US RE37256 E1 Abstract A GPS system and method for generating precise position determinations. The GPS system includes a ground based GPS reference system which receives with a reference receiver GPS signals and makes phase measurements for the carrier components of the GPS signals. The GPS reference system then generates and broadcasts an initialization signal having a carrier component and a data link signal having a data component. The data component of the data link signal contains data representing the phase measurements made by the reference receiver. The GPS system also includes a GPS mobile system which receives with a mobile position receiver the same GPS signals as were received by the reference system. In addition, the GPS position receiver receives the data link and initialization signals broadcast by the reference system. The GPS position receiver then makes phase measurements for the carrier components of the GPS signals during and after an initialization period and makes phase measurements for the initialization signal during the initialization period. In response to the phase measurements made by both the reference receiver and the position receiver during the initialization period, the position receiver generates initialization values representing resolution of the integer ambiguities of the received signals. In response to the initialization values and the phase measurements made by both the receivers after the initialization period, the position receiver generates precise position determinations to within centimeters of the exact location.
Claims(25) 1. A method of resolving integer wavelength ambiguities associated with phase measurements made for GPS carrier signals transmitted by GPS satellites, the method being used with an aircraft on a final approach trajectory to a runway, the method comprising the steps of:
positioning one or more pseudolites each at a fixed known location with respect to a reference coordinate system in front of the runway below the final approach trajectory of the aircraft;
with the one or more pseudolites, transmitting one or more pseudolite carrier signals;
with a mobile GPS receiver system mounted on the aircraft:
receiving the transmitted one or more pseudolite carrier signals and the transmitted GPS carrier signals;
making phase measurements for the received one or more pseudolite carrier signals and the received GPS carrier signals at measurement epochs while the aircraft is on the final approach trajectory, there being an integer wavelength ambiguity associated with the phase measurements made for each of the received GPS carrier signals;
determining directions to the GPS satellites with respect to the reference coordinate system at the measurement epochs; and
resolving the integer wavelength ambiguities in response to the phase measurements, the known location of each of the one or more pseudolites, and the determined lines of sight directions to the GPS satellites.
2. The method of claim
1 wherein:the final approach trajectory has an along track component;
the one or more pseudolites comprise two pseudolites further positioned in the positioning step on opposite sides of the along track component of the final approach trajectory.
3. The method of claim
1 wherein:each of the one or more pseudolite carrier signals is transmitted in the pseudolite carrier signal transmitting step as a low power signal bubble;
the phase measurements are made in the phase measurement making step while the aircraft flies through the one or more low power signal bubbles on the final approach trajectory.
4. The method of claim
3 wherein each of the one or more pseudolite carrier signals is transmitted in the transmitting step with a pseudo-random code signal as an L1 C/A GPS signal.5. The method of claim
1 wherein:the mobile receiver system comprises a top side antenna mounted on top of the aircraft and a bottom side antenna mounted on bottom of the aircraft;
the GPS carrier signals being received in the receiving step with the top side antenna;
the one or more pseudolite carrier signals being received in the receiving step with the bottom side antenna.
6. The method claim
1 wherein:the phase measurements are made in the phase measurement step during a period in which the aircraft flies over the one or more pseudolites on the final approach trajectory and a large angular change in geometry occurs between the mobile GPS receiver system and the one or more pseudolites;
the integer ambiguities are resolved in the resolving step with without searching through a set of potential solutions by batch processing of (A) the phase measurements, (B) the known location of each of the one or more pseudolites, and (C) the determined directions to the GPS satellites.
7. The method claim
6 wherein:the mobile GPS receiver has undetermined positions with respect to the reference coordinate system at the measurement epochs;
the integer wavelength ambiguities are resolved with the batch processing in the resolving step based on a set of simultaneous equations that relate (A) the phase measurements, (B) the known location of each of the one or more pseudolites, (C) the determined directions to the GPS satellites, (D) the integer wavelength ambiguities, and (E) the undetermined positions of the mobile GPS receiver system, the number of the measurement epochs and the pseudolite and GPS carrier signals being such that the set of simultaneous equations is overdetermined.
8. The method of claim
7 further comprising the step of:with the mobile GPS receiver system, computing initial guesses for the undetermined positions of the mobile GPS receiver system;
the set of simultaneous equations comprising a set of non-linear equations that are linearized so that the undetermined positions of the mobile GPS receiver system are represented as estimates and precise differences between the estimates and the undetermined positions;
the integer wavelength ambiguities being iteratively resolved with the batch processing in the resolving step by (A) resolving the integer wavelength ambiguities and computing the corrections precise differences in iterations based on the set of simultaneous equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a directly preceding one of the iterations adjusted by the precise differences computed in the directly preceding one of the iterations.
