Method for positioning by radiating cables without measurement bias

Abstract

The present invention relates to a method for positioning a mobile terminal along at least one radiating cable located in an indoor environment. A first subset of synthetic GNSS signals is injected into a first end of the cable and a second subset of synthetic GNSS signals is injected into a second end of the cable, the two subsets corresponding to signals that would be received from two separated subsets of satellites that would be visible from a first reference point and from a second reference point, respectively, in open-sky configuration. The GNSS receiver of the mobile terminal estimates its position along the cable from the respective deviations between, on the one hand, the pseudoranges measured for the different synthetic GNSS signals received by the terminal and, on the other hand, the reference pseudoranges calculated for the synthetic GNSS signals received at the reference points. An embodiment with two parallel radiating cables is also proposed for two-dimensional positioning.

Description

[0001]METHOD OF POSITIONING BY RADIATING CABLES WITHOUT MEASUREMENT BIAS TECHNICAL FIELD The present invention relates generally to the field of indoor positioning systems, and in particular those enabling continuity of positioning service to be ensured with an outdoor environment. STATE OF THE PRIOR ART Satellite positioning systems, also called GNSS (Global Navigation Satellite System) systems, are currently the most commonly used geopositioning systems. The various GNSS type satellite constellations (GPS, Galileo, Beidou, GLONASS, IRNSS, etc.) emit satellite positioning signals to the GNSS receiver, to position themselves at any point on the Earth.However, the absence of GNSS signals in indoor environments, and a fortiori in those qualified as deep indoors, such as, for example, an underground tunnel, does not allow satellite positioning. This constraint has led to the development of positioning systems specific to indoor environments. A large number of possible techniques have been used for this purpose. For example, it is known to deploy in such an environment beacon networks allowing a dedicated receiver to estimate its position by TDOA (Time Difference Of Arrival) or by triangulation from arrival times, TOA (Time Of Arrival). It is also possible to use existing access points, for example a Wi-Fi network to determine the position of a terminal from fingerprints of power measurements (RSSI).However, the aforementioned indoor positioning systems are generally location-specific and require dedicated reception equipment. In addition, they do not allow for easy and seamless transition from an outdoor environment to an indoor environment, and vice versa. Indeed, continuity of service is generally not guaranteed between these two environments, with outdoor positioning being achieved by using GNSS signals while indoor positioning is achieved using specific signals. Patent FR-B-3074921, in the name of the present Applicant, presents a positioning system using a radiating cable (leaky feeder) at the ends of which synthetic GNSS signals are injected, these signals being synchronized with real GNSS signals, as they would be received in the outdoor environment.Thus, a user equipped with a GNSS receiving terminal can determine his position along a radiating cable arranged in an indoor environment and does not have to suffer from a service interruption when entering or leaving this environment. However, the position measurements obtained by means of the aforementioned positioning system are affected by a bias due to the fact that the synthetic GNSS signals injected into the radiating cable propagate along the latter and that their propagation speed in the cable is lower than that in free space. To reduce the measurement bias, the aforementioned patent uses a virtual extension of the cable, on either side of the ends of the latter, ℓ ^ of a length ^ = ^ ^ ^ − 1^ where ℓ is the length of the radiating cable, ^ and ^ being respectively the propagation speed of an electromagnetic wave in a vacuum and in the cable.This bias is, however, only perfectly compensated when the user is in a middle position, equidistant from the ends of the cable. This compensation may prove insufficient for a very long cable as soon as the user moves away from the middle position. Furthermore, although the positioning method disclosed in the aforementioned patent is well suited to an interior environment of substantially linear shape (road tunnel or metro track, for example), it does not allow the position of the user to be determined in a two-dimensional or three-dimensional manner in an interior environment of any shape. Indeed, if a plurality of radiating cables are used in the positioning system of patent FR-B-3074921, only the respective projections of the position of the user onto the different cables can be determined. On the other hand, the position of the user in a direction orthogonal to these cables cannot be determined.An object of the present invention is therefore to propose a method and a system for positioning by radiating cable which allow a user to position himself in an indoor environment, without measurement bias, where appropriate in a two-dimensional or three-dimensional manner. DISCLOSURE OF THE INVENTION The present invention is defined by a method for positioning a mobile terminal in an indoor environment within which is located at least a first radiating cable having a first end and a second end, said positioning method being original in that: - a partition of at least a part of a satellite constellation is carried out into a first and a second disjoint subset of satellites, which would be respectively visible from a first point and a second reference point, in an open sky configuration; - a first (resp.a second) subset of synthetic GNSS signals corresponding to those which would be received, in an open-sky configuration, by the first (resp. the second) reference point, coming from satellites belonging to the first (resp. the second) subset, the first (resp. the second) end injecting into the radiating cable the first (resp. the second) subset