assumed to be known from the ephemeris model that is distributed around the system. The satellite velocity is calculated from the ephemeris. PosSV=(xSV, ySV, zSV), VelSV=(xVelSV, yvelSV, zVelSV).

[0231]
The GPS receiver2 has a cellphone and its location represents the main unknown in the system. All the other unknowns are nuisance parameters in the system that need to be solved or eliminated.

[0232]
The cellsite and GPS receiver are defined to be at the same (unknown) location. So, posGPS2=posCP=(x, y, z), and velGPS2=velCP=(xVel, yvel, zVel).

[0233]
In the “true” range definitions, the coordinate frame is orthonormal. The positive distance between any two points is the magnitude of the vector between the two points. The range equations can be expressed in terms of seconds. RangeGR1=k*((xSV−x1)^{2}+(ySV−y1)^{2}(ZSV−z1)^{2})^{1/2}. RangeGR2=k*((xSV−x)^{2}+(ySV−y)^{2}(zSV−z)^{2})^{1/2}. RangeCP=k*((xCP−x)^{2}+(yCP−y)^{2}(ZCP−z)^{2})^{1/2}. Where, K=the inverse of the speed of light, e.g., 2.99792458e8 meters/second.

[0234]
[0234]FIG. 9 is a visualization of how the freqDiff measurement can be taken and used. A freqDiff1 measurement is obtained between GPS receiver1 reference and the cellsite reference. The freqDiff2 measurement is obtained between GPS receiver2 reference and the cellphone reference. The same reference, e.g., the nominal frequency used in the GPS receiver, is used for both the GPS receivers. Part of the strategy is to employ the same hardware solution that contains the navigation digitalsignal processor chip at both the reference stations for DGPS and data, cellsites, and client (cellphone) solutions. Thus, the same frequency reference can be assumed, which is the nominal crystal frequency used to generate all the frequencies used to track the GPS satellite carrier.

[0235]
For the cellsystem side, it is convenient to use a common frequency reference when calculating the frequency offset from systems with different nominal frequencies. However, the same modeling can be used in either case. All the nominal frequencies need to be scaled to one master frequency. Then the frequency offset is translated from its nominal frequency to the new master frequency by multiplying the offset by the ratio, otherRefFreq/nominalRefFreq. An algebra can be performed with proper scaling. The result is converted back to the nominal reference with the inverse scaling.

[0236]
The rangerate measurements are not included in the freqDiff figure, the pseudoranges are in the timeDiff figure. The user motion and satellite are usually expressed at the GPS carrier frequency (L1=1575.42 MHz). The freqDiff observations are not affected by the user or satellite motion. Such applies to the NCO for the cellphone frequency generation. In the VCO method embodiment of the present invention, the range and cellsite clock effects do appear in the cellphone reference frequency.

[0237]
The raw measurement from the freqDiff circuit are the counts N1 from GPS receiver1 and N2 from GPS receiver2. The freqdiff in units of cycles/sec at the cellsite reference frequency can be computed with these. BaseCS=baseCP can be assumed.

ΔF 1=(N 1/M)*baseGR−baseCS (Hz at baseCSfreq)

ΔF 2=(N 2/M)*baseGR−baseCP (Hz at baseCPfreq)

[0238]
where,

[0239]
N1=freqDiff in counts from navigation digitalsignal processor1

[0240]
N2=freqDiff in counts from navigation digitalsignal processor2.

[0241]
An estimate of frequency from the cellphone is required to track the cellsite carrier. The method embodiment of the present invention is used with an NCO. The cellphone can output a number that can be scaled into units of cycles/sec at the baseCP frequency.

[0242]
The measurement from the cellphone carrier tracking loop,

φDotCP=rangeRateCP+driftCS−driftCP (Hz at baseCSfreq)

[0243]
In another embodiment, the VCO is steered to track the cellsite carrier and the effect on the cellphone nominal frequency is observed directly in the timeDiff and freqDiff circuit. It is still possible that the numerical representation of the frequency offset from nominal can be output. However, there is a different meaning of the frequency component due to the cellphone clock that appears in freqDiff. Now the freqDiff will observe the Doppler component of the cellphone motion and the frequency offset of the cellsite.

[0244]
If the transmitter has a positive frequency offset, then the receiver must increase its generated frequency to track this addition frequency offset from nominal. If the receiver has a positive frequency offset, then it must reduce its generated frequency to track the carrier. Finally, if there is a positive Doppler between the transmitter and receiver, then the receiver must increase its frequency to track this effect.

[0245]
Tracking the carrier of the cellsite, the frequency produced to allow tracking,
$\begin{array}{c}\text{\hspace{1em}}\ue89e\mathrm{FreqCPvco}\\ \text{\hspace{1em}}\ue89e=\mathrm{freqCP}\ue89e\text{\hspace{1em}}\ue89e\text{(atturnon)}+\left(\mathrm{rangeRateCP}+\mathrm{driftCS}\mathrm{driftsCP}\right)\\ \text{\hspace{1em}}\ue89e=\mathrm{baseCPfreq}+\mathrm{driftCP}+\left(\mathrm{rangeRateCP}+\mathrm{driftCS}\mathrm{driftsCP}\right)\\ \text{\hspace{1em}}\ue89e=\mathrm{baseCPfreq}+\left(\mathrm{rangeRateCP}+\mathrm{driftCS}\right)\\ \text{\hspace{1em}}\ue89e=\mathrm{baseCPfreq}+\mathrm{driftCPvco}\end{array}$

[0246]
where, when tracking the cellsite, DriftCPvco=rangeRateCP+driftCS.

[0247]
The phase error discriminator that produces the updates to the VCO frequency must remove the drift of the cellphone.

[0248]
Examining the effect on the freqDiff observation, the counter will observe the integer number of cycles of the frequency freqCPvco to track the cellsite, rather than just the cellphone frequency freqCP.

[0249]
In other words, ClockCountTrue=freqCSvco*deltaTimeTrue=Nvco+(Q1−Q2).

[0250]
Thus, when equating the observation to the unknowns, define,
$\begin{array}{c}\text{\hspace{1em}}\ue89e\mathrm{FreqDiffVCO}\\ \text{\hspace{1em}}\ue89e=\mathrm{driftCPvco}\mathrm{driftGR}*\left(\mathrm{freqCS}/\mathrm{freqGR}\right)\\ \text{\hspace{1em}}\ue89e=\left(\mathrm{rangeRateCP}+\mathrm{driftCS}\right)\mathrm{driftGR}*\left(\mathrm{freqCS}/\mathrm{freqGR}\right)\end{array}$

[0251]
The GPS receiver can make a measurement of the pseudorangerate from the frequency offset it generates in an numerically controlled oscillator that provides an additional frequency offset from the reference frequency (freqCS=baseGRfreq+driftGR). The measurement can be modeled as the derivative of the pseudorange.

[0252]
A “Dot” after φ indicates the derivative.

[0253]
φDotGR1=rangeRateGR1+driftSV−driftGR1;

[0254]
φDotGR2=rangeRateGR2+driftSV−driftGR2.

