GNSS positioning method and system

Abstract

The invention relates to a GNSS relative differential positioning method for positioning a mobile antenna with respect to a reference antenna by computing phase differences between the signals received by these two antennas and originating from a plurality of satellites, comprising: processing the digitized signal (Src1) received by the reference antenna in a first loop (10) and processing the digitized signal (Src2) received by the mobile antenna in a second loop (20), each of the loops being subjected to the signal from frequency demodulation, code-demultiplexing, correlation and discriminant-computing operations, the first loop estimating the phase of the signal used to adjust the carrier frequency in the frequency demodulation for each of the loops, the second loop computing the phase difference between the two signals; and estimating the position of the mobile antenna based on the computed phase difference.

Description

[0001]Description Title: GNSS positioning method and system Technical field The present invention relates to the field of GNSS positioning (Global Navigation Satellite System), and more particularly relates to GNSS relative differential positioning. Prior art A GNSS positioning system locates a user on the ground from signals emitted by a constellation of satellites and a receiver which receives and processes them. The navigation satellites which constitute the GNSS positioning system ensure global coverage at any time. Differential GNSS positioning consists of positioning an antenna, called a "rover", relative to a reference antenna, called a "base". The GNSS receiver of the reference antenna sends corrections over the air to the receiver of the antenna to be positioned. The accuracy of an autonomous GNSS receiver is of the order of a meter,because it calculates alone the positions of the satellites and the various signal corrections such as those linked for example to propagation in the ionosphere and the troposphere. Differential GNSS positioning systems improve the accuracy and robustness of positioning. A GNSS receiver provides a satellite-receiver pseudo-distance from the phase measurements of the GNSS signal carrier. This pseudo-distance measurement by the phase is ambiguous and is affected by different biases. The ambiguity of the measurement is the satellite-receiver distance at the time of switching on the receiver. Indeed, the receiver provides the variation of the pseudo-distance since its start-up. In addition, the signal is affected by several biases which are linked to the synchronization of the receiver clock with UTC time, the synchronization of the satellite clocks with UTC time, the propagation of the signal in the atmosphere,and satellite positioning error. Many methods have been proposed for resolving phase ambiguity, and this topic is still relevant, especially for real-time dynamic positioning. Among these methods, we can cite the RTK technique (Real Time Kinematic) or real-time kinematic, described for example in the publications Haiyang Li et al. “A novel partial ambiguity method for multi-GNSS Real-Time Kinematic positioning” and C.M. Silva et al. “GNSS ambiguity resolution with ratio and fixed failure ratio tests for long baseline network RTK under ionospheric activity”. To correct the receiver synchronization error with UTC time, the RTK method uses the double phase difference in real time. Indeed, in this approach,The reference receiver and the receiver to be positioned calculate the difference in the pseudo-distance differences obtained for two visible satellites. The accuracy obtained by this positioning mode is of the order of a centimeter, but depends on many factors such as the baseline, the number of satellites used and their geometric configuration. As in deferred time, it is necessary to go through the step of initializing the integer ambiguities. In real time, this initialization is carried out using the AROF (Ambiguity Resolution On the Fly) method described for example in the publication Erwin Frei et al. “Ambiguity Resolution On the Fly (AROF); results, facts, limitations”. This method is based on fast ambiguity resolution algorithms that use at least five satellites. Finally, the RTK technique can be used with baselines up to 10 km, but beyond,ambiguity resolution becomes much more complicated. Another approach to resolving phase ambiguity is the PPP technique (Precise Point Positioning) described for example in the publications Zumberge James et al. “Precise Point Positioning for the Efficient And Robust Analysis of GPS Data from Large Networks” and Jianghui Geng et al. “Integer ambiguity resolution in Precise Point Positioning: method comparison”. The principle of the PPP technique is to position a receiver that is connected to the internet and continuously receives precise positions and clock corrections from the satellites. The receiver connected to the internet calculates its position (the position of its antenna), the difference in synchronization time of the receiver with UTC time and the phase ambiguity of the pseudo-range measurements. Originally, the PPP technique is a positioning technique carried out on delayed phase measurements. It has been demonstrated,as an example in the aforementioned Zumberge James publication, that it is possible to achieve accuracies equivalent to those obtained with a differential technique for an observation time of several hours. Subsequently, thanks to the provision, on the internet, by the IGS ("International GNSS Service" in English) of satellite orbits and very precise clock information,The PPP technique has become usable in kinematic mode and in near real time with centimeter accuracy. Positioning by the PPP technique is done for a dual-frequency receiver with a precise estimation of orbit and satellite clock from the IGS. The dual frequency on the receiver represents an advantage in that it allows to correct for ionospheric effects. This positioning method uses ambiguous phase measurements from the receiver instead of those from the reference station as in the RTK technique. Also, in the case of the PPP technique, no difference of measurement is made. Thus, the errors that are eliminated by single or double difference are estimated by the use of adapted models and processing. This leads to a floating resolution of ambiguities (fixing ambiguities to real values). The aforementioned Jianghui Geng publications,Maorong Ge et al. “Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations” and Laurichesse Denis et al. “Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination” propose various methods for correcting real ambiguities. More recently, several integer ambiguity resolution techniques integrated with the PPP technique have emerged. This is called Integer PPP (IPPP), as described in the aforementioned Laurichesse Denis publication, which improves positioning accuracy and reduces the convergence time to the estimated position. Finally, the PPP technique can be used anywhere in the world and does not require a reference station. Therefore, no problems related to, for example, the stability of base stations or their georeferencing arise. However,This technique requires a long initialization period for the estimation of ambiguities (as demonstrated in the thesis Junbo Shi. Precise Point Positioning integer ambiguity resolution with decoupled clocks), essential to obtain a positioning of the order of the centimeter. In each of the RTK and PPP approaches, the horizontal positioning is obtained with centimeter precision. The height is obtained with decimeter precision. For these accuracies, the highest measurement frequency announced by the manufacturers is of the order of 10 Hz. In practice, this precision is observed for a measurement frequency of 1 Hz and at least 1 hour of observation of the signal. Millimeter precision is obtained after several hours of measurements. Indeed, the processing carried out by the receiver, which estimates the ambiguity of the phase measurements and filters the signals,lead to a temporal correlation of positioning errors. This correlation increases the integration time required to improve positioning accuracy. In classical phase-differential approaches, double-difference measurements are used to calculate the absolute position of the antenna. The double difference has the effect of amplifying the noise power and reducing the number of observations, because for each observation, two satellites are required. These two drawbacks, along with the calculation of ambiguity for each satellite pair, limit the positioning accuracy of current receivers. In the article Daniel Macias-Valadez et al. “Improving vertical GPS precision with a GPS-over-fiber architecture and real-time relative delay calibration”,optical fiber is used to connect the antennas. An automatic calibration method is used to calculate the delays brought by the fibers. The antenna signals are processed by a single receiver with two inputs. The classic simple difference method is used to calculate the position of the antenna. First, the evolution of the phase unfolded in cycles (ambiguity resolution, to the second) is estimated