9. A method of resolving integer wavelength ambiguities associated with phase measurements made for GPS carrier signals transmitted by GPS satellites, the method comprising the steps of:
positioning one or more pseudolites each at a fixed known location with respect to a reference coordinate system;
with the one or more pseudolites, transmitting one or more pseudolite carrier signals;
with a mobile GPS receiver system:
receiving the transmitted one or more pseudolite carrier signals and the transmitted GPS carrier signals;
making phase measurements for the received one or more pseudolite carrier signals and the received GPS carrier signals at measurement epochs while a large angular change in geometry occurs between the mobile GPS receiver system and the one or more pseudolites, there being an integer wavelength ambiguity associated with the phase measurements made for each of the received GPS carrier signals;
determining directions to the GPS satellites with respect to the reference coordinate system at the measurement epochs; and
resolving the integer wavelength ambiguities in response to the phase measurements, the known location of each of the one or more pseudolites, and the determined lines of sights directions to the GPS satellites.
10. The method claim
9 wherein the integer ambiguities are resolved in the resolving step with without searching through a set of potential solutions by batch processing of (A) the phase measurements, (B) the known location of each of the one or more pseudolites, and (C) the determined directions to the GPS satellites.11. The method claim
10 wherein:the mobile GPS receiver has undetermined positions with respect to the reference coordinate system at the measurement epochs;
the integer wavelength ambiguities are resolved with the batch processing in the resolving step based on a set of simultaneous equations that relate (A) the phase measurements, (B) the known location of each of the one or more pseudolites, (C) the determined directions to the GPS satellites, (D) the integer wavelength ambiguities, and (E) the undetermined positions of the mobile GPS receiver system, the number of the measurement epochs and the pseudolite and GPS carrier signals being such that the set of simultaneous equations is overdetermined.
12. The method of claim
11 further comprising the step of:with the mobile GPS receiver system, computing initial guesses for the undetermined positions of the mobile GPS receiver system;
the set of simultaneous equations comprising a set of non-linear equations that are linearized so that the undetermined positions of the mobile GPS receiver system are represented as estimates and precise differences between the estimates and the undetermined positions;
the integer wavelength ambiguities being iteratively resolved with the batch processing in the resolving step by (A) resolving the integer wavelength ambiguities and computing the precise differences in iterations based on the set of simultaneous equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a directly preceding one of the iterations adjusted by the precise differences computed in the directly preceding one of the iterations.
13. The method of claim
9 wherein:the mobile GPS receiver system is mounted on an aircraft on a final approach trajectory to a runway; and
each of the one or more pseudolites is positioned in the positioning step in front of the runway below the final approach trajectory;
the phase measurements are made in the phase measurement step during a period in which the aircraft flies over the one or more pseudolites on the final approach trajectory and the large angular change in geometry occurs.
14. The method of claim
13 wherein:the final approach trajectory has an along track component;
the one or more pseudolites comprise two pseudolites further positioned in the positioning step on opposite sides of the along track component of the final approach trajectory.
15. A method of making position determinations for a mobile GPS receiver system mounted on an aircraft on a final approach trajectory to a runway, the method comprising the steps of:
positioning one or more pseudolites each at a fixed known location with respect to a reference coordinate system in front of the runway below the final approach trajectory of the aircraft;
with the one or more pseudolites, transmitting one or more pseudolite carrier signals;
with a GPS reference system:
receiving GPS carrier signals transmitted by GPS satellites at a fixed known reference location with respect to the reference coordinate system;
transmitting reference phase information associated with the GPS carrier signals received with the GPS reference system;
with the mobile GPS receiver system:
receiving the transmitted one or more pseudolite carrier signals, the transmitted GPS carrier signals, and the transmitted reference phase information;
making phase measurements for the one or more pseudolite carrier signals and the GPS carrier signals received with the mobile GPS receiver system at measurement epochs during an initialization period while the aircraft is on the final approach trajectory and making phase measurements for the GPS carrier signals received by the mobile GPS receiver system at measurement epochs after the initialization period while the aircraft is still on the final approach trajectory, there being an integer wavelength ambiguity associated with the phase measurements made for each of the GPS carrier signals;
determining directions to the GPS satellites with respect to the reference coordinate system at the measurement epochs during and after the initialization period;
resolving the integer wavelength ambiguities in response to (A) the phase measurements made at the measurement epochs during the initialization period, (B) the known location of each of the one or more pseudolites, (C) the reference phase information received during the initialization period, and (D) the determined directions to the GPS satellites at the measurement epochs during the initialization period; and
computing positions for the mobile GPS receiver system with respect to the reference coordinate system at the measurement epochs after the initialization period in response to (A) the resolved integer ambiguities, (B) the phase measurements made at the measurement epochs after the initialization period, (C) the reference phase information received after the initialization period, and (D) the determined lines of sight directions to the GPS satellites at the measurement epochs after the initialization period.