[0255]
Removing unknowns for the freqDiff and pseudorangerates, driftSV is assumed to be known from the ephemeris data that is distributed around the system. The cellsite is known to be static, and rangeRateGR1 can be computed using, RangeRateGR1=(xVelSV−xVel)*uX+(yVelS−yVel)*uY+(zVelSV−zVel)*uZ, where,

[0256]
uX=(xSV−x1)/rangeGR1

[0257]
uY=(ySV−y1)/rangeGR1

[0258]
uZ=(zSV−z1)/rangeGR1 and

[0259]
“true” user velocity vector=(xVel, yvel, zVel)

[0260]
The GPS receiver at the cellsite can be assumed to have a “true” user velocity of zero. Thus, all the positions and velocities are assumed known. The GPS receiver 112 at the cellsite can compute its position, or the position can be a surveyed position. Secondly, the satellite position and velocity can be computed with the ephemeris made available to the cellsite GPS receiver.

[0261]
Because RangeRateGR1 and driftSV are known, can use the observed pseudorangerate can be used to estimate the GPS receiver drift.

[0262]
Thus, the estimate of the drift at GPS receiver1 can be computed.

[0263]
driftGR1hat=rangeRateGR1+driftSV−φDotGR1 (units are Hz at baseGRfreq).

[0264]
If more satellites are being tracked, then the drift estimate can be formed from the velocity fix, or by averaging a set of the above equations if the position is known. Such will improve the accuracy of the estimate if the position accuracy is high.

[0265]
Using the freqDiff and the estimated GPS receiver1 clock drift, the estimate of the cellsite clock drift can be formed.

DriftCShat=ΔF 1*freqGR 1hat/baseGR+driftGR 1hat*baseCS/baseGR (units are HZ at baseCSfreq)

[0266]
where,

[0267]
ΔF1=(N1/M)*baseGR−baseCS

[0268]
freqGRhat1=baseGRhat+driftGR1hat (from the GPS receiver1)

[0269]
N1=freqDiff between cellsite and GPS receiver1.

[0270]
Remove the cellphone clock drift to compute velocity with method embodiment of the present invention.

[0271]
When the cellphone is tracking frequency with an NCO, freqDiff can be used to express the cellsite drift in terms of the GPS receiver drift. This removes the cellphone clock from the measured cellphone carrier frequency to track the cellsite carrier.

[0272]
Remember:
$\begin{array}{c}\Delta \ue89e\text{\hspace{1em}}\ue89e\mathrm{F2}=\text{\hspace{1em}}\ue89e\left(\mathrm{N2}/M\right)*\mathrm{baseGRfreq}\mathrm{baseCPfreq}\\ =\text{\hspace{1em}}\ue89e\mathrm{driftCP}\mathrm{driftGR2}*\left(\mathrm{baseCSfreq}/\mathrm{baseGRfreq}\right).\end{array}$

[0273]
Thus,

DriftCPhat=ΔF 2+driftGR 2*(baseCSfreq/baseGRfreq).

[0274]
The carrier measurement can be used as an estimate of driftCP:

φDotCP 32 rangeRateCP+driftsCShat−(ΔF 2+driftGR 2*(baseCSfreq/baseGRfreq)) (Hz at baseCSfreq).

[0275]
Thus, this is an expression for the pseudorangerate where the unknown are in terms of velocity and clock bias of the GPS receiver.

[0276]
Remove the cellphone clock drift to predict the drift of the GPS receiver in the cellphone.

[0277]
Before fixing, this procedure can be used to generate an estimate of the clock drift of the GPS receiver clock in the cellphone.

[0278]
An estimate of the drift can be formed by assuming that the cellphone is static, so that the rangeRateCP term can be assumed to be zero. The accuracy of the estimate is driven by the accuracy of this assumption. However, for most low cost clocks, the frequency uncertainty caused by temperature and aging on the crystal are much larger than the user dynamics between the cellphone and cellsite, and the estimate provides a huge information gain that can be used to reduce search time and or increase sensitivity.

[0279]
For example, suppose the user is moving at 100 mph. We first convert the user velocity to meters/second:

(100 miles/hour)*(1hour/3600 seconds)*(5280 feet/1mile)*(12 inches/1 foot)*(0.0254 meters/1inch)=44.704 meters/second

[0280]
Now, for this example, assume the nominal frequency of the GPS receiver at the cellphone clock if 27.456 MHz. The wavelength of the,

λCP=Cf=speedoflight/27.456e6 cycle/sec=10.9 meters/cycle.

[0281]
The frequency Error of driftCP assuming the user is static when in fact the user is moving at 100 mph,
$\begin{array}{c}\text{\hspace{1em}}\ue89e\mathrm{freqError}\ue89e\text{\hspace{1em}}\ue89e\text{(HzatnominalGRfreq)}\\ \text{\hspace{1em}}\ue89e=\text{(}\ue89e44.704\ue89e\text{\hspace{1em}}\ue89e\text{meters/second}\ue89e\text{)}*\text{(1cycleof}\ue89e\text{\hspace{1em}}\ue89e\mathrm{baseCPfreq}/10.9\ue89e\text{\hspace{1em}}\ue89e\text{meters)}\\ \text{\hspace{1em}}\ue89e=4.1\ue89e\text{\hspace{1em}}\ue89e\mathrm{Hz}\end{array}$

[0282]
The freqError in PartsPerMillion (PPM),
$\begin{array}{c}\text{\hspace{1em}}\ue89e\mathrm{FreqError}\ue89e\text{\hspace{1em}}\ue89e\left(\mathrm{PPM}\right)\\ \text{\hspace{1em}}\ue89e=4.1/27.456\\ \text{\hspace{1em}}\ue89e=0.15\ue89e\text{\hspace{1em}}\ue89e\mathrm{PPM}.\end{array}$

[0283]
The effect on the velocity solution is that this frequency error is multiplied up to L1 whose wavelength=0.19 meters/cycle.

Thus, Frequency Error at L 1=(44.704 meters/second)*(1cycle of L 1/0.19 meters)=235 Hz.

[0284]
The PPM remains the same at any reference frequency. The freqError in PartsPerMillion (PPM), 235 Hz/1575.42=0.15 PPM

[0285]
The frequency error of the crystal may be on the order of 0.5 to 1 PPM, and the assumption of zerouservelocity still provides a big information gain in estimating the GPS receiver frequency drift. The information gain for a 1PPM uncertainty is 1/0.15=6.7. This means the frequency search can be reduced by a factor of 6.69. Such provides a major reduction in search time.

