Probabilistic ray tracing-assisted positioning

Abstract

The present invention relates to a method and apparatus for determining data representing the location of user equipment in an environment comprising a collection of base stations. According to the present invention, the method is N reception angles ([y1,...,y N Step (S01) of obtaining a vector of ]), wherein each angle of the vector corresponds to the reception angle of the signal at a given base station of the set of base stations, Step (S02) to obtain N probability distributions, where each probability distribution is obtained from the result of ray emission in the 3D representation of the environment, The process includes the step (S03) of calculating at least one probability of the position of the user device as a function of the N probability distributions and the N angle vectors.

Description

[Technical Field]

[0001] This disclosure relates to a positioning method and a positioning device. Priority is claimed in European Patent Application No. 23306926.9, filed on 8 November 2023, the contents of which are incorporated herein by reference. [Background technology]

[0002] Standard positioning systems rely on so-called "line of sight" (LOS) measurements. For example, as shown in Figure 1, when three base stations ("BS") estimate the angle of arrival (AoA) of a reference signal transmitted by user equipment ("UE") such as a telecommunications terminal, a typical triangulation method can be implemented as follows: The server recognizes the positions of two BS and the measured AoA, and finds the intersection of three rays emanating from the BS in the direction of the measured AoA. The estimated position of the UE is this intersection.

[0003] Nevertheless, the received signal at the base station (BS) may be "out of line of sight" (NLOS). The signal may have been reflected before reaching the BS. In this case, the measured AoA will indicate the direction of the last reflecting object, rather than the actual direction of the UE. Consequently, the standard triangulation described above is insufficient for positioning operations.

[0004] One solution to this problem is to use online ray tracing, where, given measured areas of area (AoA), ray tracing is performed along these AoA directions. The intersection of the rays is the estimated position. This technique is called "inverse ray tracing," and its principle is shown in Figure 2. Alternatively, geometric equations may be considered instead of conventional ray tracing.

[0005] Of course, the measurements may not be perfectly accurate, and the measured AoA may be damaged by some noise. Several rays can be fired at intervals around the measured AoA. The width of the interval considered is twice the estimated standard deviation of the estimated AoA value. A least-squares solution can also be used, assuming that the estimated AoA has iid Gaussian noise.

[0006] However, in all of these previously known techniques, conventional ray tracing-assisted positioning did not adequately consider the statistics of the measurements, and the performance was not optimal. For this reason, a method for determining the transmitter's position has been proposed in the past, which involves calculating the statistical properties of AoA and using a 3D model of the environment to obtain several weighted paths, which are then used to determine the transmitter's position.

[0007] However, while relatively efficient, this previously proposed method required firing a very large number of rays during the online Monte Carlo ray firing phase in the 3D model of the environment. This means that a large amount of resources must be available, and that the base station must possess these resources, which is usually not the case. [Overview of the project]

[0008] This disclosure is intended to improve the situation.

[0009] To that end, the present invention proposes a method for determining an estimate of the location of a transmitter in an environment comprising at least one receiver. More specifically, the present invention discloses a method for determining data representing the location of a user device in an environment including a set of base stations, the method being described as follows: A step of obtaining a vector of N reception angles of a signal transmitted by the user device, wherein each angle of the vector corresponds to the reception angle of the signal at a given base station in a set of base stations. A step of obtaining N probability distributions, wherein each probability distribution is obtained from the result of ray emission in a 3D representation of the environment, calculating at least one probability of the position of the user equipment as a function of the N probability distributions and the vector of the N angles;

[0010] According to the present disclosure, the step of obtaining the N probability distributions includes loading a set of probability distributions from a data structure.

[0011] According to the present disclosure, the step of obtaining the N probability distributions further includes selecting a set of one probability distribution for each reception angle of the signal from the set of probability distributions.

[0012] According to the present disclosure, the step of obtaining the N probability distributions includes calculating a set of probability distributions as a function of virtual reception angles for each base station.

[0013] According to the present disclosure, the step of calculating a set of probability distribution densities as a function of virtual reception angles for each base station includes repeating at least once the following steps, that is, determining one virtual reception angle of the signal from among a plurality of possible reception angles; calculating one probability distribution as a function of the virtual reception angle; saving the probability distribution associated with the virtual angle in a data structure, including repeating at least once.