of synthetic GNSS signals thus generated; - the GNSS receiver of the mobile terminal measures the pseudodistances corresponding to the synthetic GNSS signals received from the radiating cable; - for each synthetic GNSS signal of the first (resp. second) subset, the difference between the pseudodistance measured by the GNSS receiver and a reference pseudodistance calculated for the first (resp. second) reference point is determined; - the position of the mobile terminal along the cable is estimated from the differences in the pseudodistances thus obtained and from a georeferenced curve, describing the radiating cable.The position of the mobile terminal along the radiating cable can then be obtained by solving a system of navigation equations giving the deviations of the pseudodistances as a function of said position. The system of equations is advantageously given by: ^ ^ + ^ + ^ = Δ ^ ​​^. ^ ^ ^^ , ^ = 1, … , ^ ^ where ^ ^ is the ratio between the speed of light and the speed of propagation of an electromagnetic wave in the radiating cable, ^ ^ is the position of the mobile terminal along the radiating cable taking the first end as the origin, ^ ^ is the length of the radiating cable, ^ is the distance to the radiating cable, ^ is the clock offset of the GNSS receiver relative to the clock used to generate the synthetic GNSS signals, Δ^ ^ ^ ^ , ^ = are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, obtained for the synthetic GNSS signals of the first subset, Δ^ ^ ^ ^ , ^ = 1, … , ^ ^ , are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, obtained for the ^ ^ synthetic GNSS signals of the second subset. The position of the mobile terminal along the radiating cable can be deduced from: ^ where Δ^ ^^ = ^ ^ are respectively the average of the pseudodistance deviations on the first and second subsets. According to a second embodiment of the method for positioning a mobile terminal, the indoor environment comprises at least a first radiating cable and a second radiating cable, each radiating cable having a first end and a second end, the positioning method being original in that: - a partition of at least a part of a satellite constellation is carried out into a first, a second, a third and a fourth disjoint subsets of satellites, which would be respectively visible from a first, a second, a third and a fourth in an open sky configuration; - a first (resp. a second) subset of synthetic GNSS signals corresponding to those which would be received, in an open sky configuration, by the first (resp.the second) reference point, originating from satellites belonging to the first (resp. second) subset, the first (resp. second) end of the first cable injecting into the first radiating cable the first (resp. second) subset of synthetic GNSS signals thus generated; - a third (resp. fourth) subset of synthetic GNSS signals corresponding to those which would be received, in an open-sky configuration, by the third (resp. fourth) reference point, originating from satellites belonging to the third (resp. fourth) subset, the first (resp. second) end of the second cable injecting into the second radiating cable the third (resp.the fourth) subset of synthetic GNSS signals thus generated; - the GNSS receiver of the mobile terminal measures the pseudodistances corresponding to the synthetic GNSS signals received from the first and second radiating cables; - for each synthetic GNSS signal of the first (resp. second, third, fourth) subset, the difference between the pseudodistance measured by the GNSS receiver and a reference pseudodistance calculated for the first (resp. second, third, fourth) reference point is determined; - the position of the mobile terminal along the first and / or second cable and the distance to the first and / or second cable are estimated from the differences in the pseudodistances thus obtained and from georeferenced curves, describing respectively the first and second radiating cables.The position of the mobile terminal along the and / or second radiating cable and the distance to the first and / or second cable can then be obtained by solving a system of navigation equations giving the deviations of the pseudodistances as a function of the position of the mobile terminal, respectively along the first cable and the second radiating cable as well as its distance respectively to the first cable and the second radiating cable. Advantageously, the first and second radiating cables are parallel and separated by a distance ^ and the system of equations is given by:. where ^ ^ , ^ ^ is the ratio between the speed of light and the speed of propagation of an electromagnetic wave respectively in the first and second radiating cables; ^ ^ , ^ ^ is the position of the mobile terminal respectively along the first and second radiating cables, taking the first end of these cables as the origin; ^ ^ , ^^ is the respective length of the first and second radiating cable, ^ is the distance from the user to the first radiating cable, ^ is the clock offset of the GNSS receiver relative to the clock used to generate the synthetic GNSS signals; , ^ = 1, … , ^ ^ are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, respectively obtained for the synthetic GNSS signals of the first subset and ^ synthetic GNSS signals ^ ^ etic of the second subset; Δ^ ^^ , ^ = 1, … , and Δ^ ^ ^ ^ , ^ = 1, … , ^ ^are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, respectively obtained for the M 1 synthetic GNSS signals of the third subset, and the M 2 synthetic GNSS signals of the fourth subset. The position of the mobile terminal along the first, resp. the second radiating cable can be deduced from: ^ where Δ^ = ^ are respectively the pseudodistance deviations on the first and second subsets, and are respectively the pseudodistance deviations on the third and fourth subsets. The distance from the mobile terminal to the first radiating cable is given by: Regardless of the embodiment, the synthetic GNSS signals may be generated by means of a simulator receiving at least one real satellite signal from a satellite of said constellation, via an antenna located in an external environment, the synthetic GNSS signals being synchronized