US 3689926 A Abstract A method and apparatus for radio position-finding of the hyperbolic type to determine the position of a vehicle including intersecting signals of a radio position-finding hyperbole of one family with a radio position-finding hyperbole of another family, the hyperbole being derived from audio frequency direction-finding signals of predetermined phases, comparing the signals and correcting the differentials between the obtained signals.
Claims available in Description (OCR text may contain errors) iJnited States Patent fisne s i m [451 Sept. 5,1972 [54] RADIO DIRECTION-FINDING METHOD [56] References Cited AND A DEVICE FOR IMPLEMENTING SAID METHOD UNITED STATES PATENTS Inventors: Etienne ignfl Mahoney LS Emile Torcheaux, Paris, both of Franc Primary Examiner-Bemmmn A. Borchelt e Assistant ExaminerRichaId E. Berger [73] Assignee: Societe d,Etudes & Application des AttorneyWaters, ROdltl, Schwartz & Nlssen Techniques Nouvelles NEO-TEC Pan's, France ABSIRACT 22 d: If 3 1969 A method and apparatus for radio position finding of 1 16 J y the hyperbolic type to determine the position of a PP 838,943 vehicle including intersecting signals of a radio position-finding hyperbole of one family with a radio posi- [30] Foreign fl f P f' D tion-finding hyperbole of another family, the hyper- July 5, 1968 France ..'..1S8,01 1 being derived from auqio frequency direcfifms MA finding signals of predetermined phases, comparing U 8 Cl 343/105 R 235,150 272 343/105 H 11;: sigglsanglcorrecting the differentials between the 51 Int. Cl ..G0ls 1/30 tam [58] Fieldoi Search ..343/ 105 LS, 105 H; 39 Cl i 30 Drawing Figures PATENTEDSEP 5:912 3589-326 sum OlUF 12 PATENTEDSEP 5 m2 SHEET OEUF 12 Fig.4a AAAAAL AAAAA A A AAAA/27 AA A A AA AAA AAAAAA PATENTEDSEP 5 I972 SHEET OSUF 12 .mtmanw 5:912 3.689.926 SHEEI 014 OF 12 an Fl Fl Fl Fl R PATENTEDSE'P 51912 SHEET USUF 12 H mm h h m @E dvq a b PATENTEDSEP 51972 sum 08 0F 12 C INPUT CLOCK PATENTEDSEP smz sum user 1 PATENTEUSEP 51912 3.689.926 sum mar 12 Fig.17 PATENTEUSEP 5 m2 SHEET 11 [1F 12 PATENTEUSEP 5:912 SHEET 120F 12 CLOCK fiq. RADIO DIRECTION-FINDING METHOD AND A DEVICE FOR IMPLEMENTING SAID METHOD The present invention relates to a method of radio position-finding and to a device for implementing said method. Those skilled in the art will appreciate that radio position-finding is a technique of obtaining a navigational fix by means of which a vehicle, in particular a ship, can determine its position by means of radio signals received by the equipment which it carries. This method of obtaining a fix thus requires the installation of a transmitter system (fixed transmitters) for said signals, as well as the installation of a receiver system (receiver apparatus) on board the vehicle, the combination of the system of the transmitted signals and the positions of the respective transmitters being such that the receiver apparatus can deduce the position of the vehicle from the signals which it receives. In one known radio position-finding method, the phases of the received signals are employed in order to deduce the positional information (French Pat. No. 790,386). In the following, the term total phase of a sinusoidal signal varying with time tin accordance with the law A sin (211' ft where f is the frequency of the signal and s the phase at an instant of origin (t :0), will be used to designate the value I; (2mg The total phase can be split into any whole number of revolutions of Zn (whole phase) and into a fraction of 211 (partial phase): Total phase whole phase partial phase. In the case where e, 0, the partial phase is equal to the instantaneous phase (21rft t We shall also introduce the concept of total phaseshift between two sinusoidal signals of identical frequency; the total phase-shift will designate the difference between the total phases of the two signals considered from the same time origin. Similarly, the total phase-shift can be split into a whole part (multiple of 21:) and a fractional part (partial phase-shift). In French Pat. No. 790,386 hereinbefore cited, the system of electrical signals forming a transmission chain, is made up of two groups of three signals each. Each group comprises two high-frequency radio signals each produced by a different transmitter and having closely adjacent frequencies differing from one another by a value which corresponds to an audio frequency, and an HP radio frequency of different value, this being referred to as the reference frequency and being modulated by said audio frequency. These three signals are received on board the vehicle where they are processed in the receiver. In this receiver, the two first high-frequency radio signals are mixed in order to produce an audio frequency positionfinding signal, and the reference radio signal is demodulated in order to obtain an audio frequency I reference signal, the total phase-shift between the two audio signals being proportional to the difference between the distances from the vehicle to the two transmitters producing the two first high-frequency signals with the consequence that the location of the locus of the total phase-shift points associated with a group of signals is constituted by a hyperbola of which the two transmitters form the foci, the locus associated with the other group