16. The method or claim
15 wherein the reference phase information is transmitted in the reference phase information transmitting step from a fixed different location than the known location of each of the one or more pseudolites so that the transmitted reference phase information is received with the mobile GPS receiver system during and after the initialization period while the aircraft is on the final approach trajectory.17. The method of claim
15 further comprising the step of:with the GPS reference system, making phase measurements for the GPS carrier signals received with the GPS reference system at the measurement epochs during and after the initialization period;
the reference phase information transmitted during and after the initialization period in the reference phase information transmitting step comprising the phase measurements made during and after the initialization period with the GPS reference system.
18. The method of claim
15 wherein:the final approach trajectory has an along track component;
the one or more pseudolites comprise two pseudolites further positioned in the positioning step on opposite sides of the along track component of the final approach trajectory.
19. The method of claim
15 wherein:each of the one or more pseudolite carrier signals is transmitted in the pseudolite carrier signal transmitting step as a low power signal bubble;
the phase measurements made in the phase measurement making step during the initialization period are made while the aircraft flies through the low power signal bubbles on the final approach trajectory.
20. The method of claim
19 wherein each of the one or more pseudolite carrier signals is transmitted in the transmitting step with a pseudo-random code signal as an L1 C/A GPS signal.21. The method of claim
15 wherein:the mobile receiver system comprises a top side antenna mounted on top of the aircraft and a bottom side antenna mounted on bottom of the aircraft;
the GPS carrier signals being received with the top side antenna in the receiving step with the mobile GPS receiver system;
the one or more pseudolite carrier signals being received with the bottom side antenna in the receiving step with the mobile GPS receiver system.
22. The method of claim
15 wherein the phase measurements made in the phase measurement step during the initialization period are made while the aircraft flies over the one or more pseudolites on the final approach trajectory and a large angular change in geometry occurs between the mobile GPS receiver system and the one or more pseudolites.23. The method of claim
22 wherein the integer ambiguities are resolved in the resolving step with without searching through a set of potential solutions by batch processing of (A) the phase measurements made at the measurement epochs during the initialization period, (B) the known location of each of the one or more pseudolites, (C) the reference phase information received during the initialization period, and (D) the determined directions to the GPS satellites at the measurement epochs during the initialization period.24. The method claim
23 wherein:the mobile GPS receiver has undetermined positions with respect to the reference coordinate system at the measurement epochs during the initialization period;
the integer wavelength ambiguities are resolved with the batch processing in the resolving step based on a set of simultaneous equations that relate (A) the phase measurements made at the measurement epochs during the initialization period, (B) the known location of each of the one or more pseudolites, (C) the reference phase information received during the initialization period, (D) the determined directions to the GPS satellites at the measurement epochs during the initialization, (E) the integer wavelength ambiguities, and (F) the undetermined positions of the mobile GPS receiver system at the measurement epochs during the initialization period, the number of the measurement epochs and the pseudolite and GPS carrier signals being such that the set of simultaneous equations is overdetermined.
25. The method of claim
24 further comprising the step of:with the mobile GPS receiver system, computing initial guesses for the undetermined positions of the mobile GPS receiver system;
the set of simultaneous equations comprising a set of non-linear equations that are linearized so that the undetermined positions of the mobile GPS receiver system are represented as estimates and precise differences between the estimates and the undetermined positions;
the integer wavelength ambiguities being iteratively resolved with the batch processing in the resolving step by (A) resolving the integer wavelength ambiguities and computing the corrections precise differences in iterations based on the set of simultaneous linearized non-linear equations, (B) in an initial one of the iterations, using the initial guesses as the estimates, and (C) in each subsequent one of the iterations, using as the estimates the estimates used in a directly preceding one of the iterations adjusted by the precise differences computed in the directly preceding one of the iterations.