[0286]
Assuming the user dynamics are zero, first make an estimate of the cellphone frequency drift,

DriftCPhat=rangeRateCP+driftCShat−φDotCP (Hz at baseCSfreq)

[0287]
And then, using the freqDiff and assuming the rangeRateCP=0, estimate the GPS clock drift as,
$\begin{array}{c}\mathrm{DriftGR2hat}=\text{\hspace{1em}}\ue89e\left(\mathrm{driftCPhat}\Delta \ue89e\text{\hspace{1em}}\ue89e\mathrm{F2}\right)*\left(\mathrm{baseGRfreq}/\mathrm{baseCSfreq}\right)\\ \text{\hspace{1em}}\ue89e\left(\mathrm{Hz}\ue89e\text{\hspace{1em}}\ue89e\mathrm{at}\ue89e\text{\hspace{1em}}\ue89e\mathrm{baseGRfreq}\right)\\ =\text{\hspace{1em}}\ue89e\left(\mathrm{driftCShat}\phi \ue89e\text{\hspace{1em}}\ue89e\mathrm{DotCP}\Delta \ue89e\text{\hspace{1em}}\ue89e\mathrm{F2}\right)*\\ \text{\hspace{1em}}\ue89e\left(\mathrm{baseGRfreq}/\mathrm{baseCSfreq}\right)\\ \text{\hspace{1em}}\ue89e\left(\mathrm{units}\ue89e\text{\hspace{1em}}\ue89e\mathrm{are}\ue89e\text{\hspace{1em}}\ue89e\mathrm{Hz}\ue89e\text{\hspace{1em}}\ue89e\mathrm{at}\ue89e\text{\hspace{1em}}\ue89e\mathrm{baseGRfreq}\right).\end{array}$

[0288]
Remove the cellphone clock drift to compute velocity. In the case that the cellphone is using the VCO to track the cellsite frequency and the freqDiff can observe the effect on the baseCPfreq.

[0289]
The “truth” model for the observation,

FreqDiffVCO=((Nvco+(Q 1−Q 2)/M)*freqGR (in counts at CP freq).

[0290]
Because only observe Nvco, our measurement, FreqDiffVCO (observed)=Nvco (in integer counts at CP freq).

[0291]
We then form the freqDiff estimate in units of Hertz.

ΔF 2 vco=(Nvco/M)*baseGRfreq−baseCSfreq (counts at CP freq).

[0292]
Our model is then,

ΔF 2 vco=driftCSvco−driftGR 2*(baseCSfreq/baseGRfreq) (in Hertz at CP freq)=(rangeRateCP+driftCS)−driftGR 2*(baseCSfreq/baseGRfreq).

[0293]
Inserting the estimate of the cellsite drift, a measurement equation that can be used to solve for the user velocity and GPS receiver clock drift is made.

ΔF 2 vco=rangeRateCP+driftCShat−driftGR 2*(baseCSfreq/baseGRfreq) (in Hertz at CP freq).

[0294]
Remove the cellphone clock drift to predict the drift of the GPS receiver in the cellphone.

[0295]
The user velocity is zero. Such allows an estimate of the clock drift of the GPS receiver in the cellphone.

[0296]
Assume that the rangeRateCP is zero,

DriftGR 2hat=(driftCShat−ΔF 2 vco)*baseGRfreq/baseCSfreq (in Hertz at GR freq).

[0297]
This estimate can be used to reduce the frequency search required to find the GPS satellites. Thus, frequency transfer can be performed with this observation.

[0298]
To estimate the user velocity, the measurement for method embodiment of the present invention (using the NCO in the cellphone) is φDotCP=rangeRateCP+driftsCShat−(ΔF2+(riftGR2*(baseCSfreq/baseGRfreq)).

[0299]
Also the measurement for another embodiment of the present invention (using the VCO in the cellphone) is ΔF2vco=rangeRateCP+driftCShat−driftGR2*(basecSfreq/baseGRfreq).

[0300]
These equations are generalized for simplicity as,

PrrCP=C 3*rangeRateCP−driftGR 2*C 1+C 2

[0301]
where for a method embodiment of the present invention,

[0302]
PrrCP=φDotCP

[0303]
C1=(baseCSfreq/baseGRfreq)

[0304]
C2=driftsCShat−ΔF2

[0305]
C3=1/(λCP)

[0306]
λCP=C/baseCSfreq.

[0307]
For another method embodiment of the present invention,

[0308]
PrrCP=ΔF2vco

[0309]
C1=(baseCSfreq/baseGRfreq)

[0310]
C2=(driftsCShat

[0311]
C3=1/(λCellsite)

[0312]
λ=C/baseCPfreq.

[0313]
Combine the cellphone and GPS pseudorange rate measurements to estimate the user velocity and, the GPS receiver drift.

[0314]
The cellphone can track a set of J cellcites and form the jth pseudorangerate observations as:

PrrCP(j)=C 3*rangeRateCP(j)−driftGR 2*C 1+C 2 (Hz at baseCPfreq)

[0315]
K GPS satellites form the kth pseudorangerate observations as:

PrGR 2(k)=C 6*rangeRateGR 2(k)−driftGR 2*C 4+C 5 (Hz at baseGRfreq),

[0316]
where:

[0317]
C4=1

[0318]
C5=driftSVhat (from the satellite ephemeris)

[0319]
C6=1/(λGR)

[0320]
(λGR)=C/baseGRfreq

[0321]
In order to solve for velocity, first perform the position solution, and then, predict the nominal rangeRateCP(j) as follows,

RangeRateCPhat(j)=xVelCS(k)*uX(k)+yVelS(k)*uY(k)+zVelCS(k)*uZ(k),

[0322]
where,

[0323]
uXCS(j)=(xCS(j)−x)/rangeGR2

[0324]
uYCS(j)=(yCS(j)−y)/rangeGR2

[0325]
uZCS(j)=(zCS(j)−z)/rangeGR2.

[0326]
However, for the cellsite, assume it is static so, xVelCS(k)=yVelCS(k)=zVelCS(k)=0.

[0327]
Similarly, can predict the nominal rangeRateGR2(k) as follows,

RangeRateGR 2hat(k)=(xVelSV(k)−xVel)*uX(k)+(yVelS(k)−yVel)*uY(k)+(zVelSV(k)−zVel)*uZ(k),

[0328]
where,

[0329]
uXSV(k)=(xSV(k)−x)/rangeGR2

[0330]
uYSV(k)=(YSV(k)−y)/rangeGR2

[0331]
uZSV(k)=(zSV(k)−z)/rangeGR2.