being a similar hyperbola; the point of intersection between these two hyperbolae thus defines the position of the vehicle. In one embodiment, the radio reference signal is produced by one of the two transmitters which furnish the first I-IF radio signals. The HF frequency of the position-finding signal produced by the other transmitter is thus termed the characteristic frequency. In this known technique, the total phase-shift between the audio frequency position-finding and reference signals is likewise proportional to the characteristic frequency in each of the groups of signals. Since this characteristic frequency is fairly high, the total phase-shift expressed in radians exceeds 2n and therefore comprises a whole part and a fractional part. However, those skilled in the art will appreciate that phase meters only indicate the partial phase-shift of course, that is to say the fractional part of the total phase-shift, so that there is a certain indeterminacy in the position of the vehicle; in other words, knowledge of the partial phase-shift does not simply define one hyperbola but rather a family of hyperbolae, the vehicle being located upon just one of them. Similarly, the other group of signals likewise produces another family of hyperbolae. The vehicle is thus located at one of the intersections between the hyperbolae of these families. In other words, there is ambiguity in the position of the vehicle. A channel corresponds to the distance between two successive hyperbolae of one and the same family between which the phase undergoes a shift of 211' and the width of such a channel is inversely proportional to the characteristic frequency of the family. This ambiguity can be overcome in a simple manner by providing, upon a chart depicting the position-finding zone, at least one point where the whole part of the total phase-shift is known through a direct determination. All that is necessary then is for the vehicle to pass through this point and for the navigator to record at that instant, on a counter, the known value of the whole part of the total phase-shift. This counter will then count from said instant, either counting up or counting off (adding or subtracting), the number of times that the partial phase-shift reaches the value 2n. The counter will therefore always record the real value of the whole part of the total phase-shift. This is referred to as coupled operation. This system means that the vehicle or vessel etc., must pass through a determinate point before it is possible to obtain a fix. Moreover, any accidental interruption in radio reception (transmitter or receiver breakdown) or fault in the operation of the counter, will falsify the recorded value so that it will be necessary to return to the known point. In practice, in order to overcome the ambiguity, a second family of hyperbolae is used, these hyperbolae having the same foci as the first and having a different characteristic frequency, that is to say channels of different width. Advantageously, said width will be slightly different from that of the first family of hyperbolae so that the pieces of information supplied by these two families of curves can be used in the same manner as a vernier. The result is that, by combination of the pieces of information which the two families of curves supply, a third family of curves can be defined the channels of which have a width proportional to the difference between the characteristic frequencies. It is true that this does not totally overcome the ambiguity, however the characteristic frequencies of the two first families of curves are so selected that the channels of the third family are sufficiently wide to make it possible by a measurement of another type (for example an astronomical sight) to position the vehicle definitely in a precise channel. Once this operation has been carried out, the pieces of information supplied by one of the first families of curves taken on its own, are used to obtain a fine measurement. In the prior art technique, gear mechanisms were employed to combine the pieces of information supplied by the two families. These mechanisms present two major drawbacks: their characteristic frequencies have to be in predetermined ratios and it is necessary to change sets of gears when it is required to operate within an area covered by families of different characteristic frequencies. As far as the first drawback is concerned, it is well known that the allocation of wavelengths in the high-frequency band is strictly controlled and it is becoming more and more difficult, so that it is now virtually out of the question to obtain the precise frequencies required. The present invention overcomes these drawbacks by providing a radio position-finding method in which the design of the device used to implement it, combined with the exploitation of purely electronic means, makes it possible to utilize any frequency and to achieve fully automatic exploitation of the system of pieces of information supplied by the radio positionfinding signals, thus enabling direct recording and display to be effected without any ambiguity in terms of the location of the vehicle. In order to provide a better understanding of how the invention may be put into effect, a description will now be given, in the form of