[0014] According to the present disclosure, the step of calculating the probability distribution as a function of the virtual reception angle is using a Monte Carlo algorithm to emit at least one ray in a 3D representation of the environment, wherein the AoD of at least one ray is sampled as a function of the virtual angle; constructing a map of points where at least one ray is emitted in the 3D representation of the environment and at least one ray intersects a plane at a predetermined height in the 3D representation of the environment; Calculating a parametric distribution of the point within the map of the point and distributing a probability distribution related to a virtual three-dimensional angle;

[0015] According to the present disclosure, the step of calculating the position of the user equipment as a function of the N probability distributions and the vector of the N angles includes: Calculating a global probability distribution by multiplying the N probability distributions; Determining a maximum value representing the most likely position of the user equipment from the global probability distribution;

[0016] According to the present disclosure, the step of obtaining N sets of probability distributions is, for each angle of the vector of N angles: Using a Monte Carlo algorithm to emit at least one ray in a 3D representation of the environment, wherein the AoD of the at least one ray is sampled as a function of the angle; Constructing a map of points where at least one ray is emitted in the 3D representation of the environment and at least one ray intersects a plane at a predetermined height in the 3D representation of the environment; Calculating a parametric distribution of the point within the map of the point and distributing a probability distribution related to an angle;

[0017] <UNK> The present disclosure also aims at a computer program including instructions that cause an implementation of the method defined above when such instructions are executed by a processor.

[0018] The present disclosure also aims at a device for determining the position of a transmitter in an environment comprising a plurality of receivers each having a known position, the device comprising an interface for receiving measurements executed by the receivers and a processor for implementing the method defined above.

[0019] Further details are presented in the following specification with reference to the accompanying drawings.

Brief Description of the Drawings

[0020] [Figure 1] This diagram illustrates the principle of positioning based on the angle of arrival measurement in the case of line of sight (LOS). [Figure 2] This diagram shows the use of ray tracing to improve positioning. [Figure 3] This figure shows an example of an environment including three receivers Rx (for example, three base stations BS for a radio frequency environment) and obstacles. [Figure 4] This diagram shows a transmitter Tx that transmits a signal (e.g., a radio frequency signal) and is located. [Figure 5] This diagram shows the steps involved in the receiver performing the angle of arrival measurement. [Figure 6] This diagram illustrates how paths are obtained using the geometric shape of the environment, with each path having a different weight depending on the statistical properties of the corresponding AoA. [Figure 7] This is a diagram showing the estimated location of the transmitter. [Figure 8] This figure shows the steps of the positioning method according to this disclosure. [Figure 9] This figure shows a map of points obtained when a ray is fired from a single BS with a given AoA and given error statistics, where the ellipses represent a fitted GMM (Gaussian Mixture Model) on this map of points. [Figure 10] This figure shows the cumulative density function of positioning errors due to both a small number of and a large number of projectile rays. [Figure 11] An example of an embodiment of a device that performs the above method is shown. [Modes for carrying out the invention]

[0021] The following description considers a scenario in which a transmitter (or Tx), for example, a user device (UE) in the radio frequency environment of this example, transmits a positioning signal to one or more receivers (Rx), such as a base station. The purpose of the base station is to locate the UE with the help of a 3D model of the environment (e.g., via ray tracing). Thus, the geometric properties of the environment (e.g., obtained by ray tracing simulation) are intended to be utilized here. The statistical properties of the measurements can also be used to enhance positioning in the radio system.

[0022] As mentioned above, conventional methods can partially solve the problem of positioning a user device by several base stations in an environment by using a model of this environment and by using inverse ray tracing to identify the location of the user device. These methods are useful in situations where the user device cannot transmit its own location (e.g., a closed or partially closed environment, lack of global positioning signals, etc.). More specifically, such methods use uplink angle of arrival (AoA) measurements of signals transmitted by the user device and a three-dimensional digital twin of the environment, as will be described in detail below. By firing rays in a Monte Carlo method according to the AoA statistics, it becomes possible to generate a map of points for each BS. These map of points represent the intersection of rays with the XY plane at a given height of the UE and are then combined.