[0332]
Making these substitutions,
$\begin{array}{c}L\ue89e\text{\hspace{1em}}\ue89ei\ue89e\text{\hspace{1em}}\ue89en\ue89e\text{\hspace{1em}}\ue89eP\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89eC\ue89e\text{\hspace{1em}}\ue89eP\ue8a0\left(j\right)=\text{\hspace{1em}}\ue89eP\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89eC\ue89e\text{\hspace{1em}}\ue89eP\ue8a0\left(j\right)\mathrm{C3}*r\ue89e\text{\hspace{1em}}\ue89ea\ue89e\text{\hspace{1em}}\ue89en\ue89e\text{\hspace{1em}}\ue89eg\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89eR\ue89e\text{\hspace{1em}}\ue89ea\ue89e\text{\hspace{1em}}\ue89et\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89eC\ue89e\text{\hspace{1em}}\ue89eP\ue89e\text{\hspace{1em}}\ue89eh\ue89e\text{\hspace{1em}}\ue89ea\ue89e\text{\hspace{1em}}\ue89et\ue8a0\left(j\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{C3}*(u\ue89e\text{\hspace{1em}}\ue89eX\ue89e\text{\hspace{1em}}\ue89eC\ue89e\text{\hspace{1em}}\ue89eS\ue8a0\left(j\right)*x\ue89e\text{\hspace{1em}}\ue89eV\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89elu\ue89e\text{\hspace{1em}}\ue89eY\ue89e\text{\hspace{1em}}\ue89eC\ue89e\text{\hspace{1em}}\ue89eS\ue8a0\left(j\right)*\\ \text{\hspace{1em}}\ue89ey\ue89e\text{\hspace{1em}}\ue89eV\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89elu\ue89e\text{\hspace{1em}}\ue89eZ\ue89e\text{\hspace{1em}}\ue89eC\ue89e\text{\hspace{1em}}\ue89eS\ue8a0\left(j\right)*z\ue89e\text{\hspace{1em}}\ue89eV\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89el)d\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89ei\ue89e\text{\hspace{1em}}\ue89ef\ue89e\text{\hspace{1em}}\ue89et\ue89e\text{\hspace{1em}}\ue89eG\ue89e\text{\hspace{1em}}\ue89e\mathrm{R2}*\mathrm{C1}+\mathrm{C2}\\ L\ue89e\text{\hspace{1em}}\ue89ei\ue89e\text{\hspace{1em}}\ue89en\ue89e\text{\hspace{1em}}\ue89eP\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89eG\ue89e\text{\hspace{1em}}\ue89e\mathrm{R2}\ue8a0\left(k\right)=\text{\hspace{1em}}\ue89eP\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89eG\ue89e\text{\hspace{1em}}\ue89e\mathrm{R2}\ue8a0\left(k\right)\mathrm{C3}*r\ue89e\text{\hspace{1em}}\ue89ea\ue89e\text{\hspace{1em}}\ue89en\ue89e\text{\hspace{1em}}\ue89eg\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89eR\ue89e\text{\hspace{1em}}\ue89ea\ue89e\text{\hspace{1em}}\ue89et\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89eG\ue89e\text{\hspace{1em}}\ue89eR\ue89e\text{\hspace{1em}}\ue89e2\ue89e\text{\hspace{1em}}\ue89eh\ue89e\text{\hspace{1em}}\ue89ea\ue89e\text{\hspace{1em}}\ue89et\ue8a0\left(k\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{C6}*(u\ue89e\text{\hspace{1em}}\ue89eX\ue89e\text{\hspace{1em}}\ue89eS\ue89e\text{\hspace{1em}}\ue89eV\ue8a0\left(k\right)*x\ue89e\text{\hspace{1em}}\ue89eV\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89elu\ue89e\text{\hspace{1em}}\ue89eY\ue89e\text{\hspace{1em}}\ue89eS\ue89e\text{\hspace{1em}}\ue89eV\ue8a0\left(k\right)*\\ \text{\hspace{1em}}\ue89ey\ue89e\text{\hspace{1em}}\ue89eV\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89elu\ue89e\text{\hspace{1em}}\ue89eZ\ue89e\text{\hspace{1em}}\ue89eS\ue89e\text{\hspace{1em}}\ue89eV\ue8a0\left(k\right)*\\ \text{\hspace{1em}}\ue89ez\ue89e\text{\hspace{1em}}\ue89eV\ue89e\text{\hspace{1em}}\ue89ee\ue89e\text{\hspace{1em}}\ue89el)d\ue89e\text{\hspace{1em}}\ue89er\ue89e\text{\hspace{1em}}\ue89ei\ue89e\text{\hspace{1em}}\ue89ef\ue89e\text{\hspace{1em}}\ue89et\ue89e\text{\hspace{1em}}\ue89eG\ue89e\text{\hspace{1em}}\ue89e\mathrm{R2}*\mathrm{C4}+\mathrm{C5}.\end{array}$

[0333]
These are the equations in terms of only the user velocity and the GPS receiver clock drift. Thus, as long as four measurement from either multiple GPS satellites or multiple cellsites are found, the velocity and drift using conventional methods (like leastsquare or a Kalman filter) can be solved.

[0334]
To removing unknowns for the timeDiff and pseudoranges, the timeDiff measurements must be used.

[0335]
The rangeGR1 is considered to be a known quantity since its components are known.

[0336]
The satellite position and clock bias is considered known since it can be computed from the GPS ephemeris that can be circulated around the system by the server.

[0337]
Assume that GPS receiver1 is tracking enough satellites to compute at least its time solution. If its position is known, then only one satellite is needed to do this.

[0338]
In timeDiff and pseudorange measurements, the pseudorange are formed by the cellphone tracking the cellsite, φCP=rangecP+BiasCS−BiasCP.

[0339]
The pseudorange formed inside GPS receiver1 at the cellsite, φGR1=rangeGR1+biasSV−biasGR1.

[0340]
The pseudorange formed inside GPS receiver2 at the cellsite, φGR2=rangeGR2+biasSV−biasGR2.

[0341]
With timeDiff observations between the GPS receiver1 and the cellsite (Ni1 and Ni2), biasCSG=BiasGR1+TD1.

[0342]
With timeDiff observations between the GPS receiver2 and the cellphone (Ni1 and Ni2), biasCPG=BiasGR2+TD2.

[0343]
To solve for the clock bias of the GPS receiver as the cellsite, the rangeGR1 is known, and biasSV is known, and φGR1 is measured in GPS receiver1, can estimate the clock bias for GPS receiver1 as follows,

biasGR 1hat=estimate of (biasGR 1)=rangeGR 1+biasSV−φGR1.

[0344]
To solve for the clock bias of the cellsite from GPS time, use the timeDiff measurement (TD1) between GPS receiver1 and the cellsite. Estimate the bias between the cellsite and GPS time.

[0345]
Either of the timeDiff measurements (N11 or N12) can be used.

TD 1=N 11/freqGR 1hat

TD 2=N 12/freqGR 1hat

[0346]
where

FreqGRhat=baseGRfreq+driftGR 1hat.

[0347]
Assume that biasGR1hat and driftGR1hat are known and are obtained directly from GPS receiver1 at the cellsite.

[0348]
Now, using the definition of the timeDiff, solve for the cellsite drift as follows,

[0349]
using N11, then

BiasCS 1hat=TD 1+biasGR 1hat (units are seconds),

[0350]
using N12, then

BiasC 1hat=1−TD 2+biasGR 1hat (units are seconds)

[0351]
Remove the cellphone clock bias to compute position.

[0352]
Assume the cellphone produces the pseudorange measurement between the cellphone and the cellsite.

[0353]
The pseudorange formed by the cellphone tracking the cellsite is φCP=rangeCP+BiasCS−BiasCP.

[0354]
Apply the estimate of the cellsite clock bias and use the timeDiff between the cellphone and GPS receiver2. Such change of variables allows elimination of the cellphone clock and cellsite clock, and to express the cellphone derived pseudoranges in terms of the cellphone location and GPS receiver2's clock.

[0355]
The timeDiff in the cellphone has the form,

TD 1=N 11/freqGR 2hat

TD 2=N 12/freqGR 2hat

[0356]
where,

FreqGRhat=baseGRfreq+driftGR 2hat

[0357]
Forming the timeDiff without an estimate of the driftGR in the cellphone, do not know have an estimate of the GPS receiver2 drift until a position fix. Thus, reformulate the model to obtain a model that represents the explicite effect of this paramter.