non-limitative examples, of several embodiments of devices for implementing the method of the invention, said description relating to the attached drawings in which: FIG. 1 illustrates a transmitter system of the single signal kind; FIG. 2 illustrates a transmitter system of the twosignal kind, with a reference facility; FIG. 3 illustrates the block diagram of a receiver in accordance with the invention for receiving a single signal transmission; FIG. 4 illustrates a detail of part of the receiver of FIG. 3, and FIG. 4a illustrates the wave forms of the signals occurring in this part of the receiver; FIG. 5 illustrates the detail of another part of the receiver of FIG. 3; FIG. 6 illustrates the detail of a third part of the receiver of FIG. 3 and FIG. 6a and 6b illustrate the wave forms of the signals appearing in this part of the receiver, respectively in the case of a theoretical embodiment and in that of a practical embodiment; FIG. 7a to 7d illustrate the block diagram of a receiver in accordance with the invention, for receiving a two-signal transmission; FIGS. 3a to 8d and 9a to 9d show respective embodiments of a phase detector for producing k' k differences, with operation diagrams thereof; FIG. 10 illustrates a variant of the embodiments of FIGS. 8a and 9a; FIG. 11 illustrates a preferential embodiment of a unit; FIGS. 12a and 12b are respectively a detailed view of FIG. 11 and a corresponding operation diagram; FIG. 13 illustrates a simplified embodiment of a unit; FIGS. 14 and 15 illustrate variant embodiments of the device of FIG. 3; FIG. 16 illustrates the block diagram of a receiver of the two signal type; FIG. 17 illustrates an embodiment of receiver according to FIG. 3, comprising means for providing the velocity information; FIG. 18 illustrates a read-out device for the x quantity; and FIG. 19 illustrates an embodiment of a timing device for use in a receiver according to the invention. In the following, the invention will be explained in terms of two types of transmission: transmission using the single signal principle and transmission using the two-signal principle. The chief difference between these types of transmission resides in the fact that the audio frequency positionfinding signals obtained in the singlesignal system, are stable in frequency and phase which makes it possible to process them successively; however, in the case of the two-signal system, it is necessary to process the signals in pairs since they are unstable. In order to provide an explanation of these two types of transmission, we will consider the case in which a reference signal is being transmitted but it will be seen at a later point in this specification that the present invention is equally capable of handling the types of transmission referred to, without any necessity for a reference transmission. Transmission of the single signal" type, with a reference signal, FIG. 1. The transmitter arrangement corresponding to a group of signals, comprises three transmitters A, B and C. Transmitter A produces a high-frequency signal of frequency F,, modulated by a low-frequency reference signal f while transmitter B produces a high-frequency signal of frequency F 1 and transmitter C produces a high-frequency signal of frequency F 1 +f,,. The signals are received at a known fixed point D. At this point, the HF signal produced by A is demodulated in order to obtain an audio frequency for reference purpose, and the doublet system F F +f is mixed in order to obtain an audio frequency referred to as a position-finding signal. At D, the audio frequency reference and position-finding signals are compared with one another and as a result one of the transmitters B, C is controlled in order two keep said to audio frequency signals in phase. The result is that the frequency difference f, of the doublet system of high-frequency signals produced by the transmitters B and C, will always be strictly equal to the frequency f of the audio frequency signal modulating the high-frequency signal produced by A. If, in transmitter A, in order to create the audio frequency reference signal which is designed to modulate the carrier produced by A, a high-stability (for example 10') crystal is used, then the audio frequency reference signal and the audio frequency position-finding signal will both have the same frequency stability Transmission of the two signal type, with a reference signal, FIG. 2. In respect of each group of signals, likewise three transmitters A, B and C, are used. The transmitters B, C' produce a doublet of signals, of frequency F and F +fo, which is received at a known fixed location D close to A. The doublet F F, +f,, is mixed in order to obtain an audio frequency f which is transmitted to the transmitter A where it is employed to modulate an HF carrier of frequency F the audio frequency signal thus transmitted being the reference signal. It will be seen that in this fashion the audio frequency reference signal always has the same frequency f as the audio frequency position-finding signal, but the stability of this frequency 1, of the reference signal is poorer than in the case of the single signal system. If F is equal to 1.700 kHz and if high-stability crystals are used to generate the frequencies F 1 and F +f,,, then it will be seen that the