[0023] Figures 3, 4, and 5 illustrate the principle of AoA measurement in exemplary situations. Typically, consider a simple environment with only one obstacle and four walls, where three receivers are deployed (the positions of these Rx are known), as shown in the example in Figure 3. The environment is therefore fully modeled, and a 3D model is obtained that includes geometric properties such as the position, orientation, and dimensions of the walls and obstacles. There may be a need to locate a transmitter whose position is unknown within this environment. As shown in the example in Figure 4, this transmitter Tx transmits a radio signal. Each receiver Rx receives the radio signal and measures the angle of arrival (AoA) based on the received signal. The AoA measured at Rx BS1 is along the direction of the top wall, because obstacles in the environment may block the direct path between the first receiver BS1 and the transmitter UE, while Rx BS2 and BS3 measure the AoA of the direct path between them and Tx UE (see Figure 5). However, the measured AoA may be incorrect (due to noise and / or interference, etc.). As shown in Figures 6 and 7, Monte Carlo ray tracing is performed to determine the position of the UE using a 3D representation of AoA and the environment. The angle of arrival (AoA) becomes the angle of departure (AoD) of the ray, taking error into account. For example, the ray tracing simulation may be used with a 3D model of five rays, as shown in Figure 6, where each ray starts at Rx BS1 at some angle, defined as a function of error. Combining paths with associated weights from Rx BS1, BS2, and BS3, the estimated position of Tx UE can be calculated, as shown in Figure 7. For example, a default height is taken into account, and the intersection of rays with a plane at height provides a map for each point of the BS. The maps of points from all BS are joined together, making it possible to obtain a combined map of points, and the position of the UE is determined by the coordinates of the point where the most points from each BS converge.

[0024] While this method yields very good results, it turns out that a considerable number of rays need to be emitted according to AoA statistics to obtain good accuracy in determining the actual position of the user's equipment. This may be undesirable or unavailable depending on the operational implementation conditions, and may require increased power or other resource consumption.

[0025] Therefore, the inventors propose fitting a parametric distribution, such as a Gaussian mixture model (GMM), to each map of points at each base station. For a given XY plane, the parametric distribution is a two-dimensional multivariate distribution. The positional probability of the UE can be calculated by multiplying by the probability density function (also called pdf) obtained for each BS. This method produces an algorithm that is robust to rays with a reduced number of firings, which consequently means reducing the number of rays fired while maintaining the same level of results, or, as described below herein, it is possible to limit the computational resources used.

[0026] As a result, the proposed method, as explained in relation to Figure 8, is used to locate a given user device. The N receiving angles ([y1,...,y N Step (S01) of obtaining a vector of ]), wherein each angle of the vector corresponds to the signal reception angle at a given base station of the set of base stations, Steps include obtaining N probability distributions, each of which is derived from the results of ray firing in a 3D representation of the environment (S02, step of obtaining N probability distributions), The method includes the step (S03) of calculating the probability of at least one position of the user device as a function of the vector of the N probability distributions and the N angles.

[0027] The angles may be two-dimensional or three-dimensional, depending on the situation. N angles of a vector can be obtained from N corresponding base stations. In a modified example, a base station can capture two or more independent reception angles of a signal and thus transmit several reception angles of a single signal.

[0028] These probability distributions (or sets thereof) based on parametric distributions can be fitted and stored during the offline phase, thus avoiding ray emission during the online phase and thus reducing the amount of resources (power, time) required to provide the position of the user device. In fact, during the online phase, for a given measured AoA, the corresponding parameters of the distribution are directly restored from the stored table, and signal processing is performed without the need to emit rays. This significantly reduces the computational complexity of the positioning method.

[0029] As a result, the proposed method can be implemented online (i.e., in real time), meaning that the parametric probability distribution is calculated in real time (i.e., after obtaining AoA measurements from the user equipment). The proposed method can also be implemented partially offline, where the parametric probability distribution is calculated and stored offline from a set of predefined parameters (number of rays emitted, selected AoA, and assumed error of AoA). The storage device is accessible from the device implementing the online portion of the method (e.g., one of the base stations or a central station), and the parametric probability distribution is used online along with the current AoA measurement of the user equipment's signal to pinpoint the user equipment's location.