[0358]
Normalize the observed timeDiff count with baseGRfreq rather than FreqGRhat.

[0359]
In this case,
$\begin{array}{c}\mathrm{TD1}=\text{\hspace{1em}}\ue89e\mathrm{N11}/\mathrm{freqGR}\\ =\text{\hspace{1em}}\ue89e\mathrm{N11}*(1/\left(\mathrm{baseGRfreq}+\mathrm{driftGR}\right)\\ \text{\hspace{1em}}\ue89e1/\mathrm{baseGRfreq}+1/\mathrm{baseGRfreq})\\ =\text{\hspace{1em}}\ue89e\mathrm{N11}*(\left(\mathrm{baseGRfreq}\mathrm{baseGRfreq}\mathrm{driftGR}\right)/\\ \text{\hspace{1em}}\ue89e\left(\mathrm{freqGR}*\mathrm{baseGRfreq}\right)+1/\mathrm{baseGR})\\ =\text{\hspace{1em}}\ue89e\mathrm{N11}*(1/\mathrm{baseGRfreq}\mathrm{driftGR}/\\ \text{\hspace{1em}}\ue89e\left(\mathrm{freqGR}*\mathrm{baseGRfreq}\right))\\ =\text{\hspace{1em}}\ue89e\mathrm{N11}/\mathrm{baseGRfreq}\mathrm{N11}*\mathrm{driftGR}/\left(\mathrm{freqGR}*\mathrm{baseGRfreq}\right)\end{array}$

[0360]
The measurement is not a linear function of driftGR because it represents up in both the numerator and denominator (inside freqGR) of the second term. While this can be handled, it is inconvenient. Thus, perform a simple approximation that linearizes the model. Replace the freqGR in the denominator with simply baseGRfreq.

[0361]
Linearize the unknown GPS receiver drift to make the measurement linear in the variable driftGR. Remove the variable driftGR from the denominator.

[0362]
Thus, examine the approximation of

driftGR/(baseGRfreq*freqGR)=driftGR/(baseGRfreq*baseGRfreq).

[0363]
For again that driftGR=20 PPM. Solving for the “true” value,

[0364]
=549/(27.456e6*27.456549e6)

[0365]
=7.282644976e13.

[0366]
If approximate the denominator as baseGR*baseGR, then the ratio,

[0367]
=549/(27.456e6*27.456e6)

[0368]
=7.282790418e13.

[0369]
The difference=1.456220e17.

[0370]
Multiply by the max N1=baseGR, the error is 3.998:197e10=0.11 meters.

[0371]
Thus, there is still a linear error model. If this technique didn't work, then the model would not be linear since the driftGRterm represents up in the denominator.

[0372]
To use the cellphone pseudorange for positioning before have an estimate of driftGR2 is found, then include the drift term in the pseudorange. Normally, the pseudorange is only related to the position and clock bias. Thus, this formulation has an extra unknown. However, the pseudorange rates are available, all the unknowns can be solved together.

[0373]
To use the tempMeas to estimate driftGR2, suppose that driftGR=20 PPM. Suppose that N11 was almost exactly equal to baseGR. That means the cellsite is just to the left of the GPS 1PPS. The additional term proportional to driftGR is driftGR/freqGR.

[0374]
If the drift were 20 PPM, then driftGR=20*baseGR/1e6=549 Hz and driftGR2/baseGR+driftGR=0.2 seconds.

[0375]
The tempMeas observable are used. Using the SCXO calibration, the driftGR to an accuracy of +/0.5 PPM can be estimated.

[0376]
The driftGR=0.5*baseGR/1e6=13.7 Hz. Such leads to a time error of 13.7/(27,456,014)=5.0e7=50 microseconds. Such is about 50 chips of the GPS pseudorandom code that repeats every 1023 chips.

[0377]
The tempMeas will provide a good enough approximation for using the cellphone pseudorange to predict the GPS receiver clock bias. Such can be used for prepositioning.

[0378]
To work timeDiff measurement, we redefine the timeDiff for the cellphone side as follows,

[0379]
Recall the measurement model,

TD 1=N 11/baseGRfreq−N 11*driftGR/(freqGR*baseGR)

[0380]
Define,

TD 1 a=N 11/baseGRfreq

[0381]
Thus,

TD 1 a=TD 1+N 11*driftGR/(freqGR*baseGR)

[0382]
Now, inserting the measurement model for the timeDiff at the cellphone (don't include the guantization terms, so the parameters are the estimates and not the “true” parameters),

TD 1=biasCPhat−biasGR 2hat

[0383]
Thus,

TD 1 a=biasCPhat−biasGR 2hat+N 11*driftGR 2/(baseGRfreq*baseGRfreq)

[0384]
Using this form, the additional term proportional to driftGR2 will account for the error in using baseGRfreq rather than freqGR to normalize.

[0385]
Rearrange the measurement model to solve for biasCPhat.

BiasCPhat=N 11/baseGR+biasGR 2hat−N 11*driftGR/(baseGRfreq*baseGRfreq).

[0386]
The above formula is inserted into the cellphone pseudorange so that all the clock terms are in terms of GPS receiver2's clock.

φCP=rangeCP+BiasCShat−(N 11/baseGR+biasGR 2hat−N 11*driftGR/(baseGRfreq*baseGRfreq).

[0387]
Define,

PrCP(j)=φCP=D 3*rangeCP(j)−biasGR 2*D 1+D 2 (units of seconds).

[0388]
Where,

[0389]
D1=1

[0390]
D2=biasCShat−N11/baseGR+N11*driftGR/(baseGRfreq*baseGRfreq) (seconds)

[0391]
D3=1/C (units of seconds/meter).

[0392]
Remove the cellphone clock bias to predict the bias of the GPS receiver in the cellphone with a method embodiment of the present invention.

[0393]
To estimate the GPS receiver2 bias directly, simply rearrange the above formula to solve for it.

biasGR 2hat=rangeCP+BiasCShat−φcp+(N 11/baseGR−N 11*driftGR/(baseGRfreq*baseGRfreq).

[0394]
This equation gives a method to estimate the GPS receiver clock bias prior to tracking any GPS signals. For GPS, the maximum timesearch window is onemillisecond. Thus, in order to reduce the search range, a clock bias estimate with an error that is significantly less than one millisecond is needed.

[0395]
Suppose that the cellphone is only one kilometer (1000 m) from the cellsite. Such is possible in Japan where the cellsite density is quite high.

[0396]
Also suppose using the freqDiff to estimate driftGR2.

[0397]
Recall,

ΔF 2=driftCP−driftGR 2*(baseCSfreq/baseGRfreq) DriftGR 2hat=(driftCShat−φDotCPΔF 2)*(baseGRfreq/baseCSfreq)

[0398]
In this equation assume that the user velocity is zero.

[0399]
Use the tempMeas to estimate driftGRscxo, that is, the estimate of the GPS receiver2's clock drift using the tempMeas observation and the calibration model to estimate clock frequency from the tempmeas.