variation in the frequency F, can amount to AF, F '10' 1.7 Hz. Thus, if F, can vary by 1.7 Hz and F f by the same amount in the opposite sense, it will be appreciated that the value f may vary by 3.4 Hz, which, assuming that f 80 Hz, corresponds to a stability factor in the order of 510- The generation of the instantaneous phase of the audio frequency position-finding and reference signals is thus not a regular function of time and the measurement of their phase-shift is pointless unless these two audio frequency signals are processed simultaneously. RECEPTION The vehicle M whose position is to be determined, . picks up the various signals transmitted and processes them in order to obtain the corresponding audio frequency position-finding and reference signals. In a general manner, at the location of the vehicle the instantaneous phase of an audio frequency signal transmitted in the above manner, can be written as 21rf t+ e where e k Kx in which k is a known coefficient having a value between 0 and 211- and representing the par tial value of the phase 6 at a fixed location where x 0; K is likewise a known coefficient representing the signal sensitivity factor, the sensitivity factor being the ratio of phase variation to distance or distance difference variation for each radio position-finding signal, and x is a quantity characterizing the position of the vehicle. Thus, using the type of transmission system which employs a reference signal, if a is the phase of the audio frequency reference signal and e 1 is the phase of the audio frequency position-finding signal, then we can put: (K,,= 0 for a reference) c k K, x Each of these phases can be determined only in terms of its partial value, that is to say somewhere between 0 and Zn; there is thus a certain undetermined factor. Moreover, the coefficients k cannot be determined except for a certain constant (this is in addition to the indeterminacy of the number of complete revolutions or cycles), because of the arbitrary choice of the time origin. The constant K, is proportional to the frequency F or F f}, in accordance with the transmission characteristics, as a detailed calculation will illustrate. It will be assumed that the coefficient K, corresponding to the audio frequency reference signal, has the value 0. In fact e will vary a little as the distance of the vehicle from the transmitter producing the reference signal varies, but this variation would have to reach a value of 3,750 km (in the case where f, Hz) in order for s to vary by 2rr. lt can therefore be assumed that in the geographical range envisaged, the phase of the reference signal does not vary, hence the term reference. Accordingly, the reference signal can be transmitted from any point, for example from one of the transmitters B or C (in other words, in the case of FIG. 1, A coincides with B or C), since its phase does not depend upon the location of the transmitter. If the reference signal is transmitted from B, then the characteristic frequency of the group will be that of the RF signal produced by transmitter C (F f0) and K will be proportional to F +f If the reference signal is transmitted from C, then the characteristic frequency of the group will be F In the case where the reference signal is transmitted from a point A, distinct from B and C, then the characteristic frequency of the group may be made equal to F 1 or F +f it being understood of course that one is then neglecting the variations in a difference between the correcting terms applied to k and k these terms respectively taking the form: Z'rrfD A/C for k, and for k since when x=0, D =D in which: D 0,, D represent the respective distances of the vehicle from the points A, B and C; c represents the velocity of light. By taking the difference 6,, 6 we obtain We know k k,, that is to say the partial phase-shift between the two audio frequency signals at the known fixed point hereinbefore defined. Calculation shows that x, with the exception of a constant, represents the difference in the distances between M and the two transmitters of the doublet system. The quantity x can be expressed in any desired unit and all that is necessary is that the element which records or displays it shall be able to do so in a manner which indicates its total possible variation. Its total possible variation is equivalent to its variation between the two transmitters of the doublet system. It will be seen that the phase difference e e, is constant when x is constant, that is to say that the phase difference is constant around a hyperbola having the two transmitters of the doublet as its foci. If s Q, is known, it is therefore possible to situate the vehicle on such a hyperbola; if there are three other signals available, transmitted by two other transmitters in order to establish another hyperbola, then the point of intersection between the two hyperbolae will represent the position of the vehicle. It will be observed, however, that a variation of 211' in the phase-shift e E1, due to a variation in x, leads us back to the same partial value for e, 6,. If the characteristic frequency of the group is 300 kHz, the variation in x which is produced by a variation of 211- in the quantity e 6 will correspond to a variation in the difference between the distances from the vehicle