Description This is a continuation, of application Ser. No. 08/410,011 filed Mar. 22, 1995, now abandoned, which is a continuation, of application Ser. No. 08/036,319 filed Mar. 24, 1993, now abandoned. The present invention relates generally to systems and methods for generating precise position determinations for any land, sea, air, or space vehicle. In particular, it pertains to aircraft landing systems and methods. There has traditionally been a need for systems and methods which allow a user to make extremely precise position determinations. In fact, a number of attempts have been made at developing these kinds of systems and methods. However, they all suffer from serious problems which render them unfeasible or inaccurate. This is particularly true in the case of aircraft landing systems and methods. The current system, the Instrument Landing System (ILS), was developed decades ago and is very expensive to install and maintain. A proposed alternative to ILS is the Microwave Landing System (MLS). It however is also expensive to install and maintain. Other proposed alternatives are based on the Global Positioning System (GPS). GPS involves a constellation of 24 satellites placed in orbit about the earth by the United States Department of Defense. Each satellite continuously broadcasts a GPS signal. This GPS signal contains an L-band carrier component (L The PRN code provides timing information for determining when the GPS signal was broadcast. The data component provides information such as the satellite's orbital position. The carrier component allows a receiver to easily acquire the GPS signal. Position determination using Conventional GPS is well known in the art. In Conventional GPS, a receiver makes ranging measurements between an antenna coupled to the receiver and each of at least four GPS satellites in view. The receiver makes these measurements from the timing information and the satellite orbital position information obtained from the PRN code and data components of each GPS signal received. By receiving four different GPS signals, the receiver can make fairly accurate position determinations. However, Conventional GPS only allows a user to determine his actual location to within tens of meters. In applications such as aircraft landings, position accuracies of one foot must be achieved. Therefore, conventional GPS is not suitable for these applications. A more accurate version of OPS is Ordinary Differential GPS. Position determination using Ordinary Differential GPS is also well known in the art. It involves the same kind of ranging measurements as are made with Conventional GPS, except that a ground reference receiver at a precisely known location is utilized. Ideally, satellite ranging errors will affect the position determinations made by the user's receiver in the same way as they will the position determinations made by the nearby ground receiver. Since the location of the ground receiver is already known, the ground receiver can compare the position determination it has calculated with the actual known position. As a result, the ground receiver can accurately detect ranging errors. From these errors, the ground receiver can compute suitable corrections which are transmitted by data link to the user's receiver. The user's receiver can then apply the corrections to its own ranging measurements so as to provide accurate real time position determinations. Also, a pseudolite (i.e. ground based pseudo satellite) can be used to transmit these error corrections along with an unassigned PRN code. The unassigned PRN code enables the user's receiver to make a redundant fifth ranging measurement for even greater precision. And, in some cases, it enables the user's receiver to make a necessary fourth ranging measurement where one of the other GPS signals has been lost. However, even with Ordinary Differential GPS, the position determinations are only accurate to within several meters. Since, as indicated earlier, aircraft landing systems must be accurate to within a foot, Ordinary Differential GPS by itself is not suitable for such an application. An extremely accurate form of GPS is Carrier Phase Differential GPS. This form of OPS utilizes the 1.575 GHz carrier component of the GPS signal on which the PRN code and the data component are superimposed. Carrier Phase Differential GPS involves generating position determinations based on the measured phase differences at two different antennas for the carrier component of a GPS signal. However, this technique initially requires determining how many integer wavelengths of the carrier component exist between the two antennas at a particular point in time. This is called integer ambiguity resolution. A number of approaches currently exist for integer ambiguity resolution. However, all of them suffer from serious problems which render them unfit for precise position determinations in applications such as a aircraft landing. One approach is Integer Searching using redundant measurements. This involves receiving more than the standard four GPS signals in order to sort out the correct combination of integer ambiguities. The different combinations of integer candidates are systematically checked against a cost function until an estimated correct set is found. However, for antenna separations of just a few meters, the checked combinations can number in the hundreds of millions. As a result, this approach has a propensity to arrive at wrong solutions. Furthermore, the configuration of the constellation of GPS satellites can only guarantee that four satellites will be in view at any given time. Therefore, any application requiring precise position determinations at any given time must not rely on redundant satellites for reliable resolution of the integer ambiguities. Another approach is Narrow Correlator Spacing. This technique involves using the PRN code of the GPS signal to bound the integer ambiguities. However, a significant amount of the time it can yield position determination errors of as much as several meters. This does not provide the kind of consistency which is required in aircraft landing applications. Still another approach is Dual Frequency