with respect to the real satellite signal. BRIEF DESCRIPTION OF THE DRAWINGS Other characteristics and advantages of the invention will appear upon reading a preferred embodiment of the invention, made with reference to the attached figures among which: [Fig. 1] schematically represents a positioning system according to a first embodiment of the invention; [Fig. 2A] and [Fig. 2B] schematically illustrate an example of an open sky partition that can be used in the implementation of a positioning method according to the embodiment of Fig. 1; [Fig.3] schematically represents a positioning system according to a second embodiment of the invention; [Fig.4A] and [Fig.4B] schematically illustrate an example of an open sky partition that can be used in the implementation of a positioning method according to the embodiment of Fig.3; [Fig.5] schematically represents a positioning method according to the first embodiment of the present invention; [Fig.6] schematically represents a positioning method according to the second embodiment of the present invention. DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS In the following, we consider an environment in which the reception of GNSS signals is almost impossible, in particular an indoor environment, or even totally impossible (so-called “deep indoor” environment).By GNSS (Global Navigation Satellite System) signals, we mean here any type of satellite signals allowing positioning regardless of the satellite system considered (GPS, Galileo, GLONASS, Beidou, etc.). Finally, by GNSS receiver, we mean devices for receiving GNSS signals complying with the standards defined in the ICDs (Interface Control Documents) of the satellite systems in question, making it possible to extract measurements of GNSS observables such as pseudorange measurements. In the following, for illustration purposes only and without loss of generality, we will assume that the satellite system is a GPS system. The indoor environment is separated by a boundary from an outdoor environment where the reception of GNSS signals is done in the open air. Typical but non-limiting use cases of the present invention include, among others, underground infrastructures or buildings. Fig.1 schematically represents a positioning system according to a first embodiment of the invention. This system, 100, comprises means for generating synthetic signals (also referred to hereinafter as “synthetic signal simulator”), 110, receiving at least one real GNNS signal (and generally a plurality of such real GNSS signals) from an antenna, 120, located in an external environment. These generation means, detailed later, provide synthetic GNSS signals, synchronized with said at least one real GNSS signal, at the ends ^. ^ and ^ ^of a radiating cable, 150, located in the indoor environment. By synthetic GNSS signals is meant a set of simulated GNSS signals corresponding to a reception at a given reference position, i.e. GNSS signals as they would be received in an outdoor environment for a position configured by the generation means 110. In this document, we will note ^ ^^ and ^ ^^ , the reference positions configured for the simulation of satellite GNSS signals injected at each end of the cable ^ ^ and ^ ^. It should be noted that the reference positions configured for the simulation of the synthetic GNSS signals by the generation means 110 are not necessarily those of the ends of the cable. They may generally be reference positions located or not on the cable. In a particular case, the reference positions configured by 110 may be chosen to be identical to the positions of the physical ends of the radiating cables used as transmission support (i.e. the positions of the ends ^ ^ and ^ ^). By radiating cable (leaky feeder), we typically mean a coaxial cable whose outer conductor has slots at regular intervals so as to allow radial emission along its entire length. In an equivalent manner, any waveguide, with slots or openings, having a large extension along its longitudinal axis and allowing radial emission along this axis can be used. Note that the radiating cable is not necessarily rectilinear, it can be at least curvilinear over at least part of its length. However, as a preliminary point and for the purpose of simplifying the presentation of the invention, we will assume that the cable is rectilinear. The set ^ of synthetic signals generated by the generation means 110 is partitioned into two separate subsets Ω ^^ , Ω ^^ The subset Ω ^^ (resp. Ω ^^ ) associated with the end (resp. ^ ^) consists of GNSS signals which would be received at the same time at a first (resp. a second) reference point ^ ^^ (resp. ^ ^^ ) in an open sky configuration, i.e. without any propagation obstacle between this first (resp. second) reference point and the sky. For example, in the particular embodiment mentioned above, the subset Ω ^^ (resp. Ω ^^ ) of satellite signals generated by 110 and injected into the radiating cable by the end ^ ^ (resp. ^ ^ ), can be defined by a subset of simulated GNSS signals corresponding to satellite GNSS signals received at a reference point ^ ^^ (resp. ^ ^^ ). These satellite signals are associated with the satellites theoretically visible from point ^ ^^ (resp. ^ ^^ ) in a cone of visibility above the horizon, having as its apex ^ ^^ (resp. ^ ^^ ). The visibility cones of summits ^^^ and ^ ^^ (corresponding to the signals injected in ^ ^ and ^ ^ ) are chosen to be disjoint. In a particular embodiment, the first and second reference points can be taken to be identical, the subsets Ω ^^ and Ω ^^ being always chosen disjoint. Advantageously, it will be possible to provide that the directions of the visibility cones have between them an angular difference in azimuth and / or elevation greater than a threshold value. In the following, we will note ^ ^ ^ ^ , with ^ = 1, … , and ^ = 1,2, the simulated synthetic GNSS signals for a reference position ^ ^^ and injected at each end of the radiating cable ^, in other words belonging to the sub-assembly the corresponding simulated satellites. We will assume that ^ ^ , ^ ^ ≥ 1, in other words that each of the two subsets + ^ ^≥ 4 to allow the GNSS receiver to perform pseudorange