for the two signals, then the difference between these two signals is calculated. Presentation of the invention There is therefore a need to improve existing techniques, particularly in terms of positioning accuracy and acquisition time to obtain the desired accuracy. Positioning method The invention aims to meet this objective and has as its object, according to one of its aspects,a GNSS relative differential positioning method for positioning a mobile antenna relative to a reference antenna (different from the mobile antenna) by calculating the phase differences between the signals received by these two respective antennas and coming from a plurality of GNSS satellites, each of the signals having a code delay and a carrier frequency, the method comprising: - digitizing these signals; - processing the digitized signal received by the reference antenna in a first code and phase tracking loop and processing the digitized signal received by the mobile antenna in a second code and phase tracking loop, each of the loops subjecting the signal to frequency demodulation, code demultiplexing, correlation and discriminant(s) calculation operations, to estimate the code delay of the signal,the first loop estimating the phase of the signal used to adjust the carrier frequency in the frequency demodulation for each of the loops, the second loop calculating the phase difference Ψ between the two signals at each measurement cycle; and - the estimation of the position of the mobile antenna, in particular by maximum likelihood, from the phase difference Ψ thus calculated. The reference antenna is not necessarily a fixed antenna. In the case where it is mobile, its speed of movement is sufficiently low not to introduce an unacceptable error in relation to the desired precision, and preferably an error less than or equal to 1 millimeter. The term "mobile antenna" should be understood to mean an antenna whose position relative to the reference antenna can vary, continuously or not. A measurement cycle, corresponding to a code duration,is the time required to obtain information allowing the phase difference to be calculated. It can be around 1 ms, depending on the type of code. In the rest of the text, the notation .̂ represents an estimated value. Preferably, before estimating the position of the mobile antenna, phase difference values ​​Ψ are accumulated over several measurement cycles, in particular over at least 9 measurement cycles, to improve the accuracy of the antenna position estimation. The advantage is to be able to achieve the desired precision, in particular millimeter measurement precision. The invention makes it possible to obtain greater precision and a higher frequency of measurements (close to 100 Hz) than existing positioning methods. Indeed, thanks to the invention, millimeter precision is obtained for positioning. An underlying advantage of precise positioning is obtaining high-frequency measurements. In fact,the more precise the measurement, the higher the measurement frequency must be to be able to observe the millimeter evolution of the processes. The positioning accuracy and the measurement frequency are improved by a factor of 10 compared to the performance announced by the manufacturers. In addition, the performance of the method according to the invention has been defined theoretically and the positioning results obtained on real data are in agreement with the theoretical results. The method according to the invention is simpler than the classic differential methods, because it does not require calculating the phase ambiguity and the synchronization of the receiver with UTC time. In the present invention, the simple phase difference is used which makes it possible to correct the biases in the pseudo-distance measurement which are linked to propagation in the atmosphere,to the synchronization of satellite clocks with UTC time and the satellite positioning error bias. In addition, the hardware implementation of the system according to the invention makes it possible to synchronize the digitization of the signals coming from the two antennas. In this case, the simple phase difference also makes it possible to remove the error bias linked to the synchronization of the receiver with UTC time. The phase differences Ψ associated with each satellite preferentially depend on the North components N, A2 and East E A2 of the distance on the ground between the two antennas in a Lambert I projection cartographic reference frame and of the height h between them by the multiple circular linear evolution relation: k being a relative integer, λ being the wavelength of a GNSS signal, ^ being the elevation angle of the corresponding satellite seen by the reference antenna, ^ ^being the azimuth angle of this satellite seen by the reference antenna and ^ ! being a measurement noise, notably distributed according to the normal circular distribution. Thus, the estimation of the position of the mobile antenna could include a step of determining the North N components A2 and East E A2of the distance on the ground between the two antennas in a Lambert I projection cartographic reference frame and of the height h, for example from the multiple circular linear evolution relationship. The fact that the phase is observed modulo 2π makes it possible to remove the entire ambiguity. Preferably, the method according to the invention comprises, prior to the digitization of the signals, the introduction of a delay in the signal received by one of the antennas with respect to the signal received by the other antenna, via a delay line, the delay being sufficient so that the correlation functions of these signals are not superimposed. Preferably, the method according to the invention comprises the sum of the delayed signal and the undelayed signal and the digitization of the resulting signal via a single digitizer, in particular a single-channel digitizer.Thus, the method according to the invention is more economical than conventional differential methods, because it requires only a single receiver and no radio link. Furthermore, the method according to the invention is more general than conventional differential methods, because it makes it possible to estimate the position of several antennas relative to the reference antenna. Indeed, several delay lines of different distances can be used to separate the signals coming from several antennas. These signals can then be added and digitized by a single-input receiver. In one embodiment, the method according to the invention comprises the conversion of the signals received by the antennas into optical signals via photomodulators, the delay line being made of optical fiber.The method according to the invention may comprise the independent acquisition of the digitized delayed signal and the non-delayed signal, by generating for each of these signals a local replicated signal to be correlated with the associated signal to estimate the code delay of this signal and its carrier frequency and to identify the corresponding satellite, the correlation with the replicated signal being in particular calculated for several frequencies of the replicated signal. The frequency demodulation in each loop preferably comprises the multiplication of the signal by two carrier frequencies in phase quadrature obtained from a carrier frequency generator and a phase shifter, this generator initially using the carrier frequency estimated in the acquisition step then adjusting the frequency at its output by the phase estimated by the first loop.The code demultiplexing in each loop preferably comprises the multiplication of the demodulated signal by three C / A codes different by their offsets, namely a code synchronous with the demodulated signal, a code advanced with respect to the demodulated signal by an offset of d / 2 and a code delayed with respect to the demodulated signal by an offset of - d / 2, d being the offset between the advanced code and the delayed code, these codes being obtained from a code generator, this generator of each loop adjusting the three C / A codes at its output by the code delay estimated by the loop. Preferably, the correlation in each loop comprises the integration of the demultiplexed signal to produce two correlation functions (also called components) I and Q. The first loop may comprise a code discriminant and a phase discriminant respectively calculating the difference in code delays Δ". # and the phase difference Δ$ # as follows: where the function D is a coherent code discriminant, the phase estimated by the first loop and "' # the estimated code delay per first loop; and Δ$ = arctan Note that the quantities in parentheses in the expression for component I are the quantities on which this component depends. An example of a coherent discriminant is the difference function. In one embodiment, the difference in code delays Δ" # and the phase difference Δ$ #at the output of the discriminants of the first loop are each integrated to give respectively the estimated code delay and the estimated phase. The phase and the code delay estimated by the first loop can be used to decode the navigation message of the signal received by the reference antenna to