to the transmitters, of 1 km. As long as this difference between the distances varies by 1 km, therefore, the same value of partial phaseshift will be obtained. This means that there is ambiguity. In order to characterize this ambiguity, the concept of channel or lane is introduced, this being the space separating two hyperbolae and corresponding to said variation in the distances; the channel is characterized by its width on the base line between the antennas; in the case considered above, its width is 500 meters. In order to remove this ambiguity, a second group of three signals is employed; an HF signal modulated by an audio frequency signal f g, and two HF signals of frequency F and F 2 transmitted by the same transmitters. In the same way, we obtain x in all cases being defined in the manner used earlier, since the signals are transmitted by the same transmitters and the constant K being proportional to F (or F +12 so that we have: In this way, a new family of hyperbolae is established. For reasons associated with propagation and for technological reasons, the frequencies F and F, are in the same order of magnitude. F 2 is chosen to be close to F, in order to obtain a family of hyperbolae exhibiting channels of slightly different width to the width of the channels associated with the earlier family. For example, F is chosen at 310 kHz so that a channel corresponds to a variation of about 970 meters in x. By combining these two families, a new family is obtained in which the width of the channels corresponds to a variation of around 30 km in x. In other words, if we take the difference of the two phase-shifts: (e e e e known constant+ (K 1( 1: here, the sensitivity factor is K, K, and thus proportional to the difference F F, kHz) between the frequencies. This difference between the phase-shifts is itself a phase-shift and will not amount to a full revolution or cycle until x has undergone a variation of 30 km. There is still an ambiguity but this can be removed by a different measurement, for example by taking a sight with a sextant. It is possible to use still other, similar families in order to obtain intermediate sensitivity factors. In accordance with the present invention, the different signals are processed in a sequential manner. The result is two different types of variations depending upon whether the transmission is of the single signal" or two-signal type. Since it is purely the phase-shift e e, or s e, which provides any useful information (because it is only the difference k,,, k or k,,, k, which can be measured as a reference, given the arbitrary nature of the time origin used to define the k, values), it is not possible to receive and successively process the various audio frequency position-finding and reference signals on board the vehicle, unless the frequencies of these audio frequency signals are stable as in the case of the single signal system. On the other hand, in the case of the two-signal system, the apparatus processes simultaneously each pair of audio frequency position-finding and reference signals of one and the same group, in other words, it handles them as an inseparable pair; in other words, the k, values are then variables as a function of time and this means that the phase 6 of the signal taken on its own, conveys no sense. It is only the phase-shift between the two signals of the same pair when considered simultaneously, that conveys any sense since the coefficients k, of the two signals are rigidly linked with one another, In the twosignal case, therefore, it is exclusively the measurement of the phase-shift between the audio frequency position-finding and reference signals, which provides any useful information. The same kind of expression for this phase-shift will be used in the two-signal case, as is used to describe the phase of a signal in the single signal case. Thus the phaseshift between the audio frequency reference and position-finding signals of one and the same pair, can be written: where 6 represents the phase-shift at the vehicle, k the magnitude of this phase-shift at a known location and K the sensitivity factor of the group in question. In the single signal case, there is quite obviously an immediate simplification to be made due to the fact that the reference signals can be combined into one reference signal and, consequently, for all the groups transmitted by the same two transmitters, a single unique reference signal will be obtained: It is even possible to provide a single, unique reference signal in respect of a complete system, that is to say an arrangement providing at least two families of hyperbolae (in the broad sense of the term) having different foci, since the phase of the reference signal does not depend upon the unknowns 1:. It is important at this juncture to make a further general comment with relation to the reference signal. The examples which have been taken here have been of transmissions using a reference signal, however the present invention applies equally to the case where no such reference signal is used, instead the doublet signals alone. In this case, it is necessary to combine at least two audio frequency signals obtained from these doublet systems, in order to produce any useful information. In the following, two embodiments of a sequential