measurements in a conventional manner. Thus, in Fig. 1, the end ^ ^ receives at time ^, from generation means 100, the synthetic GNSS signals ^ ^ ^ ^ ( ^ ) , ^ ^ ^ ^ ( ^ ) which would be received at the same time by the first simulated reference point ^ ^^ , in an open sky configuration. Similarly, the end ^ ^ receives at time ^, from generation means 100, the synthetic GNSS signals which would be received at the same time by the second simulated reference point ^ ^^, in an open-sky configuration. In the following, the time ^ will be omitted, it being understood that the means for generating the synthetic GNSS signals are synchronized with the time of a real GNSS signal. More precisely, the local clock of the simulator 110 is set to said at least one real GNSS signal received from the antenna 120, the offset between the local clock of the simulator and the GPS time being constant. It should also be noted, in particular for a spatially extended positioning system, that the signals provided by the generation means can be offset in time, in order to compensate for the respective propagation times in the supply cables (not shown) connecting the simulator and the ends ^ ^ and ^ ^ . Synthetic GNSS signals ^ ^ ^ ^ , ^ = 1, … , of the subset Ω ^^ are injected in ^ ^ in the radiating cable 150 and propagate there in the direction of ^ ^while being radiated radially along the cable. Similarly, synthetic GNSS signals ^ ^ ^ ^ , ^ = 1, … , ^ ^ of the subset Ω ^^ are injected into the radiating cable 150, and propagate there in the direction of ^ ^ while being radiated radially along the cable. By definition of synthetic GNSS signals ^ ^ ^ ^ , ^ = 1, … , ^ ^ of the subset Ω ^^ , a GNSS receiver synchronized to the same internal clock as the simulator and receiving these signals directly at the output of the simulator 110, as injected in ^ ^ , would measure pseudodistances ^ ^ ^ ^ relating to the distances between the simulated reference position ^ and the ^ ^ ^ s simulated satellites ^ ^^ , ^ = These pseudodistances ^ ^ ^ ^, can be calculated at any time by the simulator, from the almanac, ephemeris and GPS time information. The almanac and ephemeris information of each satellite can be obtained directly by demodulating the navigation messages of the real GNSS signals received by the simulator or by a remote server. The GPS time can be given by one of the real GNSS signals received. Thus, it is not necessary for all the real GNSS signals to actually be received by the antenna 120. The navigation messages of the missing real signals (for example emitted by satellites masked by obstacles in an urban environment) can be provided by a remote server. The pseudodistances ^ ^ ^ ^ , ^ = 1, … , ^ ^^ , ^ = 1.2 are called in the following pseudo reference distances because they are calculated without resorting to measurements, for each of the reference points ^ ^^,^ = 1.2. It should be noted that, for a given simulated satellite constellation, the reference pseudoranges depend only on the reference positions ^ ^^ ,^ = 1,2,of the position of the satellites ^ ^ ^ ^ and GPS time. A GNSS signal receiver located at point ^, for example part of a user's mobile terminal, measures the pseudodistances ^^ ^ ^ ^ following, relating to the synthetic GNSS signals received, ^ ^ ^ ^ , by the following relation: [Math.1] ^^ ^ ^ = ^ ^ ^ + ^ ^ ^ + ^ ^ ^ ^ ^ ^ + ^ + ^ ^^ (1) where ^ ^^ is the distance separating the end ^ ^ of the cable and the orthogonal projection of ^ onto the radiating cable; ^ ^ = is the celerity factor in the cable (ratio of the speed of light and the propagation speed ^ ^of a wave in the radiating cable); ^ corresponds to the offset between the clock of the GNSS receiver and that of the simulator 110; ^ is the distance between the position ^ of the GNSS receiver and the cable; ^ ^ ^ ^ is a pseudorange measurement noise. Since the synthetic GNSS signals of the same subset Ω ^^ follow the same propagation path, we can legitimately consider that the measurement noises ^ ^ ^ ^ do not depend on the index of the simulated satellite ^. If we neglect the measurement noise in question, the difference between a measured pseudodistance, ^^ ^ ^ ^ by the GNSS receiver and the reference pseudorange ^ ^ ^ ^ corresponding is only a function of the propagation distance in the cable, the distance of the GNSS receiver from the cable and the clock offset of the receiver relative to the simulator. This difference between the reference (or theoretical) pseudodistance associated with ^ ^and this same pseudodistance measured after propagation of the signal in the cable, noted Δ^ ^ ^ ^ , is expressed as follows: [Math.2] Subsequently, we will arbitrarily take the first end of the cable as a reference ^ ^ . The distance ^ ^ along the cable is none other then that ^ ^ = ^ ^^ and we have ^ ^^ = ^ ^ − ^ ^ where ^ ^ is the length of the cable. The measured pseudodistances ^^ ^ ^ ^ , ^ = 1, … , ^ ^^ , ^ = 1,2 are directly provided by the GNSS receiver of the mobile terminal. The reference pseudodistances ^ ^ ^ ^ , = 1, … , ^ ^^ , ^ = 1,2 are also known to the mobile terminal. Indeed, the latter only depend on the simulated reference position ^ , and the associated visible satellites ^ ^ ^ ^ ^^. To do this, different variants are possible: According to a first variant, the reference pseudodistances are calculated at each instant by the simulator, from navigation messages received from the different satellites and / or almanac / ephemeris data provided by a remote server, and the positions of the reference points. In this case, the reference pseudodistances can be transmitted via an auxiliary channel, to the mobile terminal. According to a second variant, the reference pseudodistances are calculated at each instant by a remote server, from the almanac / ephemeris data of the different satellites, as well as the positions of the reference points. The reference pseudodistances thus calculated can be transmitted to the mobile terminal via Wi-Fi access points located within the indoor environment or via a communication system deployed within this environment.According to a third variant, the theoretical pseudodistances are calculated at each instant by the mobile