[0400]
Assume the range from the cellsite is 1000, and use the driftGR estimate,

biasGR 2hat=(1000/c)+biasCShat−φcp+N 11/baseGR−N 11*(driftCShat−φDotCP−ΔF 2)/(baseCSfreq*baseGRfreq).

[0401]
The accuracy of the estimate is dominated by the assumption that the distance to the cell site is 1000 m. Even at a distance of 2000 m, the accuracy would be about 1000/c=3.3e1=3.3 microsecond. The timeuncertainty has been reduced from 1 msec to 3.3 microsecond. That is an information gain of almost a factor of 300. Such is the kind of information gain that will allow a superthin GPS client.

[0402]
Remove the cellphone clock bias to compute position.

[0403]
Derive the measurement models when the cellphone uses the VCO method embodiment of the present invention to track the carrier. The frequency is adjusted to match the phase of the incoming signal. The meaning of the timeDiff changes since the PPS associated with the cellphone reference also moves as the frequency is adjusted.

[0404]
The timeDiff no longer observes the cellphone bias, but rather, it observes the cellsite bias and the range between the cellsite and the cellphone. For example, if the cellsite clock bias is positive, then the cellsite must also increase its phase to be in alignment. To compensate for the travel time of the signal from the cellsite to the cellphone, the cellphone must further delay its signal in order to track the incoming signal. A phase advance is a positive increase in the phase.

[0405]
The cellphone clock bias is replaced by the rangeCP and the cellsite bias.

[0406]
The “true” timeDiff models is:

TD 1=BiasCPvco−biasGR 2,

[0407]
where,

BiasCPvco=rangeCP+biasCS.

[0408]
We have the same issue for the actual measurement, i.e, to normalize the timeDiff by the correct frequency. Normalize baseGRfreq and then account for the driftGR2 term explicitely.

[0409]
Define,

TD 1 a=N 11/baseGRfreq.

[0410]
Thus,

TD 1 a=TD 1+N 11*driftGR/(baseGRfreq*baseGRfreq).

[0411]
Now, inserting our model for the “true” TD1, and inserting the estimated parameters, (not including the quantization terms in our measurement model),

TD 1 a=rangeCP+biasCShat−biasGR 2+N 11*driftGR/(baseGRfreq*baseGRfreq).

[0412]
Define,

PrCP(j)=N 11/baseGR=D 3*rangeCP(j)−biasGR 2*D 1+D 2 (units of seconds).

[0413]
Where,

[0414]
D1=1

[0415]
D2=baseCShat−N11/baseGR+N11*driftGR/(baseGRfreq*baseGRfreq) (seconds)

[0416]
D3=1/C (units of seconds/meter).

[0417]
Have an expression for the cellphone pseudorange where the unknowns are the user position, and the GPS receiver clock errors. Even though the GPS receiver drift appears, the equations can still be solved.

[0418]
Remove the cellphone clock bias to compute position.

[0419]
For time transfer for aiding the GPS acquisition, simply rearrange the above equation to solve for biasGR. Once again, have two sources to estimate the GPS receiver clock drift. Either use the tempMeas observation or use the freqDiff and assume the user velocity is zero.

BiasGR 2=rangeCP+biasCShat−N 11/baseGRfreq+N 11*driftGR 2/(baserGRfreq*baseGRfreq).

[0420]
Use the data from the tempmeas observation,

biasGR 2hat=rangeCP+biasCShat−N 11/baseGRfreq+N 11*driftGR 2 SCXO/(baserGRfreq*baseGRfreq).

[0421]
The combination of the freqDiff at the cellphone assumes the cellphone rangeRate is zero,

DriftGR 2hat=(driftCShat−ΔF 2 vco)*baseGRfreq/baseCSfreq (in Hertz at GR freq).

[0422]
Inserting this,

biasGR 2=rangeCP+biasCShat−N 11/baseGRfreq+N 11*(driftCShat−ΔF 2 vco)/(baserCSfreq*baseGRfreq) (units are seconds)

[0423]
To solving for Position/Velocity in the Dual mode system.

[0424]
Combine the cellphone pseudoranges with the GPS pseudoranges.

[0425]
Define for a method embodiment of the present invention (NCO method embodiment of the present invention),

PrCP(j)=φCP=D 3*rangeCP(j)−biasGR 2*D 1+D 2 (units of seconds).

[0426]
Where,

[0427]
D1=1

[0428]
D2=biasCShat−N11/baseGR+N11*driftGR/(baseGRfreq*baseGRfreq) (seconds)

[0429]
D3=1/C (units of seconds/meter).

[0430]
Or define for method embodiment of the present invention (VCO method embodiment of the present invention),

PrCP(j)=N 11/baseGR=D 3*rangeCP(j)−biasGR 2*D 1+D 2 (units of seconds).

[0431]
Where,

[0432]
D1=1

[0433]
D2=baseCShat−N11/baseGR+N11*driftGR/(baseGRfreq*baseGRfreq) (seconds)

[0434]
D3=1/C (units of seconds/meter).

[0435]
And define the GPS observations as,

PrGR 2(k)=D 6*rangeSV(k)−D 4*driftGR 2+D 5.

[0436]
Where,

[0437]
D4=1

[0438]
D5=biasSV

[0439]
D6=1/C.

[0440]
As with the pseudorangerates, linearize them with respect to position by subtracting the nominal range.

[0441]
Define the delta vector as the error between the “true” position vector and the starting estimate of the position. In the estimation process, compute the delta vector and then add it to the starting position to get the position estimate. Thus, assume that when forming the predicted quantities where the user position is needed, use xNominal.

[0442]
Define the error in our nominal estimate (xNominal) as delX.

[0443]
delX=x−xNominal

[0444]
delY=y−yNominal

[0445]
delZ z−zNominal

[0446]
Assume having measurement to J cellsites and K satellites. The linearized measurement for the jth cellsite and the kth GPS satellite are,
$\begin{array}{c}\mathrm{LinPrCP}\ue8a0\left(j\right)=\text{\hspace{1em}}\ue89e\mathrm{PrCP}\ue8a0\left(j\right)\mathrm{D3}*\mathrm{rangeCPhat}\ue8a0\left(j\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{D3}*(\mathrm{uXCS}\ue8a0\left(j\right)*\mathrm{delX}\mathrm{uYCS}\ue8a0\left(j\right)*\\ \text{\hspace{1em}}\ue89e\mathrm{delY}\mathrm{uZCS}\ue8a0\left(j\right)*\mathrm{delZ})\mathrm{biasGR2}*\mathrm{D1}+\mathrm{D2}\\ \mathrm{LinPrGR2}\ue8a0\left(k\right)=\text{\hspace{1em}}\ue89e\mathrm{PrGR}\ue8a0\left(k\right)\mathrm{C3}*\mathrm{rangeGRhat}\ue8a0\left(j\right)\\ =\text{\hspace{1em}}\ue89e\mathrm{D6}*(\mathrm{uXSV}\ue8a0\left(k\right)*\mathrm{delX}\mathrm{uYSV}\ue8a0\left(k\right)*\\ \text{\hspace{1em}}\ue89e\mathrm{delY}\mathrm{uZSV}\ue8a0\left(k\right)*\mathrm{delZ})\mathrm{biasGR2}*\mathrm{D4}+\mathrm{D5}\end{array}$

[0447]
where the uXCS and uXSV are the same as defined in the pseudorangerate section.