date this signal in order to associate the elevation and azimuth angles of the satellites with the calculations of phase differences Ψ. The second loop can comprise a code discriminant and a phase discriminant respectively calculating the difference in code delays Δ" ^ and the phase difference Ψ as follows: Δ" ^ = D (89"' ^ , $ * # :, %9"' ^ , $ * # :), where the function D is a discriminant of inconsistent code, $ * # the phase estimated by the first loop and "' ^ the code delay estimated by the second loop; Ψ = $ ^ - $ # + ^′ ! , where $^ is the phase of the signal received by the mobile antenna, $ # is the phase of the signal received by the reference antenna, ^′ ! noise resulting from the calculation of Ψ and the estimation of $ # An example of an inconsistent discriminant is Early-Late Power: E being the early C / A code and L the late C / A code. The difference in code delays Δ" ^at the output of the code discriminant of the second loop can be integrated to give the estimated code delay. Positioning system The invention also relates, according to another of its aspects, to a GNSS relative differential positioning system comprising a receiver connected to a reference antenna and a mobile antenna, for positioning the mobile antenna relative to the reference antenna by calculating the phase differences Ψ between the signals received by these two antennas and coming from a plurality of GNSS satellites, each of the signals having a code delay and a carrier frequency, the receiver comprising: - a single digitizer, in particular a single-channel digitizer, for digitizing the signals; - a digital processing module, comprising: -- two code and phase tracking loops, a first loop configured to process the signal received by the reference antenna and a second loop configured to process the signal received by the antennamobile antenna, each of the loops comprising a frequency demodulator, a code demultiplexer, a correlator and at least one discriminant calculator, for estimating the code delay of the signal, the first loop being configured to estimate the phase of the signal used to adjust the carrier frequency in the frequency demodulator for each of the loops, the second loop being configured to calculate the phase difference Ψ between the two signals at each measurement cycle; and -- an estimator of the position of the mobile antenna, in particular by maximum likelihood, from the phase difference Ψ thus calculated. Preferably, the system is configured to accumulate, before estimating the position of the mobile antenna, in particular over at least 9 measurement cycles, phase difference values ​​Ψ to improve the accuracy of the estimation of the position of the antenna. The system preferably comprises, upstream of the digitizer, a delay line configured todelay the signal received by one of the antennas relative to the signal received by the other antenna so that the correlation functions of these signals are not superimposed. In one embodiment, the system comprises a sub-module for acquiring the digitized delayed signal and the non-delayed signal, configured to generate for each of these signals a local replicated signal to be correlated with the associated signal to estimate the code delay of this signal and its carrier frequency and to identify the corresponding satellite. Preferably, the frequency demodulator comprises: - a carrier frequency generator, this generator being configured to initially use the carrier frequency of the signal received by the reference antenna estimated by the acquisition sub-module and then adjust the frequency at its output by the phase estimated by the first loop; - a phase shifter configured to introduce a phase shift of ^ / 2 to the generated carrier; and - two multipliers configured tomultiply the input signal by the two carriers in phase quadrature. Preferably, the demultiplexer comprises: - a code generator configured to generate three C / A codes different by their offsets, namely a code synchronous with the demodulated signal, a code advanced with respect to the demodulated signal by an offset of d / 2 and a code delayed with respect to the demodulated signal by an offset of -d / 2, d being the offset between the advanced code and the delayed code, the code generator being configured to adjust the three C / A codes at its output by the code delay estimated by the loop; - two multipliers configured to multiply each of the components in phase quadrature of the demodulated signal by the three codes at the output of the code generator. Brief description of the drawings The invention may be better understood by reading the detailed description which follows, of non-limiting examples of implementation thereof, and by examining the appended drawing, in which: [Fig 1] TheFigure 1 is a 3D geometric view of a system comprising a reference antenna, a mobile antenna and a GNSS satellite in different reference frames; [Fig 2] Figure 2 represents: (a) a partial view of Figure 1 and (b) a top view of Figure 1 in two dimensions; [Fig 3] Figure 3 is a block diagram of an example of an analog processing module of a system according to the invention; [Fig 4] Figure 4 is a block diagram of an example of a digital processing module of a system according to the invention; [Fig 5] Figure 5 schematically represents an example of an acquisition sub-module of a system according to the invention; [Fig 6] Figure 6 schematically illustrates an example of two code and phase tracking loops forming part of a system according to the invention; [Fig 7] Figure 7 schematically represents an example of a code generator forming part of a system according to the invention; [Fig 8] Figure 8 represents the evolution curve of thephase difference between two signals received by the reference antenna and the mobile antenna, for each visible satellite, as well as the curve of its noise-free theoretical model; [Fig 9] Figure 9 represents the correlation function of a composite signal obtained after introducing a delay; [Fig 10] Figure 10 represents the curves of the square root of the CRLB (Cramér-Rao Lower Bounds) and the standard deviation of estimation as a function of κ, the measurement noise concentration parameter, (a) in the case of a single satellite and (b) in the case of the fusion of measurements obtained by two satellites; [Fig 11] Figure 11 represents the curves of the square root of the CRLB for different variations of the azimuth and elevation evolution, (a) in the case of a variation of the azimuth, and (b) in the case of a variation of the elevation; [Fig 12] Figure 12 schematically illustrates the position of the sensors (satellites) on the unit sphere: in solid bold line V Az = 2π and V θ= π / 2, in broken line ---- V Az = 0 and V θ = π / 2, in broken line -.-.- V Az = 2π and V θ = 0; [Fig 13] Figure 13 schematically represents an example of an experimental device for a system according to the invention, positioned on a roof; [Fig 14] Figure 14 represents the estimation curves of the three components of the position (NA2, EA2, h) for 20 s; and [Fig 15] Figure 15 schematically illustrates the estimation deviations of the parameters NA2 and EA2. Detailed description Figure 1 is a 3D geometric view of a system comprising a reference antenna A1, a mobile antenna A2 and a GNSS satellite S in different reference frames. Figure 2 represents: (a) a partial view of Figure 1 and (b) a top view of Figure 1 in two dimensions. Antenna A2 is placed in a plane P2 parallel to the ground represented by a plane P1. Antenna A1 is placed at a height h from antenna A2. Both antennas receive GNSS signals Sr1 and Sr2 arrivingof satellite S and are connected to a GNSS receiver (not shown in Figure 1) where signal processing is performed. The elevation and azimuth angles for satellite S are denoted θ and Az respectively. Figure 1 shows the path difference δ between signals Sr1 and Sr2. Point B is the orthogonal projection of antenna A2 on the line which represents the signal trajectory from satellite S to antenna A1. The distance between A1 and B is the path difference δ. It is shown later that this path difference can be observed with the phase difference between signals Sr1 and Sr2. Three map markers are considered in this representation. The (O, E, N, z) coordinate system is the reference coordinate system that positions the different elements in the Lambert I cartographic coordinate system. The (O, x, y, z) coordinate system is defined such that the vertical plane (O, x, z) contains the position of the two antennas marked A1 and A2. The (O, X, Y, z) coordinate systemis defined such that the vertical plane (O, X, z) contains the antenna A1 and the satellite S. Γ is the rotation angle around the axis (O, z) between the coordinate systems (O, x, y, z) and (O, X, Y, z). Γ′ is the rotation angle around the axis (O, z) between the coordinate systems (O, E, N, z) and (O, x, y, z) such that there is an angle Az between the axes (O, X) and (O, N). ∆x is the abscissa of the antenna A2 in the coordinate system (O, x, y, z). We then have for the geometry of figure 1 the relation between the coordinate systems (O, x, y, z) and (O, X, Y, Z) which is defined by the following rotation (A.1): We have: D G = 0 And (A.2): C G = A G tan B From the system of equations (A.1), we also deduce: @ G = A G cos B + C G sin B Let (A.3): Similarly, from the system of equations (A.1), we can deduce (A.4): E G = F G The elevation angle θ being the angle between the horizontal plane containing the antenna A1 and the line (A1B), we have: (A.5): (A.6): B being the orthogonal projection of antenna A2 on the line going from antenna A1 to a satellite in view considered, we have (A.7): ^ MMMM 1 MMM L M . ^ MMMM 2 MMM L M = 0 Let (A.8): (A.9): By factorization, we have (A.10): Let (A.11): Therefore (A.12): O A − ℎ c tan ^ HAS G = os B 1 + tan² B + tan² ^ c os² B We obtain (A.13): By simplification, we have (A.14): A G = (OA cos ^ cos B − ℎ sin ^^ cos ^ cos Bcos^ ^ (cos² B + sin² B^ + sin² ^Finally, we have (A.15): A G = (OA cos ^ cos B − ℎ sin ^^ cos ^ cos BA from equations (A.2) and (A.6), we can write: (A.16): ‖^ # L ‖^ = ( OA cos B cos ^ − ℎ sin ^ ^^ (A.17): V = ‖^ #L‖ = |OA cos B cos ^ − ℎ sin ^| But according to figure 2(b): So (A.18): (A.19): V = ‖ ^ # L ‖ = | OA sin ( ^ ^ + B Y^ cos ^ − ℎ sin ^ | By applying the trigonometric formulas, we have (A.20): V = |OA sin ^ ^ cos B Y cos ^ + OA cos ^ ^ sin B′ cos ^ − ℎ JZ[ ^ | From Figure 2(b), we have the following expressions: (A.21): ^ ^^ = OA cos B′ (A.22): ^ ^^ = OA sin B′ Substituting expressions (A.21) and (A.22) into (A.20), we arrive at (A.23): V = \^ ^5 cos ^ cos ^ ^ + ^ ^5 cos ^ sin ^ ^ − ℎ sin ^\ Finally, we show that the expression for the path difference δ in the cartographic reference frame (O, E, N, z) is given by (A.23) where ^ ^5 and ^ ^5are the North and East components of ∆x. In the present invention, it is proposed to estimate these components from the phase observables of the signals Sr1 and Sr2. Figure 3 is a block diagram of an example of an analog processing module 1 ("front-end" in English) of a system according to the invention. The objective of this analog module 1 is to digitize the GNSS signals received by the two antennas. The analog module 1 comprises an antenna power supply unit 50, two couplers 501, 502 connected to the power supply unit 50, a delay line 60, a summer 70 and a digitizer 80. In the implementation of a demonstrator by the inventors, the power supply to the antennas is provided by two NovAtel receivers which also make it possible to recover the ephemerides of the satellites and the approximate positions of the antennas.The delay line 60 is preferably made of optical fiber and is placed either on the signal path received by the antenna A1 or on that of the signal received by the antenna A2. The purpose of the delay line 60 is to shift one of the signals in time. The length of the delay line can be at least 1 km. Its length is equal to 1.5 km in this demonstrator. The length of the delay line used in the inventors' experimental work introduces a delay of approximately 50 µs. The adder 70 adds the delayed signal and the undelayed signal. The digitizer 80 digitizes the sum of the signals at the output of the adder to obtain a composite signal Src. The digitizer 80 is preferably a single-channel receiver, in particular of the 1-channel, 1-bit, 1-band GNSS type. The digitizing card can be the one developed by the company Syntony. Such a card records GNSS signals on two bands, L1 and L5, in the form of one- or two-bit quantized samples.In the inventors' experiments, a sampling frequency of 25 MHz and 1-bit quantization are used, and the antenna output signals with a duration of 20s are recorded. Figure 9 represents the correlation function of a composite signal obtained after introducing a delay. This is a Delay Doppler Map. In this representation, the code delay in meters is on the abscissa, the Doppler frequency in Hertz is on the ordinate, and the correlation value defines the third dimension, represented in the form of shades of gray. Two separate correlation peaks associated with the signal from the first antenna and the delayed signal from the second antenna can be observed in Figure 9. In practice, to differentiate the satellites, different CDMA codes are used. In the receiver of the present invention, to differentiate the signals from the antennas, these different CDMA codes are shifted in time.The duration of the CDMA code of the GPS signal being 1 ms (300 km), this shift is unambiguous if it is less than a millisecond. Figure 4 is a block diagram of an example of digital module 2 of a system according to the invention. This digital module 2 processes the composite signal obtained at the output of the digitizer 80 to extract therefrom the measurements and parameters used to calculate the position of the mobile antenna. The digital module 2 comprises an acquisition sub-module 30, a code and phase tracking sub-module 100 and an information extraction sub-module 40. The acquisition sub-module 30 has as input the composite signal Src. An example of this sub-module 30 is described in Figure 5. The objective of the acquisition step is to obtain an initialization of the code delays and Doppler frequencies of the received satellite signals. The acquisition stage uses the correlation principle to estimate code delays, frequencies and to identify visible satellites.Thus, upon receiving the signal, the receiver generates a local replicated signal that it correlates with the received signal. The correlation calculation can be done in the frequency domain to speed up the calculations. The correlation function can be calculated for several frequencies of the signal replicated locally by the receiver. This is called frequency acquisition. Figure 5 represents the acquisition for a given frequency f. i . The sub-module 30 comprises a generator 31 of carrier frequency fi, a phase shifter configured to introduce a phase shift of π / 2 to the generated carrier and two multipliers configured to multiply the input signal by the two carriers thus obtained in phase quadrature. Figure 5 shows FFT as the Fast Fourier transform, IFFT as its inverse and FFT* as the conjugate of the Fourier transform. The calculation of the correlation function carried out for different frequencies makes it possible to obtain the auto-correlation functions R(τ, fi) where τ is the delay of the local code generated by the receiver. In the present invention, the acquisition step is performed independently on the two received signals, but the tracking step is performed jointly on the two signals. The code and phase tracking sub-module 100 comprises two code and phase tracking loops: a first loop 10 having as input the digitized signal Src1 received by the reference antenna and a second loop 20 having as input the digitized signal Src2 received by the mobile antenna. These loops are illustrated schematically in Figure 6 and are described in detail later. The information extraction sub-module 40 has as input the estimates of the phase and the code delay of the signal received by the reference antenna at the output of the first loop 10. It can extract, from these estimates, the navigation message of the satellite S. This message is used to date the signal.Signal dating consists of finding the transmission time of each CDMA code, therefore of each phase difference measurement. This transmission time is used to position the satellites and therefore to calculate the azimuth and elevation of each satellite as a function of time. In the experimental implementation carried out by the inventors, the satellite ephemerides are obtained from the RINEX files provided by a NovAtel receiver. Each of the code and phase tracking loops 10, 20 comprises at least one frequency demodulator 200, one code demultiplexer 300, one correlator 400 and one discriminant calculator 106, 206, to track and correct the code delay of the associated signal. The architectures of the loops 10 and 20 are represented respectively in figures 6(a) (top figure) and 6(b) (bottom figure).The frequency demodulator 200 comprises in this example a carrier frequency generator 101, a phase shifter 102 and two multipliers 103. The generator 101 is configured to initially use the carrier frequency ]. #^ of the Src1 signal estimated by the acquisition sub-module 30 then adjust the frequency at its output by the corrected phase of the signal Src1, produced at the output of the first loop 10. The phase shifter 102 is configured to introduce a phase shift of ^ / 2 to the generated carrier. The two multipliers 103 are configured to multiply the input signal by the two carriers in phase quadrature. The first loop 10 is configured to track and correct the phase of the signal received by the reference antenna by producing a corrected phase $ * # . The second loop is configured to use this corrected phase in order to calculate the phase difference Ψ between the two signals Src1 and Src2. The demultiplexer 300 comprises in this example a code generator 104 and two multipliers 103. An example of code generator architecture is illustrated in Figure 7. The code generator 104 is configured to generate three C / A codes different by their propagation delays, namely a synchronous code (denoted P in Figure 7) with the demodulated signal, a code advanced with respect to the demodulated signal by a shift of d / 2 (denoted