receiver in accordance with the invention will be described in relation to the single signal and twosignal cases. audio frequency reference and position-finding signals, and delivers the latter in a determinate but arbitrarily selectable order, to the input 2 of a difference detector 3: memories d, 5 and 6 for coefficients k,,, k and k a memory 7 for a quantity x; a control unit 8 which supplies a local signal of the same audio frequency as the signals applied to the input 2, and which is applied to the second input 9 of the interval detector 3; and units Ill and 11 for producing a quantity y and a memory 12 for storing same. It will be assumed, for example, that a transmission is such that the three following audio frequency signals are received successively and in the order mentioned: the audio frequency reference signal of phase 6,, k, the first audio frequency position-finding signal of phase and characteristic frequency 6 k, k x; F, 300 kHz the second audio frequency positionfinding signal of phase and characteristic frequen- Cy 2=k2+K2x; F2: kHz. The processing of these signals is obviously a. periodic operation; the term sequence will be employed to designate the time interval devoted to the processing of each signal: each cycle of the receiving programme obviously contains a certain number of sequences and at least as many as there are signals to be processed. Let us assume, first of all, that the vehicle is at a standstill, so that x does not change. Stored in its memory 4, the receiver contains a coefficient k, representative 'of a phase. When the audio frequency reference signal is applied to the input 2 of the difference detector 3, the control unit applies to the other input 9 of said same detector a local reference signal of phase 4),, k, and frequency identical to the reference frequency (for example 80 l-lz). The difference detector 3 compares the phases of the audio frequency reference and local signals. If a phase difference 1b,, is detected, the latter is then used to more or less completely correct the value of k, stored in the memory 4. Then, during a new sequence in the next cycle, the control unit establishes a new local signal of phase (35,, which is equal to the corrected value of k',,, and this indeed until 111,,= 0, viz: in other words Similarly, when the first audio frequency positionfinding signal is applied to the input 2 of the difference detector 3, the control unit applies to the other input g of this detector a local signal of phase ii, k, K, x (k', being the coefficient which represents a phase and which is stored in the memory 5) and of the same frequency as the first audio frequency position-finding signal (e.g. 80 Hz). The difference detector 3 compares the phases of the audio frequency position-finding and local signals. If it determines a phase difference of 41 then the latter is used to more or less completely correct the value of k in the memory 5. Then, during a new sequence in the next cycle, the control unit will establish a new local signal on the basis of this corrected k value, and indeed until in other words The same procedure is gone through during each reception cycle, in respect of the second audio frequency position-finding signal, so that if k, is the coefficient representing a phase and stored in the memory 6, ultimately the following will result: We shall call 8,, the difference between the coefficient k stored in the store 4 and its real value k from which, when we have Similarly, we shall call 8 the difference between the coefficient k, stored in the store 5 and its real value k, In other words, the error made by storing k, instead of k provides us with information on the error made by storing x instead of x. This arises from the fact that the stored k, and x values are used to produce a local signal which is in phase with the audio frequency position-finding signal, and that an error in one of the elements affects the other element. Similarly, we shall use the symbol 6 to designate the difference k' k and, when we have The quantities 6, thus produce information on the difference x x. If one could know the values of these quantities 6 exactly, any one of them could be used in order to modify 1: in the desired position in order to completely cancel out the relevant 6, value and thus reduce the difference x x to 0, this operation being carried out with a factor of K However, the values of the 8, quantities cannot be completely known: on the one hand, the values of the quantities k, are known with the exception of a constant which is a function of the arbitrarily chosen time origin. The same applies to the quantities k, and, since it is not possible to have the same time origin at the transmitting and receiving ends of a system, the result is that the quantities 6 are known except for an unknown constant; on the other hand, since the coefficients k, and k, represent phases and are consequently located somewhere between 0 and 2n, the same applies to the 8, values. lll However, if the difference x x is substantial and if the coefficient K, has a high value, the product K, (x x) which is homogeneous at a phase and therefore at an angle, may be substantially greater than 2nand comprise a certain number of full revolutions so that the equation: should be written 8, fractional