Wide-Laning. This approach also utilizes a second GPS signal broadcast by each satellite. This second GPS signal has an L-band carrier component (L One successful approach to integer ambiguity resolution is motion-based and has been utilized in static surveying applications. This approach involves taking a number of phase measurements while the user's antenna and the reference antenna are stationary. These phase measurements are made over a period of about 15 minutes. The phase measurements made during the slowly changing geometry of the GPS satellites will reveal the integer ambiguities. But, in many situations in which precise position determinations are required, such as aircraft landing, it would be impractical to require the user's antenna to remain stationary for 15 minutes while the integer ambiguities are resolved. Another motion-based approach has been used for aircraft attitude determination. It involves placing an antenna on the tail, on the fuselage, and on each wing tip. The antenna on the fuselage serves as the reference antenna. The integer ambiguities can be resolved in seconds by rotating the aircraft and taking several phase measurements. Taking the phase measurements during this rapid change in geometry with respect to the slowly changing GPS satellite geometry will reveal the integer ambiguities. However, since the reference antenna and the other antennas are fixed to the aircraft, this approach is limited to attitude determinations and is not suitable for precise position determinations for the aircraft itself. It is an object of the invention to provide a complete GPS system and method for making precise position determinations to within centimeters of the exact location. It is another object of the invention to provide a mobile GPS system used in conjunction with a reference GPS system for making precise position determinations to within centimeters of the exact location. It is further an object of the invention to provide a reference GPS system used in conjunction with a mobile GPS system for making precise position determinations to within centimeters of the exact location. It is another object of the invention to provide a mobile GPS position receiver capable of making GPS position determinations to within centimeters of the exact location. It is another object of the invention to provide a mobile GPS receiver capable of precise GPS attitude determinations, coarse GPS position determinations to within meters for navigation, and precise GPS position determinations to within centimeters for landing. It is further an object of the invention to provide a ground based GPS reference transceiver capable of supplying a mobile GPS position receiver with the information necessary for making precise GPS position determinations to within centimeters of the exact location. The foregoing and other objects of the invention may generally be achieved by a GPS system and method which employs Carrier Phase Differential GPS. The system and method utilize a ground based reference GPS system and a mobile CPS system mounted on a moving vehicle. The elements of the reference system are stationary. They include a GPS reference receiver, an initialization pseudolite, a data link pseudolite, and a reference antenna. The data link pseudolite generates and broadcasts a data link signal in the form of a signal beam. This data link signal has at least a carrier component and data component. The initialization pseudolite generates and broadcasts an initialization signal in the form of a low power signal bubble. The initialization signal has at least a carrier component. The reference antenna receives GPS signals broadcast by GPS satellites and provides them to the reference receiver. The reference receiver makes phase measurements at periodic measurement epochs for the carrier components of the GPS signals and may do the same, depending on the configuration of the reference GPS system, for the carrier component of the initialization signal. Data representing these phase measurements is received by the data link pseudolite and broadcast to the mobile system via the data component of the data link signal. The elements of the mobile system are mounted on the moving vehicle and are therefore mobile. The mobile system includes a GPS position receiver and two antennas. The first antenna receives the same GPS signals as were received by the reference antenna. This is done both during and after an initialization period. The second antenna receives the initialization and data link signals broadcast by the two pseudolites during the initialization period. After the initialization period is over, the second antenna only receives the data link pseudolite signal. Each of the GPS signals received by the first antenna and the reference antenna has an integer ambiguity associated with these two antennas. The initialization period is used to resolve these integer ambiguities so that the mobile GPS position receiver can generate subsequent precise position determinations for the first antenna using Carrier Phase Differential GPS. During the initialization period, the GPS position receiver receives from the first antenna the CPS signals and from the second antenna the initialization and data link signals. While the moving vehicle is within the signal bubble and receives the initialization signal, there is a large angular change in geometry between the moving vehicle and the initialization pseudolite as the vehicle moves through the signal bubble. The mobile GPS position receiver makes and records phase measurements for the GPS signals and the initialization signal over this large angular change in geometry. These phase measurements are made at the same epochs as those made by the GPS reference receiver over this same change in geometry. Furthermore, the mobile GPS receiver receives via the data link signal the phase measurements made by the GPS reference receiver and records them. From the recorded phase measurements of both receivers, the GPS position receiver can accurately compute initialization values representing resolutions of the integer ambiguities of the GPS signals. Thus, the large angular change in geometry