E in Figure 7) and a delayed code (denoted L in Figure 7) with respect to the demodulated signal by a shift of -d / 2, d being the shift between the advanced code and the delayed code. The code generator 104 is also configured to adjust the three C / A codes at its output by the corrected code delay "' # , "' ^by the associated loop 10, 20. The two multipliers 103 are configured to multiply each of the quadrature phase components of the demodulated signal by the three codes at the output of the code generator. The correlator 400 comprises in this example two integrators, each integrator referenced 105 being configured to integrate one of the quadrature phase components of the demultiplexed signal and produce a correlation component I or Q. The first loop 10 comprises a code discriminant and a phase discriminant, represented diagrammatically by the same block 106, and configured to respectively calculate the difference in code delays Δ" # and the phase difference Δ$ # as follows: Δ" # = D (% where the function D is a discriminant of the consistent code, $ * # the phase estimated by the first loop and "' # the code delay estimated by the first loop; and Δ$ = arctan The first loop 10 includes a final integrator 107 configured to integrate the code delay difference Δ" # and the phase difference Δ$ # at the output of the discriminants of the first loop to give respectively the corrected code delay "' # which is used retroactively in the code generator 104 of the first loop, and the corrected phase which is used retroactively in the carrier generator 101 of each of the 10, 20. The second loop 20 comprises a code discriminator and a phase discriminator, schematized by the same block 206, and configured to respectively calculate the difference in code delays Δ" ^ and the phase difference Ψ as follows: Δ" ^ = D (89"' ^ , $ * ^ :, %9"' ^ , $ * ^ :), where the function D is a code discriminant; Ψ = $ ^ - $ # + ^′ ! , where $ ^is the phase of the signal received by the mobile antenna, $ # is the phase of the signal received by the reference antenna, ^′ ! noise resulting from the calculation of Ψ and the estimation of $ # . It should be noted that the phase difference Ψ is obtained in open loop. The phase difference Ψ is proportional to the path difference between the signals arriving at each antenna. Indeed, a phase cycle (2π radians) corresponds in distance to the wavelength λ of a GNSS signal, i.e. 19.04 cm. In this context, Ψ is an ambiguous measure in [−π, π] of the path difference which can be noted: k being a relative integer, λ being the wavelength of a GNSS signal, ^ being the elevation angle of the satellite and ^ ^being the azimuth angle of this satellite. This expression is a multiple linear circular regression. Figure 8 shows the evolution of the phase difference and its linear-circular evolution model. Phase difference observations are obtained for all visible satellites. Figure 8 shows that the linear circular evolution model has an abscissa defined on an interval [0, 1] and an ordinate observed by several satellites positioned differently on the interval [−π, π]. We can conclude that the evolution model is multiple linear circular with three parameters EA2, NA2 and h. These parameters are estimated by maximum likelihood. Indeed, if we refer to the expression of the phase difference Ψ established theoretically above in connection with Figure 1, we note that: The second loop 20 includes a final integrator 207 configured to integrate the code delay difference Δ" ^at the output of the code discriminator of the second loop to give the corrected code delay which is used retroactively in the code generator 104 of the second loop 20. Thus, in the present invention, the simple phase difference is used which makes it possible to correct the biases in the pseudo-distance measurement which are linked to propagation in the atmosphere, to the synchronization of the satellite clocks with UTC time and the satellite positioning error bias. In addition, the hardware implementation of the system according to the invention makes it possible to synchronize the digitization of the signals coming from the two antennas. In this case, the simple phase difference also makes it possible to remove the error bias linked to the synchronization of the receiver with UTC time. Finally, the phase is observed modulo 2π which makes it possible to remove the entire ambiguity. Figures 10 to 12 relate to results of simulations made by the inventors.To evaluate the proposed maximum likelihood estimator in a simulated context, we compare the approximate CRLB (Cramér-Rao Lower Bounds) (obtained theoretically) with the variance of the estimator. In this simulation, we consider 1000 signal realizations and 90 samples of the elevation angle and the azimuth angle. The elevation varies between 0 and π / 2 and the azimuth between 0 and 2π. Figure 10 shows the square root of the approximate CRLB and the standard deviation of the estimation of the parameters NA2, EA2 and h as a function of κ, the measurement noise concentration parameter, (a) in the case of a single satellite and (b) in the case of the fusion of measurements obtained by two satellites. From Figure 10(a), it is shown that a maximum likelihood estimator defined in the circular domain can achieve the approximate CRLB of the parameter estimation of multiple linear-circular regression.In Figure 10(a), we consider 1 satellite and we vary on the abscissa the noise power (where b is approximately the inverse of the standard deviation of the noise distribution on the phase measurement). The convergence of our estimator is obtained with 90 observations and the estimation accuracy obtained is in this case of the order of a millimeter. In Figure 10(b), we show the improvement in the estimation accuracy when using two satellites. From Figure 10(b), we show that a maximum likelihood estimator defined in the circular domain is indeed the fusion operator in the circular domain, because its accuracy reaches the approximate CRLB of the fusion operator. This estimator combines the sensor measurements taking into account the accuracy of each sensor (the sensors being the GNSS satellites).The observability of the parameters NA2, EA2 and h depends on the predictors of the multiple linear circular regression which themselves depend on the azimuth and elevation of the satellite. Figure 11 represents the approximate CRLB for different variations of the azimuth and elevation evolution. Each variation domain is observed by 90 measurements. The abscissas V Az and V θ of Figure 11 represent the maximum values ​​of the variation intervals [0;V Az] and [0;V θ]. In Figure 11(a), V Az varies between 0 and 2π. We note in this figure that the estimation error increases when V Az tends towards 0. This effect is more remarkable on the CRLB of EA2. Indeed, Az and θ define the position of the sensors on a sphere of unit radius in the cartographic reference frame (O,E,N,z).Figure 12 schematically illustrates the position of the sensors (satellites) on the unit sphere: in solid bold line V Az = 2π and V θ = π / 2, in broken line ---- V Az = 0 and V θ = π / 2, in broken line -.-.- V Az = 2π and V θ = 0. In Figure 12, when V Az varies between 0 and 2π, the sensors are located around the sphere on the curve in solid bold line. When V Az tends towards 0, the sensors only travel part of the way around the sphere. In this same figure, when V Az = 0, the sensors travel a quarter of a circle in the plane (O,N,z) on the curve in broken line ----. In this case, the E axis and therefore the parameter EA2 is no longer observable. Therefore, when V Az tends towards 0, the identifiability of the parameter EA2 decreases and the CRLB of its estimate increases. In Figure 12(b), V θ varies between 0 and π / 2. We notice in this figure that the estimation error increases when V θ tends towards 0.In Figure 12, when V θ = 0, the sensors travel a circle in the (W, E, N) plane on the dashed curve -.-.-. In this case, when V θ tends towards 0, the identifiability of the parameter h decreases and the CRLB of its estimation increases. To evaluate the performance that can be expected from the differential positioning system that we propose, we evaluate the proposed estimator in a real context. The real context consists of using a real satellite constellation described in a RINEX file. The elevations and azimuths of the satellites that are used are reported in Table 1. This information is given for the 5 dial configurations studied.