part of K, (x x' the term fractional part being intended to convey a fractional part of a revolution thus, if 8, is expressed in radians, a quantity between and Zn. It will not suffice, therefore, to reduce 6, to 0 in order to make x equal to x; this result is only obtained if the product K, (x x) is comprised within [-w, 1m in absolute value. In the general case, therefore, there is an ambiguity in the value of the unknown x. For all these reasons, it is impossible, at least within the framework of the single signal system, to directly employ the 8, quantities for reaction upon the x value. In order to eliminate the above difficulties, A, quantities are used which are obtained by the linear combination with whole number coefficients, of the 8, quantities: (1,, should be constituted by whole number integers'in order that the ambiguity in A, shall be no greater than that in 8. The coefficients should be simple ones (in most cases they will be equal to +1, 0 or l) in order not to excessively increase the value of the probable difference in the final result; they are fixed by design considerations. In addition, for a given A, value, the coefficients a should be selected in such fashion that the unknown constant affecting each 8, value is eliminated and that A, is known without any uncertainty than that of the whole number of 271' values (ambiguity). We then have: It appears, therefore, that if we know a top limit on the difference x x (x' being determined roughly by an astronomical sight for example), we can select the coefficients a,,, abiding by the conditions set out hereinbefore, so that 2,01,,K, (x-x') is always somewhere between 0 and 1r in absolute value. It will then be possible to employ the quantity A, in order to modify x in the position required to cancel out A, and, therefore, to cancel out the difference at x without any ambiguity. This operation is effected with a sensitivity factor 2, 01,, K, which is the weaker the larger the difference at x can be made; thus, a rough position for x will be obtained, making it possible to considerably reduce the value of the difference x x. The operation will be repeated by selecting other coefficients 01,, in order to improve the sensitivity factor 2, a,, K, and thus obtain a more accurate position for x. This procedure is continued until the probable difference of the result thus obtained for the value of x' has become uniform with the errors which are due to causes outside the process. In the light of the definition of the quantities 8,, the A, values can be regarded as linear combinations with whole number coefficients, of the k, values and, in practice, the quantities A, will be produced directly from the coefficients k,. These various points are illustrated in FIG. 3. In FIG. 3 a unit 10 has been illustrated, in which a quantity A, is generated such that The differences k, k, and k, k, are completely determined since a common time origin is taken for the k, values and likewise for the k, values (taking into account these differences, brings about the elimination of the unknown constants involved in the determination of the k, and k, values). In addition, it can be contrived that at transmission k, k, k, so that we obtain A1 k g k in other words A, represents the difference between the two coefficients k, and k, stored in the memories 5 and 6. A, is used to influence x in such a way as to reduce A, to zero and thus to cancel out the difference x x. Simultaneously, k, and k, are influenced in proportions such that the (,5, functions determined by the control, are not modified; in other words, it has been assumed that the vehicle is at a standstill (therefore 6, constants) so that at all times we have s, d), and therefore up, 0. Because of the fact that x tends towards x, the 8, quantities tend towards 0 or, in other words, the k, coefficients tend towards their real value k,. It will be seen that the sensitivity factor of this correction of x is (K, K,) this corresponding to correction channels having a width of 15 km (on the base line) starting from the hypothesis made earlier in which F, 300 kHz and F 310 kHz. It is sufficient, therefore, to have been able to determine x' in such a manner that x x' is less than 7.5 km, in order for the expression (K K,) (x x) always to be less than 1r in absolute value, and that, consequently, the above process makes it possible to determine a value of x which is substantially equivalent to x which value, although possibly not very accurate, is nevertheless not ambiguous. In order to improve the accuracy of this determination, in the unit 11 another combination of 8, values is produced, namely, A,= 8, 8,,=K, (x-x') since the condition 6= 0, i.e., K K is true or further it has been assumed that by fixed conditions at transmission so that we are left with In the same way as before, A will be employed to influence x in a way which tends to reduce A to zero and thus to more precisely cancel out the interval x x. At the same time, k, and k (although k is not involved in the definition of A will be influenced in proportions such that the operation of the control is not disturbed. In a general way, at the same that a A, quantity is employed to modify the value of x, it is used equally to modify the values of all the k, coefficients which