terminal itself on the basis of the almanac / ephemeris data of the different satellites, and the positions of the reference points. To do this, the almanac / ephemeris data and the reference positions can be transmitted by a remote server, via Wi-Fi access points or via any other communication system deployed in the indoor environment. Regardless of the implementation variant, the local coordinates ^^. ^^ , ^ ^^ , ^ ^^ ^ ends ^ ^ ,^ = 1,2 of the cable are known in a cartographic reference system (geographic reference, building or infrastructure plan) are known to the mobile terminal, and can be provided to a navigation application. The mobile terminal solves a system of + ^ ^ navigation equations with three unknowns, namely the coordinate ^^ , the distance to the cable ^, and the clock deviation ^, where the observables are the pseudodistances relating to synthetic GNSS signals, ^ ^ ^ ^ ^ , received via the radiating cable and ^^ ^ the associated theoretical pseudodistances: [Math.3] Knowing the local coordinates of each cable end and eliminating the sum ^ + ^ between the equations allows us to determine the coordinate ^ ^ , in other words the coordinate of the position of the mobile terminal along the axis of the cable taking as origin. On the other hand, this first embodiment alone does not allow the ordinate ^ and the clock offset ^ to be determined separately. The system of navigation equations (3-1), (3-2) can be solved in a conventional manner, for example by a least squares method, if the system is overdetermined, in a manner known per se. According to an exemplary embodiment, it will be possible to simply average the pseudodistance deviations for each of the subsets Ω ^^ : [Math.5] ^ Δ^ ^ ^ ^ = ^ ^ ^ ∑ ^^^ Δ^ ^ ^ ^ (4-1) [Math.6] and deduce the coordinate ^ ^ of the position of the mobile terminal by the following relation: [Math.7] Knowing the coordinates ^ ^ ^^ , ^ ^^ , ^ ^^ ^ ends ^ ^,^ = 1,2 of the cable in a local coordinate system, we can deduce the position of the orthogonal projection of the point R where the user is located in this same coordinate system and provide this to a specific navigation application (tunnel, underground road network, for example). It has been assumed so far that the radiating cable is rectilinear. Those skilled in the art will however understand that the positioning method according to the first embodiment also applies to a curvilinear cable whose curve in space is known to the mobile terminal. Indeed, the coordinate ^ ^ is then none other than the curvilinear abscissa along the cable taking the first end as the origin, this coordinate giving the position of the orthogonal projection of point R on the cable. Figs. 2A and 2B schematically illustrate an example of an open sky partition that can be used in the implementation of a positioning method according to the first embodiment of the invention. 210 shows an open sky configuration in top view showing a satellite constellation at a given time. This configuration is here partitioned into two parts, 211, 212, corresponding here to two opposite directions. Fig. 2B illustrates the radiating cable in the indoor environment and the allocation of satellites / GNSS signals to each of its ends. It is verified that the subsets Ω ^^, ^ = 1,2 are well disjoint and that each of them comprises at least one element. Fig. 3 schematically represents a system for positioning a mobile terminal according to a second embodiment of the present invention. Unlike the first positioning system illustrated in Fig.1, the positioning system according to the second embodiment of the invention comprises two parallel coplanar radiating cables, 350 and 370, located in an indoor environment, namely a first cable A, 350, of length ^ ^ and a second cable B, 370, of length ^ ^ . We will first assume that these two cables are straight and separated by a distance ^. Generation means 310 receive at least one real GNSS signal from an antenna, 320, located in the external environment and provide synthetic GNSS signals, synchronized with said at least one real GNSS signal, at the ends ^ ^ and ^ ^of the first radiating cable, 350, on the one hand, and at the ends ^ ^ and ^ ^ of the second radiating cable, 370, on the other hand. The set Ω of synthetic signals generated by the generation means 310, is partitioned into four separate subsets two by two, namely Ω ^^ ,Ω ^^ , respectively associated with a first and a second simulated reference point, noted ^ ^^ and ^ ^^ , the signals of Ω ^^ ,Ω ^^ being respectively injected into the radiating cable in ^ ^ and ^ ^ ; and Ω ^^ ,Ω ^^ , respectively associated with a third and a fourth simulated reference point, noted ^ ^^ and ^ ^^ , the signals of Ω ^^ ,Ω ^^ being respectively injected into the radiating cable in ^ ^ and ^ ^. At a given instant, the subset of GNSS signals associated with a reference point consists of signals that would be received at the same instant at this point in an open sky configuration, i.e. without any propagation obstacle between this point and the sky. As in the first embodiment, the subsets Ω ^^ , resp. Ω ^^ , and Ω ^^ , resp. Ω ^^ , can be defined by subsets of GNSS signals received from satellites visible from the simulated positions ^ ^^ , resp. ^ ^^ in ^ ^ , resp. ^ ^ , and ^ ^^ , resp. ^ ^^ in ^ ^ , resp. ^ ^ , in visibility cones defined in elevation above the horizon, and in azimuth. The four visibility cones being chosen to be disjoint 2 by 2. In the particular embodiment mentioned above, the subset Ω ^^ (resp. Ω ^^) can be defined by a subset of GNSS signals received from satellites visible from the simulated reference point ^ ^^ (resp. ^ ^^ ) in a cone of visibility above the horizon, defined in elevation and azimuth. The cones of visibility of summits ^ ^^ , ^ ^^ , ^ ^^ , ^ ^^ corresponding to the simulations of GNSS signals injected in ^ ^ , ^ ^ , ^ ^ , ^ ^ are chosen to be disjoint. Advantageously, it will be possible to provide that the directions of the visibility cones have between them an angular difference in azimuth and / or elevation greater than a threshold value. We will note ^ ^ ^ ^ , ^ = ^ = 1,2, the synthetic GNSS signals injected at each end of the radiating