[Table 1] Satellite constellation PRN of satellites, elevations and azimuths West side 14 (10°, -39°), 10 (12°, -94°), 32 (33°, -53°), 25 (34°, -116°), 12 (80°, -121°) East side 6 (9°, 86°), 15 (17°, 174°), 17 (22°, 41°), 19 (3°, 59°), 24 (69°, 115°) Northeast side 6 (9°, 86°), 17 (22°, 41°), 19 (37°, 59°) Southwest side 10 (12°, -94°), 25 (34°, -116°), 12 (80°, -121°) Four quadrants All visible satellites Table 2 presents the evaluation of the integration time required to calculate the maximum likelihood estimator (MLE) defined in the circular domain by the experimenters to reach the CRLB. The integration times for the estimation of NA2, EA2 and h are given as a function of the satellite constellation and C / N0. In this table, the CRLB and the standard deviation of the proposed MLE estimator obtained in STD(N) simulation are indicated. e A2), STD( e EA2) and STD *(h), de NA2, EA2 et h. [Table 2] Constellation C / N0Intégration CRLB STD CRLB STD CRLB STD de satellites (dB Hz) (ms) (N e A2^ (N e A2) ( e EA2 ) ( e EA2 ) (h h ^ ( * h)(cm) (cm) (cm) (cm) (cm) (cm) West side 40 17 0.27 0.28 0.22 0.22 0.25 0.25 35 25 0.43 0.44 0.35 0.35 0.4 0.4 30 60 0.45 0.49 0.38 0.42 0.43 0.46 East side 40 19 0.21 0.21 0.25 0.25 0.26 0.26 35 45 0.25 0.26 0.31 0.32 0.26 0.26 30 72 0.34 0.37 0.42 0.45 0.44 0.46 North side- 40 100 0.26 0.27 0.13 0.14 0.36 0.36 East 35 180 0.37 0.37 0.19 0.19 0.52 0.53 30 500 0.37 0.4 0.19 0.2 0.51 0.53 South Side- 40 140 0.39 0.4 0.1 0.11 0.1 0.1 West 35 500 0.4 0.4 0.11 0.11 0.1 0.11 30 950 0.48 0.49 0.13 0.14 0.13 0.14 Four 40 9 0.21 0.21 0.16 0.16 0.19 0.19 dials 35 11 0.37 0.37 0.28 0.29 0.33 0.33 30 15 0.53 0.58 0.41 0.43 0.48 0.51 In Table 2, the proposed multiple regression estimator is assumed to have converged when the values ​​of STD(N e A2), STD( e EA2 ) and STD( *h) are close to those of their respective CRLB. Indeed, it is assumed here that if the standard deviation of the estimation error is close to its minimum value defined by the CRLB, then the estimate obtained is indeed that of the maximum likelihood. The second column of Table 2 indicates the minimum integration time N to reach the CRLB. It is noted that the integration period increases when C / N0 decreases. It can be observed in columns 4 to 7 of the first part of Table 2 and in columns 4 and 5 of the second part of Table 2 that the best performances, in terms of integration time, are obtained for the configurations with the most satellites. The reduction in the integration period is due to the increase in the number of visible satellites.Finally, we note that the standard deviations of the regression parameter estimates are always close to the approximate CRLB and that we obtain millimeter precision on each of the estimated parameters. Therefore, we conclude that when we combine observations from several satellites with a sufficiently long integration period, the proposed estimator converges. Indeed, in this case, the standard deviations of the parameter estimates are close to the approximate CRLB. The integration period decreases as the number of satellites increases. The rest of the description presents the evaluation of the positioning on real data. Since we want to estimate the relative position (NA2, EA2, h) of antenna A2 with respect to antenna A1 in the three dimensions of space, we need, in addition to the satellite elevations, the azimuths of the visible satellites.For the experiment carried out by the inventors, all visible satellites are used. Figures 13 to 15 present the experimental device and the results of the experiments carried out by the inventors. Figure 13 schematically represents an example of an experimental device for a system according to the invention, positioned on a roof. Table 3 reports the elevations and azimuths of the visible satellites and the power of the GPS signal for each satellite. The height h between the two antennas of the experimental device of Figure 13 is approximately 50 cm and the relative horizontal position of antenna A2 is approximately NA2 = 42 cm, EA2 = 139 cm. The PRN numbering (Pseudo Random Noise) makes it possible to identify the satellite and is provided in the navigation message of the GPS signal. [Table 3] PRN 1 3 4 6 9 12 17 19 22 31 Az (°) 133.63 65.32 173.26 - - - - - 81.45 54.17 55.34 155.95 19.99 99.59 72.51 θ (°) 35.53 71.15 57.78 28.16 25.49 5.3 45.68 42.02 48.59 20.41 C / N047.63 53.07 49.67 46.01 46.26 43.32 49.97 49.6 50.33 47.26 (dB Hz) It can be observed in Table 3 that the GPS signal power of the satellites is higher than that tested in simulation. Thus, given the satellite visibility on 4 quadrants and the power of the GPS signals, the signal integration time was set to 9 ms. For this integration time and this satellite configuration, the theoretical standard deviations of the estimates of NA2, EA2 and h, obtained from simulated data, are respectively 2.01 mm, 1.92 mm and 1.68 mm. We consider consecutive periods of 9 ms of signal for a total signal duration of 20 s. Each period of 9 ms is associated with a triplet of estimated values ​​N. e A2, E * A2 and h h. The standard deviation on each estimated parameter provides us with an estimation precision for each of them. Figure 14 shows the 2222 estimates obtained for the three components of the relative position of antenna A2. The estimation results of the position components presented in Figure 14 show a variation of the values ​​in the millimeter range. In addition, the evolution of the estimated parameters is constant. This shows the stability of the developed estimator. Table 4 below shows the estimated precision for the three components of the position. In Table 4, we note that the precisions obtained are millimeters. We also note that the precision obtained on real data is slightly better than that obtained in simulation. This is explained by the fact that the noise level used for the simulated data (C / N0 = 40 dB Hz) is higher than that recorded on the real data (C / N0 = 50 dB Hz).Finally, the difference in antenna position obtained by RTK with novAtel's GrafNav software and after 2 hours of recording is NA2 = 42.01 cm, EA2 = 138.78 cm and h = 49.69 cm. This result is consistent with that obtained by the method according to the invention. [Table 4] Parameter Mean (cm) Standard deviation (mm) N. e A2 42.35 1.77 E * A2 138.10 1.24 h h 49.45 0.86 Figure 15 shows the deviations of the estimated NA2 and EA2 parameters from their average values. The variations on E are shown on the abscissa. * A2 in mm and in ordinate the variations on N eA2 in mm. Figure 15 shows that the point cloud is distributed evenly around the origin, which shows that the method according to the invention is as accurate in the North direction as in the East direction. It can also be seen from the results reported in Table 4 that the method according to the invention is more accurate for estimating the height than for the horizontal position. This result, which confirms the results obtained by simulation, is different from the results obtained by conventional differential positioning techniques. Indeed, using conventional approaches, the positioning errors in the North direction and in the East direction are different and the height accuracy is significantly lower. The study of the reproducibility of the measurement is calculated on signals acquired over several days of the same month (September 2020) at approximately the same time.Table 5 below shows the estimate of NA2, EA2 and h obtained for 9 days in September 2020. The estimates are obtained with an integration time of 9 ms. Table 5 also shows the means and standard deviations of the estimates. [Table 5] Day of 03 04 07 08 10 11 12 14 17 month Time 13:12 13:15 13:14 13:12 13:11 13:12 13:10 13:13 13:15 (UTC). N e A2 (cm) 43.17 42.88 43.29 42.41 43.28 42.49 43.24 42.17 43.03 E * A2 138.66 137.88 138.62 137.79 138.56 138.46 138.49 138 138.3 (cm) h h 49.17 49.1 49.18 49.35 49.28 49.29 49.24 49.28 49.3 (cm) N e A2 E * A2 h hAverage 42.89 138.31 49.25 (cm) Standard deviation 4.2 3.3 0.8 (mm) It can be seen in Table 5 that the positioning accuracy obtained over the 9 days is millimeters. Indeed, for an integration time of 9 ms, the standard deviations of NA2, EA2 and h are respectively 4.2 mm, 3.3 mm and 0.80 mm. These results are close to those obtained in simulation and in theory. The small number of measurements does not allow us to conclude that there is a significant difference between the results obtained and the theory. Finally, we can conclude that the method according to the invention is not significantly dependent on the signal propagation conditions which change every day. Indeed, the difference between the positions obtained each day is of the order of a millimeter. The invention is not limited to the exemplary embodiment described above, and can be applied to the positioning of several mobile antennas relative to a reference antenna.The method according to the invention can be used for precise relative positioning outdoors. An example of use is the positioning of a gun on a tank. Indeed, the positioning of the tip of the gun is of prime importance for the accuracy of the shot, and given the range of the guns, this positioning must be millimetric. By the approach proposed according to the invention, the reference antenna is located in the center of the turret and the antenna to be located on the tip of the gun. Another application is the measurement of deformation of an aircraft in flight. Indeed, one can consider a reference antenna on the cockpit and antennas to be located on the wings and parts that deform during the flight. The positioning system then makes it possible to monitor these deformations during the flight so that they remain acceptable by the structure of the aircraft.Applications can also be considered in the fields of agriculture and public works which use machines with multiple tools to be positioned.