correspond to K, coefficients which are other than 0, and this in proportions such that the operation of the control is not modified. The sensitivity factor of this new correction is K corresponding to channels having a width of 500 meters (on the base line) and always based on the hypothesis that F 300 kHz; the determination is thus a much more accurate one than the foregoing one. If required, the receiver may also be arranged to process other HF signals (for example F 350 kHz) enabling a third audio frequency position-finding signal to be produced and thus making it possible to obtain a quantity A ergo which would enable an intermediate mean sensitivity factor correction (K K to be effected, corresponding to channel widths freak of 3 km (on the base line). The above formulae are simplified by the fact that there is a reference signal, but it will be obvious that the same means could be employed in the case where no reference signal is transmitted, since the said formulae are general ones anyway. It will be abundantly clear from the foregoing description that no more than one A, value is used at any one time; the various A, values are operated successively. Thus far, it has been assumed that 1: does not change, but of course in practice the vehicle will be moving and therefore x will change and it is required that x shall follow the variations in x; it is therefore necessary to continue to efiect corrections of x by means of the finest A, quantity compatible with the speed of displacement of the vehicle. However, since the data are processed in a sequential manner, the corrections in question cannot be effected in a continuous way and x will vary in a discrete manner. In order to overcome this drawback, advantageously the system described hereinafter and illustrated in FIG. 3, will be used. The receiver comprises, additionally, a velocity memory or store 12, the content v of which represents in magnitude and sign the velocity of the variation in the unknown x, which variation is due to the movement of the vehicle. This velocity information is supplied to the store through the medium of the differences 11:, coming from the phase difference detector 3. For a given value of v, the store 12 produces a continuous variation in the content x of the store 7. It is obvious, of course, that the difference 41,, corresponding to the reference signal, cannot, since it is not due to a variation in x, affect the velocity memory 12. If the value v stored in the store 12 truly corresponds to the real velocity of the vehicle, then the variation in x will follow that in x and consequently the difference x x, and therefore the quantities 8, and A will' that corresponding to the highest sensitivity (A in the case of FIG. 3), in order to influence not x but the v value stored in the velocity store 12, this through the agency of the link 13. In other words, as soon as x' commences to diverge from x, the quantity A taken will adopt a value other than zero. It will then immediately influence the content of the velocity memory in the desired sense, so that x varies more rapidly or more slowly, as the case may be. The mode of operation of the receiver is as follows: By a previous determination (for example by taking an astronomical sight), a sufficiently close approximation to the value of x is obtained in order to position the vehicle in a channel corresponding to the coarsest sensitivity factor K K,. This estimated value is fed into the store 7 (quantity 1:). The receiver then receives the high-frequency signals, derives from them the audio frequency direction finding and reference signals, and stores the corresponding coefficients k',. Then, the A value corresponding to the coarse regulating function (A,) is produced and this is used to correct the estimated x value stored. Subsequently, the A value of the fine regulating system (A is employed to more accurately determine the x value thus produced, x then being furnished in the form of a number; a determinate and unambiguous hyperbola (the hyperbola on which the vehicle is located). During the whole of its correcting phase, the value v stored in the velocity memory is make 0. Subsequently, the differences #1, are used to determine said v value (velocity taken into account). In order to determine the other hyperbola (defined by the transmission of other HF signals by other transmitters), the intersection ofwhich with the first determines the position of the vehicle, it is of course possible to employ a second receiver identical to the one just described. However, because of the design of the receiver in accordance with this invention and of the sequential nature of the process employed, it is possible to effect dual exploitation of numerous of its elements in order to determine said second hyperbola. Amongst other things, it is quite sufficient to provide the receiver with supplementary stores for the coefficients k,, the value x and the velocity v which are characteristic of the second hyperbola. In particular when a reference signal is transmitted, since the coefficient k is independent of the unknown x, one and the same reference signal and thus the same k value stored in the store 4, can be used for the determination of the two hyperbolae. 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