[0448]
The Dual Mode system has derived the solution equations that relate all observable in the system to the user position/velocity and clock bias and drift of the GPS receiver in the cellphone. All other system clocks have been calibrated out of the system.

[0449]
Standard solution techniques can then be used to solve for the eight unknowns.

[0450]
To get a solution, many observations have unknowns. That means that four observation that have the user position are needed. The derivative measurements are also needed. Estimate the GPS receiver velocity and clock drift.

[0451]
The cellphone measurements along with the timeDiff, freqDiff), and tempMeas observables can be used to improve the acquisition of the GPS satellites by reducing the search range for those signals. Estimate the GPS receiver clock bias and drift with respect to the cellphone and the calibration of the cellsites.

[0452]
The system is a truly distributed processing system. Depending on the client type, all the calibrations and calculation could either be done in the cellphone, in the network server, or spread between the two systems. However, the server is the conduit that sends the calibration numbers for the cellsites so that the data can be used for both time and frequency transfer that improves GPS acquisition times, and for Dual mode operation where use the range and rangerates from both systems to compute the cellphone position.

[0453]
A communications means between the cellsite, the server, the cellphone, and the GPS receivers at both the cellsite and the cellphone is assumed. However, the details of the specific methods used are not critical to the equations presented here.

[0454]
GPS receiver1 is at the cell site. It tracks GPS continuously and estimates its position, clock bias and clock drift. It performs a timeDiff and freqDiff between the GPS receiver and the Cellsite clock. It sends the measurements and its solutions back to the network server. Server computes the cellsite clock bias and drift. It also send other GPS data to the network server such as the 50 bps Navigation data message.

[0455]
The network server accepts the data from the cellsite and builds a table of the clock bias and drift of each cellsite. It also can generate a cellsite position from the GPS receiver position. The network server builds a Navigation Data database that is distributed throughout the system as a source of data for computing the satellite position, velocity, clock bias and drift.

[0456]
GPS receiver2 is at the cellphone to compute the position of this receiver. At turn on, don't know the GPS receiver clock bias, drift, or position. It performs a timeDiff, freqDiff, and tempMeas. The cellphone receiver tracks a cellsite (at least one). By tracking the phase and frequency of the carrier, it can also form pseudoranges and pseudorangerates between the cellsite. Using these measurements, plus the cellsite data that includes the cellsite clock bias and drift, and the cellsite position, and using the timeDiff, freqDiff, and tempMeas observations, can perform time and frequency transfer between the cellphone and the GPS receiver. After acquitting one GPS satellite, can also use the observations to compute the dualmode position/velocity.

[0457]
The time and frequency transfer allows us to improve the acquisition of the GPS satellites by reducing the search range. Such improves acquisition time and sensitivity. Such allows the superthinclient.

[0458]
After at least one GPS satellite is acquired, the range and rangerate measurements from both systems can be combined to compute the cellphone position. Such should allow a positioning capability when fewer than normal of the measurements from each system are available. For example, a threedimensional fix can be made with only 1 GPS satellites, and 3 cellsites, or 2 GPS satellites and 2 cellsites, or 3 GPS satellites and only one cellsite.

[0459]
Actually, one can compute the cellphone position without any GPS satellite tracked at the cellphone. Because the cellsites do significant relative vertical displacement, the threedimensional solution is very noisy. However, a twodimensional solution is possible if altitude of the cellphone is available. (Remember, the GPS satellites are still needed at the cellsites for synchronizing the cellsites.) A threedimensionalCDMAonly is also possible if the cellsites have good vertical separation.

[0460]
GPSnavigation almanac and ephemeris are acquired and reduced by the webserver 106 with its own referencestation GPSreceiver to supply simple polynomials that respectively represent each satellite's position and velocity. Such polynomials will, of course, go stale over time, but periodic contact between the cellsite 102 and webserver 106 via the Internet are critically depended upon to provide freshenough orbit data. The GPS receiver 112 is therefore relieved of the storageintensive requirement to hold current ephemeris and almanac data in local RAM/ROM, and relieved of the processorintensive job of locally computing doubleprecision floatingpoint math the satelliteorbit positions for every position fix.

[0461]
In a businessmodel embodiment of the present invention, the webserver 106 is owned and operated by an independent service provider. Peruse or subscription fees are charged to users who operate the cellphone 104 and/or cellsite 102. The cellphone 104 is alternatively further bundled in an intellectual property (IP) package for semiconductor integrated circuit device designs of applicationspecific network clients. Such IP is sold for a license fee and hardwaredevice cost to original equipment manufacturers (OEM's) of network clients.

[0462]
In operation, the GPS receiver 112 must simultaneously search for GPSmicrowave signals in two domains, e.g., frequency and codephase. The local oscillator and Doppler shift caused by satellite vehicle relative velocity create carrier frequency uncertainties that are resolved. The instantaneous GPSsatellite pseudorandom number (pseudorandom number) code phase is another unknown. Received signals that are above the “noise floor” are relatively easy and quick to search. But weak signals, as exist inside buildings, are buried in as much as twenty decibels of noise. Each visit to a frequency/codephase bin must dwell there long enough to “beat down” the noise floor with processing gains provided by code correlators. Weak signals also require that the search bins have finer steps between bin frequencies and bin codephase, e.g., due to aliasing. So more bins are needed to be searched and each bin needs more processing dwell, all of which increases search time exponentially.

[0463]
The webserver 106 publishes realtime navigation data to the Internet. Other services currently exist that put up partial or nonrealtime navigation and initialization data on the Internet, and these can be used partially in place of, or to check the validity of realtime navigation data being sent to the GPS receiver 112. A primary and critical role job for webserver 106 is the offloading of navigationcomputational chores from the GPS receiver 112. The degree to which such offloading can be carried depends on the regularity of communication contact that can be realized between the GPS receiver 112 and the webserver 106. The actual measurements obtained by the GPS receiver 112 are forwarded to the webserver 106.

[0464]
Alternative embodiments of the present invention incorporate webservers 106 that do database processing for higherlevel abstractions and purposes. For example, the server platform includes a health and quality monitor for checking said static observations and preventing an inclusion of incorrect information in said database of measurement errors and satellite data messages. On another front, webserver 106 could collect position solution information over time for the pattern of locations that GPS receiver 112 visits over a period of hours, days, weeks, months, years, etc. Such information can then be processed to estimate where the user of GPS receiver 112 is, where the user has been, or where the user is likely to be in the future. Such information is useful to dispatch, timeclock, housearrest, deployment, inventory, asset management, military, security, and other kinds of applications. Position information can be interpreted to intelligently guess at what the user is doing at any one moment. For example, if the user's position matched that of a local grocery store, the user could be assumed to be shopping. Logs can also be generated by the user at the webserver 106, e.g., by city maintenance department collocating with and “marking” in the electronic database the permanent location of a fire hydrants, power transformers, roadways, etc.