reveals the integer ambiguities. Once these initialization values have been computed, the initialization period is over and the moving vehicle will have left the signal bubble. The mobile GPS receiver can then compute precise positions for the first antenna at each measurement epoch to within centimeters of the exact location. This is done using the computed initialization values, the phase measurements for the GPS signals made by the mobile position receiver, and the phase measurements made by the GPS reference receiver provided to the GPS position receiver via the data link signal. The foregoing and other objects of the invention will become more apparent on reading the following detailed description and upon reference to the drawings, in which: FIG. 1 shows a general view of a GPS system which employs two initialization pseudolites in accordance with the invention; FIG. 2 shows a more detailed view of the GPS system shown in FIG. 1; FIG. 3 provides an illustration of how integer ambiguities at an initial epoch arise which are then resolved during an initialization period required for generating precise position determinations; FIG. 4 provides an illustration of the integer ambiguities at an epoch after the initial epoch; FIG. 5 shows the vector relationships associated with the integer ambiguities shown in FIGS. 3 and 4; FIG. 6 shows the vectors representing the surveyed positions of antennas which are mounted on an airplane with respect to the body coordinate system of the airplane; FIG. 7 shows the rotation of the body coordinate system of the airplane with respect to the runway coordinate system; FIG. 8 shows a general view of a GPS system employing a single initialization pseudolite in accordance with the invention; FIG. 9 illustrates elimination of cross track uncertainty by use of two initialization pseudolites; FIG. 10 illustrates elimination of cross track error by overlying a single initialization pseudolite twice; FIG. 11 provides an illustration of the vector relationships associated with the integer ambiguities which are resolved during an initialization period required for generating precise GPS attitude determinations; FIG. 12 shows rotation of the attitude antennas about a single axis of the runway coordinate system during the initialization period required for GPS attitude determinations; FIG. 13 shows a detailed description of a ground base GPS reference system which is part of the entire GPS system of FIG. FIG. 14 shows an alternative embodiment for the GPS reference system where pseudolite signals are received directly by a reference receiver from pseudolite signal generators; FIG. 15 shows another embodiment for the GPS reference system where the GPS reference receiver and the pseudolite signal generators share a common synthesizer; FIG. 16 shows yet another embodiment for the GPS reference system where the GPS reference receiver and the pseudolite signal generators are combined into a single GPS reference transceiver; FIG. 17 provides a detailed illustration of a portion of a GPS mobile system which is part of the entire GPS system of FIG. FIG. 18 provides a detailed illustration of another portion of the GPS mobile system including a GPS attitude receiver and several antennas; FIG. 19 shows another embodiment of the GPS mobile system where a single GPS receiver generates both position determinations and attitude determinations; FIG. 20 shows another embodiment of the GPS mobile system where an inertial measurement unit is employed; FIG. 21 shows another embodiment for the GPS mobile system where a single antenna and a single GPS position receiver are employed. FIGS. 1-21 provide illustrations of the invention described herein. In these figures, like components are designated by like numerals. FIG. 1 shows a general view of a GPS system FIG. 2 shows GPS system Located near runway The GPS signals The L The PRN code provides timing information enabling the position receiver The position receiver The computed phase difference represents the time it takes for the PRN code of the broadcasting GPS satellite The data component of each of the GPS signals The information in the data component of each GPS signal As indicated earlier, FIG. 1 shows airplane The initialization of position receiver FIG. 3 provides an illustration of how three integer ambiguities n GPS satellite Ranging link pseudolite Initialization pseudolite Both of the receivers As mentioned previously, antennas As shown in FIG. 3, the unknown range r The unknown range r The unknown integer components n FIG. 4 shows an epoch after the initial epoch. This second epoch could be during or after the initialization period. Each of the measurements Φ The relationship between Φ Equations (1) and (2) can be differenced so as to form the single difference phase relationship provided as follows in Equation (3): where n The relationship between Φ Equations (4) and (5) can be differenced so as to form the single difference phase relationship provided as follows in Equation (6): where n The relationship between Φ Equations (7) and (8) can be differenced so as to form the single difference phase relationship provided as follows in Equation (9): where n In order to make proper position determinations for airplane The position of reference antenna where t The position of top side antenna where x The position of bottom side antenna where y The known direction to GPS satellite where s The known position of pseudolite antenna where p The known position of pseudolite antenna where p The vector A The known position of bottom side antenna where k The attitude matrix A is known and can be determined from attitude solutions generated by attitude GPS receiver where each element of the matrix represents the rotation of a coordinate of the body coordinate system From the preceding vector relationships, the following mathematical relationships in Equations (20)-(25) may be established: Equation (20) can be combined with Equation (3) to establish the single difference phase relationship provided in Equation (26): Equations (21) and (22) can be combined with Equation (6) to establish the single difference phase relationship provided in Equation (27): Equations (23) and (24) can be combined with Equation (9) to establish the single difference phase relationship provided in Equation (28): In order to cancel out the clock synchronization errors ΔT where N Equations (29), (30), and (31) may then be linearized for each epoch to provide the following relationships in Equations (35), (36), and (37): where (A) the guess for the estimate x The relationship between the vectors x and x