cable ^ , i.e. belonging to the subset Ω ^ ^ ^ and ^ ^^ , ^ = 1, … , the corresponding simulated satellites. We will assume that ^ ^ , ^ ^ ≥ 1 and that ^^ + ^ ^ + ^ ^ ≥ 4 to enable the GNSS receiver to perform pseudorange measurements in a conventional manner. As in the first embodiment, the means 310 for generating the synthetic GNSS signals are synchronized with the time of a real GNSS signal. Furthermore, the signals provided by the generating means may be shifted in time, in order to compensate for the respective propagation times in the supply cables (not shown) connecting the simulator and the ends Synthetic GNSS signals ^ ^ ^ ^ , ^ = 1, … , of the subset Ω ^^ are injected into the radiating cable 370 in ^ ^ and spread there in the direction of ^ ^ while being radiated radially along the cable. Similarly, synthetic GNSS signals ^ ^ ^ ^ , ^ = 1, … , ^ ^ of the subset Ω ^^are injected into the radiating cable 370 in ^ ^ and spread there in the direction of ^ ^ while being radiated radially along this same cable. By definition of synthetic GNSS signals ^ ^ , ^ = 1, … , ^ = of the subset Ω ^^ , a GNNS receiver receiving simulated GNSS signals, directly at the output of the simulator 110, as injected in ^ ^ ,and equipped with the same internal clock as the simulator, would measure pseudodistances ^ ^ ^ ^ relating to the distances between the position located at the reference point ^ ^^ and the position of the satellites ^ ^ ^ ^ , ^ = 1, … , visible in the associated visibility cone. Thus, a GNSS signal receiver located at point ^, for example part of a user's mobile terminal, measures the pseudodistances, relative to the simulated reference positions ^ ^^ , ^ = 1,2 and ^ ^^ , ^ = 1,2 , and to the simulated satellites [Math.8] [Math.9] with the same notations as before and where ^ ^^ is the distance separating the point ^ ^ and the orthogonal projection of ^ onto the second radiating cable; ^ ^ = is the speed factor of the second radiating cable, and ^ ^ ^ ^ is measurement noise. If we neglect measurement noise ^ ^ ^ ^ ^ and ^^ ^ , and similarly to equation (2), the deviations between the pseudodistances measured by the GNSS receiver and the reference pseudodistances are given by: [Math.10] As in the first embodiment, the measured pseudodistances, ^^ ^ ^ ^ and ^^ ^ ^ ^ are directly provided by the GNSS receiver, and the reference pseudodistances, ^ ^ ^ ^ and ^ ^ ^ ^are known to the mobile terminal, the different variants described in the context of the first embodiment also being applicable to the second embodiment. Whatever the embodiment variant, the local coordinates ^^ ^^ , ^ ^^ , ^ ^^ ^ ends ^ ^ ,^ = 1.2 of the first radiating cable as well as those ^^ , ^ ^^ , ^ ^^ ^ of the ends ,^ = 1.2 of the second radiating cable known to the mobile terminal. The mobile terminal solves a system of + ^ ^ navigation where the distances ^ ^ = ^ ^^ (resp. ^ ^ − ^ ^ = ^ ^^ ), ^ ^ = ^ ^^ (resp. ^ ^ − ^ ^ = ^ ^^ ), ^, and the clock deviation ^ are unknowns: [Math.12] [Math.13] [Math.15] The system of navigation equations (8-1) to (8-4) is a system of at least 4 equations with 4 unknowns, ^^ , ^ ^ , ^, ^. It can be solved in a classical way as in the first embodiment. For example, the pseudodistance deviations, Δ^ ^ ^ ^ and Δ^ ^ ^ ^ can be averaged over the subsets Ω ^^ and Ω ^^ , respectively associated with the ends ^ ^ and ^ ^ of the first cable, according to (4-1) and (4-2). Similarly, the pseudodistance deviations Δ^ ^ ^ ^ ^ and Δ^^ ^ can be averaged over the subsets Ω ^^ and Ω ^^ , respectively associated with the ends ^ ^ and ^ ^ of the second cable: [Math.16] [Math.17] In a similar way to equation (5), we then deduce the abscissas on the axes of the two radiating cables: [Math.18] [Math.19] However, unlike the first embodiment, the second mode makes it possible to determine the ordinate ^ and the clock deviation ^ of the GNSS receiver with the synthetic GNSS signals, namely: [Math.20] [Math.21] The presentation of the second embodiment was made under the assumption that the two radiating cables were rectilinear, coplanar and parallel. However, those skilled in the art will understand that these constraints can be relaxed and that in practice it is sufficient for the cables to be georeferenced, that is to say that their curves are known in space. Indeed, in application of the first embodiment, it is possible to determine the curvilinear coordinates of the orthogonal projections of the point , respectively on the first and second radiating cables. The distance ^ can then be estimated from: [Math.22] where (^ ^^, ^ ^^ , ^ ^^ ) and (^ ^^, ^ ^^ , ^ ^^) are the respective Cartesian coordinates of the orthogonal projections of point ^ onto the first and second radiating cables, deduced from the estimation of the distances ^ ^ and ^ ^ . Figs. 4A and 4B schematically illustrate an example of an open sky partition that can be used in the implementation of a positioning method according to the second embodiment of the invention. 410 shows an open sky configuration in top view showing a satellite constellation at a given time. This configuration is here partitioned into four quadrants, 411, 412, 413, 414 corresponding for example respectively to the NW, NE, SW and SE directions. Fig. 4B illustrates the first and second radiating cables in the indoor environment and the allocation of satellites / GNSS signals to the ends of each of these cables. It is verified that the subsets Ω ^^ , ^ = 1,2 and Ω ^^, ^ = 1,2, are indeed disjoint and that each of them comprises at least one element. Fig. 5 schematically represents a positioning method according to the first embodiment of the present invention. We are here in the context of a positioning system using a radiating cable as represented in Fig.1. In a first step, 510, a satellite constellation ^ is partitioned into two disjoint subsets, each subset ^ ^^ being associated one-to-one with one end of the cable, ^ ^ , the satellites of this subset all being visible from the reference point ^ ^^ , in an open sky configuration. In step 520, we generate for each end ^ ^ , ^ = 1,2, a subset of synthetic GNSS signals, , ^ = 1, … , ^ ^ ^ , corresponding to the satellites of the subset ^ ^^ which