[0465]
The presence on the Internet of information about a user's position can be used by advertisers and marketers to direct contextual messages to the user in realtime. Such data is sold in realtime in a business model embodiment of the present invention.

[0466]
In general, embodiments of the present invention use Internet webservers to process data collected by remote GPS receivers in such ways that signal sensitivity is increased and search times are shortened compared to conventional receivers and methods.

[0467]
Recent test data indicates the a priori worstcase modeling error for a typical crystal frequency is around ±0.5 PPM (±787 Hz) with temperature modeling. To be conservative, and leave some uncertainty for user position error effect on the frequency, a frequency range of ±1000 Hz for the first satellite is preferably searched. If there is a high degree of confidence about the frequency information learned in a first search, the frequency search range of subsequent satellites can be constrained to save time and effort. Alternatively, such searchingtime savings could be traded for a slower clock speed as would be found in less expensive hardware.

[0468]
[0468]FIG. 10 is a functional block diagram of a second infrastructureassisted navigation system embodiment of the present invention, and is referred to herein by the general reference numeral 1000. The special case in which system 1000 is needed is where no political or economic opportunity exists to include a GPS receiver at a cellulartelephone base site, e.g., system 100 (FIG. 1). So a cellphone and GPS receiver combination permanently parked at a stationary location can be adapted to serve instead. A business model embodiment of the present invention deploys apparently ordinary cellphones on fixed station in each cell site where business coverage is needed but not otherwise available. Such nonavailability can result from hostile base cellsite operators, adverse or cumbersome laws, too little time, too much expense, etc.

[0469]
System 1000 includes a service provider 1002 connected to a data network 1004, e.g., the Internet. A cellular base station 1006 simply handles ordinary cellular telephone calls between stations with telephone numbers. A visiting, mobile cell user 1008 is able to make and receive telephone calls through the cellular base station 1006. A business that operates the service provider 1002 has previously deployed a permanent, parked cell station 1010 that is within the service area of the cellular base station 1006. It too is accessible to other parts of the system via telephone calls made through the cellular base station 1006.

[0470]
The service provider 1002 includes a GPS receiver 1012, a network server 1014, and a database 1016 for storing temperature, time, and frequency data and models. The cellsite 1006 comprises a cellular transceiver 1018 and no GPS receiver. The cellphone 1008 also includes its own GPS receiver 1020 and cellular transceiver 1022. The permanent, parked cell station 1010 has a GPS receiver 1024 and a cellularphoneserviceband transceiver 1026 that is used to track the frequency and phase of signals it receives from the cellsite 1006. The network server 1014 receives and distributes time information and other data from both the cellsite and cellphone GPS receivers over data network 1004. A database 1016 of positions and their time and frequency offsets from GPS time is collected for later reference.

[0471]
As in system 100 (FIG. 1), three hardwarebased measurements can be used to synchronize the local clocks in two independent systems, e.g., (1) timedifference, (2) frequency difference, and (3) crystal temperatureversusfrequency models. Any or all three can be used to synchronize clocks. In a timeDiff observable, if the time difference between time events from two different time sources is known, the time of an event at one time source can be used to compute the time of the event at the other time source. In a freqDiff observable, if the frequency difference between two clocks is known, then finding the frequency of one can be used to predict the frequency of the other. In a tempMeas observable, a temperaturefrequency calibration model is used to predict the frequency of a local GPS clock by measuring the crystal temperature. If one of the time sources is a GPS receiver, other clocks can be related to GPS time. Such potentially allows devices all around the world to be time and frequency synchronized to a common and stable reference, for example, the GPS system atomic clocks.

[0472]
Passive network synchronization embodiments of the present invention use the GPS receiver 1024 to measure the cellsite 1006 clocks in GPS time. Then the cellphone GPS receiver 1020 clock and the cellphone 1022 clock can be synchronized to GPS time by the network server over a network infrastructure, e.g., the Internet. A typical GPS receiver generates a onepulsepersecond (1PPS) time reference that can be compared and related with timeDiff circuitry to a 1PPS clock derived from each of the cellsite and cellphone cellulartelephony radio carriers. Other observation intervals besides one second would also work the same way, but the mathematics are simpler when a one second time interval is used.

[0473]
Embodiments of the present invention can use three different communication links to transfer time and frequency data. One links the GPS reference receivers 1024 with the network server 1014. A second carries softwareAPI or packetcommunication between the cellphone 1022 and GPS receiver 1020 in the cellphone, either directly in the cellphone or indirectly through the network server. Sharing data directly between the GPS receivers helps improve system performance. A third connection links the network server 1014 to both the cellphone 1022 and GPS receiver 1020.

[0474]
Timedifferenceofarrival measurements (TDOA), e.g., from a cellphone 1010 to a cellphone 1008, can be used for positioning inside a combined cellphone and GPS receiver to improve positioning availability and accuracy. Timestamps sent from the cellphone 1010 to the cellphone 1008 can be combined with a priori knowledge of the cellphone 1010 position, the cellphone 1010 clock bias and the cellsite 1006 drift from GPS time. Such timestamps can be used to transfer time information from the cellphone 1010 to the cellphone 1008 with an accuracy affected only by the radiosignal propagation distance between.

[0475]
The corrective frequency offset of the cellphone carrierfrequency synthesizer loop is again used here in this embodiment to estimate the GPS receiver frequency offset. Such estimate is used to reduce the frequency uncertainty and thus reduce the timetofirstfix, improve receiver sensitivity, and/or reduce the size and powerconsumption of the hardware. Digital numericcontrolled oscillator (NCO) and analog voltagecontrolled oscillator (VCO) are both commonly used in such carrierfrequency synthesizer loops.

[0476]
Any tempMeas measurement can be used to further improve the frequencytransfer accuracy passing from a cellphone to a GPS receiver, e.g., by building temperature models. The freqDiff observation can be used alone in frequency transfers without any timeDiff observation. The timeDiff observation can also be used without the freqdiff observation for combined time and frequency transfers. The time transfer accuracy is preferably improved by reducing the timeDiff hardware quantization noise with softwarebased filters. Cellphone observations of the cellphone 1010 frequency and phase can be used in dualmode positioning system alternative embodiments of the present invention.

[0477]
The term “passive synchronization” as used herein means the time and frequency offsets of the clocks in the cellphone 1010 and cellphone are only observed with respect to a GPS receiver clock. Calibrations are made later by sending the measured offsets through the communication layers, e.g., using transfer control protocol/Internet protocol (TCP/IP) packets on the Internet. The real clocks in the cellphone and cellphone 1010 are not controlled. The signals from these clocks are merely observed, and the corrective data obtained is not in any way fed back to the source to change the clocks. Rather, the data is used mathematically at the network server and in the GPS receiver software to assist in the GPSsatellite search and then in the position calculation.

[0478]
Although the present invention has been described in terms of the presently preferred embodiments, it is to be understood that the disclosure is not to be interpreted as limiting. Various alterations and modifications will no doubt become apparent to those skilled in the art after having read the above disclosure. Accordingly, it is intended that the appended claims be interpreted as covering all alterations and modifications as fall within the “true” spirit and scope of the invention.