Furthermore, the vector δx can be expressed as follows in Equation (39): where δx One method for computing the values N Where the ground system The phase measurements made by the receivers In the case where only one initialization pseudolite As was the case in the dual initialization pseudolite configuration, the phase measurements made by the receivers For greater accuracy, receiver Another way of adding accuracy to the computation of the unknowns associated with either configuration, is to utilize additional GPS satellites As a variation of the two configurations described earlier, pseudolite Most importantly, the computation of the unknown vector δx at each of the epochs employed in the initialization process and the computation of the unknown values N Once the values N In this method, receiver Another method for resolving the integer ambiguities involves making and recording phase velocity measurements at a number of epochs while airplane As in the earlier described method, the phase measurements and the phase velocity measurements are made over a number of epochs while airplane The phase velocity measurements are also made by receivers These phase velocity relationships are obtained by differentiating over time the Equations (9) and (26). These relationships are provided as follows in Equations (40) and (41): where (A) {dot over (Φ)} Since {circumflex over ({dot over (s)})} Since the relationship Δ{dot over (T)} Furthermore, the actual rate of change {dot over (r)}
where (A) {dot over (r)} Equation (42) can also be linearized to provide the following relationship in Equation (43): where (a) δx is the unknown constant vector representing the difference between the actual trajectory vector x and the estimated trajectory vector x The values δ{dot over (r)}, {dot over (r)} The calculation for δx is iteratively repeated until it converges to within a desired level. This is done by substituting the value of δx obtained in the previous iteration into Equation (37) and computing the vector x. This calculated vector x is then used as x Once δx is computed, the integer ambiguities n As with the previous method, receiver The fact that the integer ambiguities n Once the integer ambiguities n Receiver Once the precise position vector x is computed, the position vector y for the bottom antenna Furthermore, where pseudolite Still another built-in integrity check is the use of Ordinary Differential GPS position determinations by receiver In the single initialization pseudolite configuration of FIG. 8, airplane However, in most cases the initialization trajectory One way in which the cross track error can be reduced to within centimeters is to employ the configuration of FIG. 1 which utilizes two initialization pseudolites Another way of reducing the cross track error to within centimeters is to overfly the single initialization pseudolite With the first overflight, a first set of integer ambiguities n During the second overflight, the coarse initial guess for position vector x Another significant advantage to Carrier Phase Differential GPS position determinations is that the integer ambiguities n The same approach can be utilized for GPS signal The attitude matrix A is generated by receiver
where (A) r Receiver Differencing Equations (1) and (43) provides the single difference phase relationship given as follows in Equation (44):
where (A) n In order to resolve the integers ambiguities n The baseline vectors b where b The direction to GPS satellite where ŝ From the preceding vector relationships in Equations (45) and (46), the following mathematical relationship is provided in Equation (47): Combining Equation (47) with Equation (44) results in the following relationship in Equation (48): The integer ambiguities n The static method is similar to that used in surveying applications. After several epochs of measuring Φ In order to insure greater accuracy for the computed values, receiver Furthermore, receiver Additionally, where possible, phase measurements Φ The second approach to resolving the integer ambiguities n In FIG. 12, antennas where Δb The equations generated from Equation (49) at the initial and the second epoch can be subtracted to establish the following relationship in Equation (50): where ΔΦ The equations generated from Equation (50) may be stacked at a number of epochs after the initial epoch to solve for the vectors Δb The antennas However Equation (51) can also be mathematically expressed as follows in equation (52): Thus, the Equations (51) and (52) can be combined to form the following relationship in Equation (53): Equation (53) can be stacked by receiver For greater accuracy more than the minimum number of epochs needed to calculate the baseline vectors b Once these baseline values are computed, receiver Once the integer ambiguities have been resolved, the initialization process is over and attitude solutions for airplane FIG. 7 shows the vector relationships associated with antennas where k FIG. 8 shows the vector relationships associated with antennas where x From the preceding vector relationships in Equations (46) and (55), the following relationship is provided in Equation (56): Combining Equations (56) and (44) results in the following relationship in Equation (57): Since, as discussed earlier, the attitude matrix A represents the rotation of the body coordinate system Combining equation (58) with Equation (57) results in the following relationship provided by Equation (59): A complete attitude solution can be generated by receiver where w Starting with an assumed estimate A where δA [3×3] is an attitude correction matrix of small angle rotations. Thus, the attitude matrix A may be expressed as follows in Equation (62):