Claims

Claims 1. GNSS relative differential positioning method for positioning a mobile antenna (A2) relative to a reference antenna (A1) by calculating the phase differences between the signals received (Sr1, Sr2) by these two respective antennas (A1, A2) and coming from a plurality of GNSS satellites, each of the signals having a code delay (" # , " ^ ^ and a carrier frequency (] # , ] method comprising: - the digitization of these signals (Sr1, Sr2); - the processing of the digitized signal received by the reference antenna (Src1) in a first code and phase tracking loop (10) and the processing of the digitized signal received by the mobile antenna (Src2) in a second code and phase tracking loop (20), each of the loops subjecting the signal to frequency demodulation, code demultiplexing, correlation and discriminant(s) calculation operations, to estimate the code delay ("' # ; of the signal, the first loop (10) estimating the phase of the signal ($ * #) used to adjust the carrier frequency in the frequency demodulation for each of the loops, the second loop (20) calculating the phase difference Ψ between the two signals at each measurement cycle; and - estimating the position of the mobile antenna (A2), in particular by maximum likelihood, from the phase difference Ψ thus calculated.

2. Method according to the preceding claim, in which, before estimating the position of the mobile antenna (A2), phase difference values ​​Ψ are accumulated over several measurement cycles, in particular over at least 9 measurement cycles, to improve the accuracy of the estimation of the position of the antenna. 3.Method according to the preceding claim, the phase differences Ψ associated with each satellite (S) depending on the North NA2 and East EA2 components of the distance to the ground (Δx) between the two antennas (A1, A2) in a Lambert I projection cartographic reference frame (o, E, N, z) and the height h between them by the multiple circular linear evolution relationship:. k being a relative integer, λ being the wavelength of a GNSS signal, ^ being the elevation angle of the corresponding satellite seen by the reference antenna (A1), ^ ^ being the angle azimuth of this satellite seen by the reference antenna (A1) and ^ !being measurement noise, in particular distributed according to the normal circular distribution.