would be received at the reference point ^ ^^at time ^, in open sky configuration. The generated synthetic GNSS signals are injected at each end of the radiating cable ^ ^ associated. In step 530, the GNSS receiver of the mobile terminal measures the pseudodistances, ^^ ^ ^ ^ , corresponding to the synthetic GNSS signals received, after propagation in the radiating cable, i.e. ^ ^ ^ ^ , ^ = 1, … , ^ ^ , ^ = 1.2. In step 540, the mobile terminal calculates the deviations Δ^ ^ ^ ^ between the pseudodistances ^^ ^ ^ ^ measured by the GNSS receiver in the previous step and the corresponding reference pseudodistances, ^ ^ ^ ^ , obtained by calculation. In step 550, the terminal solves a system of navigation equations ((3-1), (3-2)) giving the position of the point ^ of the mobile terminal along the radiating cable, namely the distance ^ , e ^ ^ ^ n as a function of the deviations Δ^ ^^ and Δ^^ ^between measured pseudodistances and reference pseudodistances. The distance ^ ^ is the distance separating the orthogonal projection of point ^ on the cable from its end ^ ^. For example, the resolution of the aforementioned system of navigation equations may be done according to (5). In step 560, the position of the mobile terminal is estimated from the solution of the system of navigation equations obtained in the previous step. For example, if the cable is straight, it may be determined in a relative manner with respect to the coordinates of the ends of the radiating cable and the coordinate of the orthogonal projection of the position ^ onto this cable. If the cable is curvilinear, it may be determined from the knowledge of the curve described by the cable in space and the curvilinear coordinate of the projection of the position ^ onto this cable. Fig. 6 schematically represents a positioning method according to a second embodiment of the present invention. Here, we are in the context of a positioning system using a pair of radiating cables as shown in Fig. 3.In step 610, a satellite constellation ^ is partitioned into four disjoint subsets, each subset ^. ^^ (resp. ^ ^^ ) being associated in a one-to-one manner with one end of the first radiating cable, ^ ^ (resp. of the second radiating cable ^ ^ ). The satellites of the subassembly associated with a cable end are all visible from a simulated reference point ^ ^^ (resp. ^ ^^ ), in an open sky configuration. In step 620, we generate for each end ^ ^ of the first cable, (resp. of the second cable) a subset of GNSS signals corresponding to the satellites of the subset ^ ^^ , (resp. ^ ^^ ) which would be received at the reference point ^ ^^ (resp. ^ ^^ ) at time ^, in open sky configuration. The generated synthetic GNSS signals are injected at the associated ends ^ ^ (resp. ^ ^) of the first (resp. second) radiating cable. In step 630, the GNSS receiver of the mobile terminal measures the pseudodistances, ^^ ^ ^ ^ (resp. ^^ ^ ^ ^ ) corresponding to the synthetic GNSS signals received from the first (resp. second) radiating cable, i.e. ^ ^ , ^ = = (resp. In step 640, the mobile terminal calculates the deviations Δ^ ^ ^ ^ ^ (resp. Δ^^ ^ ) between the pseudodistances ^^ ^ ^ ^ ^ (resp. ^^^ ^ ) measured by the GNSS receiver in the previous step and the corresponding reference pseudodistances, ^ ^ ^ ^ ^ (resp. ^^ ^ ), obtained by calculation. In step 650, the GNSS receiver terminal solves a system of navigation equations ((8-1) to (8-4)) giving, on the one hand, the positions of point ^ of the mobile terminal along the first and second radiating cables and, on the other hand, the distances from point ^ to these cables, as a function of the deviations Δ^ ^ ^ ^ , Δ^ ^ ^ ^, Δ^ ^ ^ ^ , Δ^ ^ ^ ^ between the observed pseudodistances and the reference pseudodistances and the distance ^ separating the two cables. For example, the resolution of the system of navigation equations may be done according to relations (10-1) to (10-4). Finally, in step 660, the position of the mobile terminal is estimated from the solution of the system of navigation equations obtained in the previous step. For example, it may be determined in a relative manner with respect to a first origin taken at one end of the first cable (or the second cable). As mentioned previously, the second embodiment extends to the case of curvilinear radiating cables, the coordinates of ^ ^^ ,^ ^^of the projection of the position of the mobile terminal on the axes of the cables being replaced by the curvilinear coordinates along these cables. Those skilled in the art will understand that the invention also extends to the case of at least three non-coplanar radiating cables, making it possible to estimate the three-dimensional position of the receiver in question.

Claims

CLAIMS 1. Method for positioning a mobile terminal in an indoor environment in which at least one first radiating cable is located having a first end and a second end, characterized in that: - at least one part of a satellite constellation is partitioned (510) into a first and a second disjoint subset of satellites, which would be respectively visible from a first point and a second reference point, in an open-sky configuration; - for the first (resp. the second) end (520) a first (resp. a second) subset of synthetic GNSS signals corresponding to those which would be received, in an open-sky configuration, by the first (resp. the second) reference point, coming from satellites belonging to the first (resp. the second) subset, the first (resp. the second) end injecting into the radiating cable the first (resp.the second) subset of synthetic GNSS signals thus generated; - the GNSS receiver of the mobile terminal measures (530) the pseudodistances corresponding to the synthetic GNSS signals received from the radiating cable; - the deviation between the pseudodistance measured by the GNSS receiver and a reference pseudodistance calculated for the first (resp. second) reference point is determined (540) for each synthetic GNSS signal of the first (resp. second) subset; - the position of the mobile terminal is estimated (550-560) along the cable from the deviations of the pseudodistances thus obtained and from a georeferenced curve, describing the radiating cable.