The correction matrix δA is expressed as follows in Equation (63):
where (A) I [3×3] is an identity matrix, and (B) Θ The unknown vector δΘ [3×1] can be expressed as follows in Equation (64): where δΘ The skew symmetric matrix Θ After combining Equations (62)-(65) with Equation (61), the attitude cost function can be expressed as follows in Equation (66): where the dot product of the matrix K The matrix K By minimizing Equation (66), the vector δΘ may be computed by receiver The estimate A from the previous iteration is used as the current solution A Another significant advantage to this approach is that the integer ambiguities n FIGS. 13-17 provide detailed illustrations of the elements of the ground system FIG. 13 shows the reference system Reference antenna Reference GPS receiver In this configuration, the signal receiving block The signal processing block Furthermore, with the signal processing control signals provided by the computer The computer The CPU The computer memory The signal processing routine The carrier phase measuring routine The PRN code phase measuring routine The carrier phase velocity measuring routine The routines The formatting routine The synthesizer The down converting signal is received by the signal receiving stage The clock signal is received by the signal processing stage Pseudolites The signal generators The computers The reference system data bases The data formatting routines The synthesizers The computers The PRN code generators The mixing stages The amplifiers In the dual initialization configuration of FIG. 1, the amplifiers In the preferred embodiment, the nominal altitude for a flight trajectory inside the signal bubbles In the single initialization pseudolite configuration of FIG. 8, the amplifier As was the case in the dual pseudolite configuration, in the preferred embodiment, the nominal altitude for a flight trajectory inside the signal bubbles In the dual initialization pseudolite configuration of FIG. 1, pseudolite antennas Pseudolite antennas As indicated earlier, pseudolite antenna Pseudolite antenna FIG. 14 shows another embodiment of the reference system In this embodiment, reference receiver Thus, in this embodiment the signal receiving block The signal receiving stage Furthermore, in this embodiment, the integer ambiguities n FIG. 15 shows still another embodiment of the reference system This connection replaces the oscillators Equations (5) and (8) in this configuration no longer include any clock synchronization errors. Unlike the case for the configurations of FIGS. 13 and 14, the Equations (5) and (8) are no longer required for cancelling out the clock synchronization errors ΔT This configuration has an advantage over the configuration of FIG. 13 in that the number of channels required by the signal processing block This configuration also has an advantage over the configuration of FIG. 14 in that it eliminates the three signal receiving stages FIG. 16 shows a variation of the embodiment in FIG. The computer memory In alternative arrangements to any of configurations in FIGS. 13-16, the pseudolite signals But, in order to minimize hardware costs by utilizing existing GPS receiver technology, signal generators FIGS. 17-21 provide detailed illustrations of the GPS mobile system FIG. 2 shows one embodiment of mobile system FIG. 17 provides a more detailed illustration of part of the configuration of FIG. The antenna The antenna GPS position receiver In this configuration, the signal receiving block The signal processing block The computer The CPU The computer memory The signal processing routine The carrier phase measuring routine The PRN code phase measuring routine The Carrier phase velocity measuring routine The routines The coarse position generating routine The accurate position generating routine The unit directional vector computation routine The initialization routine The routine Then, routine The initialization routine The routine Then, routine Next, routine Routine The guesses {dot over (r)} Then, routine The precise position generating routine The precise position routine The integer hand-off routine The synthesizer The clock signal generated by the synthesizer FIG. 18 provides another detailed illustration of part of the mobile system Antennas The GPS attitude receiver GPS receiver In this configuration, the signal receiving block The signal processing block The computer The CPU The computer memory The signal processing routine The carrier phase measuring routine The routine The unit directional vector computation routine The static attitude initialization routine The motion based attitude initialization routine First, routine Routine Once the baseline vectors b The attitude determination routine First, routine Routine The routine Routine The routine The routine The routine The integer hand-off routine The synthesizer The clock signal generated by the synthesizer FIG. 19 shows an alternative embodiment for the airborne components of system Receiver Thus, in this embodiment the signal receiving block The signal receiving stages Furthermore, computer memory FIG. 20 shows another embodiment for the airborne components of system In one embodiment, the IMU FIG. 21 shows another embodiment for the airborne components of system Thus, in this embodiment the signal receiving block The signal receiving stage The computer Many of the individual elements of the components of system Specifically, the GPS antennas The signal receiving stages The reference oscillators Although these figures and the accompanying description are provided in relation to an airplane, one skilled in the art would readily understand that the invention is applicable to Carrier Phase Differential Position determinations for any land, sea, air, or space vehicle. Furthermore, while the present invention has been described with reference to a few specific embodiments, the description is illustrative of the invention and is not to be construed as limiting the invention. Indeed, various modifications may occur to those skilled in the art without departing from the true spirit and scope of the invention as defined by the appended claims. Patent Citations
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