4. Method according to one of the three preceding claims, comprising, prior to the digitization of the signals, the introduction of a delay in the signal received by one of the antennas with respect to the signal received by the other antenna, via a delay line (60), the delay being sufficient so that the correlation functions of these signals are not superimposed.

5. Method according to the preceding claim, comprising the sum of the delayed signal and the undelayed signal and the digitization of the resulting signal via a single digitizer (80), in particular a single-channel digitizer.

6. Method according to one of the two preceding claims, comprising the conversion of the signals received by the antennas (A1, A2) into optical signals via photomodulators, the delay line (60) being made of optical fiber. 7.Method according to any one of claims 4 to 6, comprising the independent acquisition of the digitized delayed signal and the undelayed signal, by generating for each of these signals a local replicated signal to be correlated with the associated signal to estimate the code delay ("'. # ; of this signal and its carrier frequency (] #^ ; ] ^^ ^ and to identify the corresponding satellite, the correlation with the replicated signal being in particular calculated for several frequencies of the replicated signal.

8. Method according to the preceding claim, the frequency demodulation in each loop (10; 20) comprising the multiplication of the signal by two carrier frequencies in phase quadrature obtained from a carrier frequency generator (101) and a phase shifter (102), this generator initially using the carrier frequency (] #^ ; ] ^^^ estimated at the acquisition stage then adjusting the frequency at its output by the estimated phase ($ * # ) by the first loop.

9. Method according to any one of the preceding claims, the code demultiplexing in each loop comprising the multiplication of the demodulated signal by three C / A codes (E, P, L) different by their offsets, namely a synchronous code (P) with the demodulated signal, an advanced code (E) with respect to the demodulated signal by an offset of d / 2 and a delayed code (L) with respect to the demodulated signal by an offset of -d / 2, d being the offset between the advanced code and the delayed code, these codes being obtained at from a code generator (104), this generator of each loop adjusting the three C / A codes (E, P, L) at its output by the estimated code delay ("' # ; by the loop.

10. Method according to any one of the preceding claims, the correlation in each loop comprising the integration of the demultiplexed signal to produce two correlation components I and Q.

11. Method according to the preceding claim, the first loop (10) comprising a code discriminator (106) and a phase discriminator (106) respectively calculating the difference in code delays Δ" # and the phase difference Δ$ # as follows: Δ" # = D (% where the function D is a coherent code discriminant, the phase estimated by the first loop and "' # the estimated code delay per first loop; and Δ$ # = arctan 12. Method according to the preceding claim, the difference in code delays Δ" # and the phase difference Δ$ #at the output of the discriminants of the first loop being each integrated to give respectively the estimated code delay ("' # ^ and the estimated phase ($ * #^.

13. Method according to claim 10, the second loop (20) comprising a code discriminator (206) and a phase discriminator (206) respectively calculating the difference in code delays Δ" ^ and the phase difference Ψ as follows: Δ" = D $ * # :), where the function D is an inconsistent code discriminant, the phase estimated by the first loop and "' ^ the code delay estimated by the second loop; Ψ = $ ^ - $ # + ^′ ! , where $ ^ is the phase of the signal received by the mobile antenna, $ # is the phase of the signal received by the reference antenna, ^′ ! noise resulting from the calculation of Ψ and the estimation of $ #.

14. Method according to the preceding claim, the difference in code delays Δ" ^ at the output of the code discriminant (206) of the second loop (20) being integrated to give the estimated code delay ("' ^ ^.

15. GNSS relative differential positioning system comprising a receiver connected to a reference antenna (A1) and a mobile antenna (A2), for positioning the mobile antenna (A2) relative to the reference antenna (A1) by calculating the phase differences Ψ between the signals received (Sr1, Sr2) by these two antennas (A1, A2) and coming from a plurality of GNSS satellites, each of the signals having a code delay (" # , " ^ ^ and a carrier frequency (] # , ] receiver comprising: - a single digitizer (80), in particular a single-channel digitizer, for digitizing the signals (Sr1, Sr2); - a digital processing module (2), comprising: -- two code and phase tracking loops (10, 20), a first loop (10) configured to process the signal received by the reference antenna (A1) and a second loop (20) configured to process the signal received by the mobile antenna (A2), each of the loops comprising a frequency demodulator (200), a code demultiplexer (300), a correlator (400) and at least one discriminant calculator (106; 206), for estimating the code delay ("' # ; "' ^ ^ of the signal, the first loop (10) being configured to estimate the phase of the signal ($ * #) used to adjust the carrier frequency in the frequency demodulator (101) for each of the loops, the second loop (20) being configured to calculate the phase difference Ψ between the two signals at each measurement cycle; and -- an estimator of the position of the mobile antenna, in particular by maximum likelihood, from the phase difference Ψ thus calculated.

16. System according to the preceding claim, being configured to accumulate, before the estimation of the position of the mobile antenna (A2), in particular over at least 9 measurement cycles, phase difference values ​​Ψ to improve the accuracy of the estimation of the position of the antenna.

17. System according to claim 15 or 16, comprising upstream of the digitizer (80) a delay line (60) configured to delay the signal received by one of the antennas relative to the signal received by the other antenna so that the correlation functions of these signals are not superimposed. 18.System according to the preceding claim, comprising an acquisition sub-module (30) for the digitized delayed signal and non-delayed signal, configured to generate for each of these signals a local replicated signal to be correlated with the associated signal to estimate the code delay of this signal and its carrier frequency and to identify the corresponding satellite.

19. System according to the preceding claim, the frequency demodulator (200) comprising:. - a carrier frequency generator (101), this generator being configured to initially use the carrier frequency (] #^ ; ] ^^ ^ of the signal received by the reference antenna (A1) estimated by the acquisition sub-module (30) then adjust the frequency at its output by the estimated phase by the first loop (10); - a phase shifter (102) configured to introduce a phase shift of ^ / 2 to the generated carrier; and - two multipliers (103) configured to multiply the input signal by the two carriers in phase quadrature.

20. System according to any one of claims 15 to 19, the demultiplexer (300) comprising: - a code generator (104) configured to generate three C / A codes (E, P, L) different by their offsets, namely a synchronous code (P) with the demodulated signal, a code advanced € with respect to the demodulated signal by an offset of d / 2 and a delayed code (L) with respect to the demodulated signal by an offset of -d / 2, d being the offset between the advanced code and the delayed code, the code generator (104) being configured to adjust the three C / A codes at its output by the estimated code delay ("' # ; "' ^^ by the loop; - two multipliers (103) configured to multiply each of the quadrature phase components of the demodulated signal by the three C / A codes at the output of the code generator (104).

Images