2. Method for positioning a mobile terminal according to claim 1, characterized in that the position of the mobile terminal along the radiating cable is obtained by solving (550) a system of navigation equations giving the deviations of the pseudodistances as a function of said position.

3. Method for positioning a mobile terminal according to claim 2, characterized in that the system of equations is given by: ^ ^ + ^ + ^ ^ ^ ^ = Δ^ ^^ , ^ = 1, … , ^ ^ where ^ ^ is the ratio between the speed of light and the speed of propagation of an electromagnetic wave in the radiating cable, ^ ^ is the position of the mobile terminal along the radiating cable taking the first end as the origin, ^ ^is the length of the radiating cable, ^ is the distance to the radiating cable, ^ is the clock offset of the GNSS receiver relative to the clock used to generate the synthetic GNSS signals, Δ^ ^ ^ ^ , ^ = are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, obtained for the synthetic GNSS signals of the first subset, Δ^ ^ ^ ^ , ^ = 1, … , ^ ^ , are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, obtained for the ^ ^ synthetic GNSS signals of the second subset. 4.Method for positioning a mobile terminal according to claim 3, characterized in that the position of the mobile terminal along the radiating cable ^ where Δ^ ^^ = ^ ^ are respectively the average of the pseudodistance deviations on the first and second subsets. 5.Method for positioning a mobile terminal in an indoor environment in which at least a first radiating cable and a second radiating cable are located, each radiating cable having a first end and a second end, characterized in that: - a partition of at least a part of a satellite constellation is carried out (610) into a first, a second, a third and a fourth disjoint subsets of satellites, which would be respectively visible from a first, a second, a third and a fourth in an open sky configuration; - a first (resp. a second) subset of synthetic GNSS signals corresponding to those which would be received, in an open sky configuration, by the first (resp.the second) reference point, originating from satellites belonging to the first (resp. second) subset, the first (resp. second) end of the first cable injecting into the first radiating cable the first (resp. second) subset of synthetic GNSS signals thus generated; - a third (resp. fourth) subset of synthetic GNSS signals corresponding to those which would be received, in an open-sky configuration, by the third (resp. fourth) reference point, originating from satellites belonging to the third (resp. fourth) subset, the first (resp. second) end of the second cable injecting into the second radiating cable the third (resp. fourth) subset of synthetic GNSS signals thus generated;. - the GNSS receiver of the mobile terminal measures (630) the pseudodistances corresponding to the synthetic GNSS signals received from the first and second radiating cables; - the deviation between the pseudodistance measured by the GNSS receiver and a reference pseudodistance calculated for the first (resp. second, third, fourth) reference point is determined (640) for each synthetic GNSS signal of the first (resp. second, third, fourth) subset; - the position of the mobile terminal is estimated (650-660) along the first and / or second cable and the distance to the first and / or second cable from the deviations of the pseudodistances thus obtained and from georeferenced curves, describing respectively the first and second radiating cables. 6.Method for positioning a mobile terminal according to claim 5, characterized in that the position of the mobile terminal along the and / or second radiating cable and the distance to the first and / or second cable is obtained by solving (650) a system of navigation equations giving the deviations of the pseudodistances as a function of the position of the mobile terminal, respectively along the first cable and the second radiating cable as well as its distance respectively to the first cable and the second radiating cable. 7.Method for positioning a mobile terminal according to claim 6, characterized in that the first and second radiating cables are parallel and. separated by a distance ^ and that the system of equations is given by: where ^ ^ , ^ ^ is the ratio between the speed of light and the speed of propagation of an electromagnetic wave respectively in the first and second radiating cables; ^ ^, ^ ^ is the position of the mobile terminal respectively along the first and second radiating cables, taking the first end of these cables as the origin; ^ ^ , ^ ^ is the respective length of the first and second radiating cable, ^ is the distance from the user to the first radiating cable, ^ is the clock offset of the GNSS receiver relative to the clock used to generate the synthetic GNSS signals; ^ = 1, … , ^ ^ are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, respectively obtained for the synthetic GNSS signals of the first subset and ^ synthetic GNSS signals of the second subset ^ ^ us-set; Δ^ ^^ , ^ = 1, … , and Δ^ ^ ^ ^ , ^ = 1, … , ^ ^are the deviations between the pseudodistances measured by the GNSS receiver and the corresponding reference pseudodistances, respectively obtained for the M 1 synthetic GNSS signals of the third subset, and the M 2 synthetic GNSS signals of the fourth subset.

8. Method for positioning a mobile terminal according to claim 7, characterized in that the position of the mobile terminal along the first, resp. of the second radiating cable is given by: are respectively the average of the pseudodistance deviations on the first and second subsets, and are respectively the average of the pseudodistance deviations on the third and fourth subsets.

9. Method for positioning a mobile terminal according to claim 8, characterized in that the distance from the mobile terminal to the first radiating cable is given by:

10. Method for positioning a mobile terminal according to any one of the preceding claims, characterized in that the synthetic GNSS signals are generated by means of a simulator receiving at least one real satellite signal from a satellite of said constellation, via an antenna located in an external environment, the synthetic GNSS signals being synchronized with respect to the real satellite signal.

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