[0030] Whether or not this method is performed entirely or partially online, it includes, in at least one example, the step of fitting a parametric probability distribution, such as a Gaussian mixture model (GMM), to the map of points acquired for each BS. An example of a corresponding fitted GMM with a map of points and four clusters is shown in Figure 9 below. This figure shows the results of ray firing in Monte Carlo for a given BS, along with default AoA measurements and default AoA error statistics (provided as parameters). The ellipses represent the four clusters, and the distance separating the ellipses within a given cluster represents the spread of the distribution. In a given cluster, the closer this distance, the more accurate the location of the point. Given the measurements performed by each BS, the probability that an UE is at a particular location is obtained by multiplying each BS by the probability density function (pdf).

[0031] The method of disclosure can be implemented in two different modes. In the first mode, rays are fired during the online phase, their distribution is calculated during the online phase, and their positional probabilities are obtained by multiplying them by the probability density function of each BS. This has the advantage of being more robust to a reduction in the number of rays fired during the online phase. The second mode is divided into offline and online phases. First, rays are fired for each BS and for the set of discretized AoA, and a map of points for each discretized AoA is obtained. A parametric distribution is fitted, and the parameters are saved. Then, in the online phase, the AoA is measured by each BS, and the corresponding distribution parameters in the saved table are restored. The distribution is then used in the same way as in the first implementation mode. This has the advantage that ray firing is not required in the online phase. The following describes all embodiments of the disclosure method.

[0032] For simplicity, a general description of positioning a device according to the inverse ray tracing positioning method is provided. For this purpose, the height of the UE to be localized is known or estimated. According to the general method, the AoAy is measured at one BS. i Given a given direction, a ray is executed from the BS in this direction; that is, the measured AoA becomes the ray's starting angle (AoD), and the intersection of the projected ray with the drawing yields a map of points on one BS. This process is repeated for all BS, and the intersection of rays (on the map of points) is the estimated position of the UE.

[0033] If the AoA measurement is noisy, the following approach can be taken: for each BS, the angle of the emitted ray is sampled according to the statistics of the AoA measurement error. This method is called the Monte Carlo method. In short, the result of this ray emission is a set of points in the xy plane at the height of the UE. These points correspond to the positions where the emitted ray crosses the xy plane, providing a map of points. As explained earlier, this method requires emitting a large number of rays to obtain good results.

[0034] As explained earlier, to avoid the need to fire from a large number of points, it has been proposed to group the points on the map into clusters and, in effect, assign probabilities to those points.

[0035] The following paragraphs disclose a precise description of embodiments of the proposed method.

[0036] Statistical Modeling and Notation Let X be a random variable representing the position of the UE. Let Θ be a random variable representing the exact AoA of the signal, and let Y be a random variable representing the BS measurement value of AoA. Regarding notation, p(θ|y) is used for p(Θ=θ|Y=y), and similarly, p(x|y) is used for p(X=x|Y=y). The distribution p(θ|y) is a statistical value of the uplink AoA measurement error, for example, p(θ|y)~N(θ|σ 2) represents. n,

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[0037] Probability distribution fitting To address the accuracy issues that arise with a small number of rays, it is proposed to fit a 2D (two-dimensional) probability distribution to a map of points obtained when rays are fired from a single BS using the Monte Carlo method. Parametric probability density estimation involves selecting a common distribution and estimating the parameters of the density function based on a data sample. Nonparametric probability density estimation involves estimating the probability distribution as a histogram, for example, via binning techniques.

[0038] In the techniques disclosed herein, one distribution is fitted to the map obtained by each BS (for example, in the case of three BS, there is one distribution for each BS, resulting in three distributions). Using a continuous parametric distribution makes it possible to have a probability value for each location in the scene.

[0039] p(x|y i ) is the measured value y i This is defined as the probability that the uplink signal resulting from this was transmitted from position x. The result of the fitting process is therefore, for each BSi, the distribution p(x|y i )

[0040] Thus, representing this distribution as a function of p(θ|y i )(the AoA statistics of one BS), we have

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[0041] The above terms emphasize that two special cases should be considered 1 One ray crosses the xy plane several times, and it is possible to consider focusing on the term p(x|θ). When the ray corresponding to AoD θ crosses the plane xy only once at position x1, p(x1|θ) = 1 and p(x k |θ) = 0 for all other x k . When the ray crosses the plane xy at two positions x1 and x2, p(x1|θ) = p(x2|θ) = 0.5 and p(x k |θ) = 0 for all other x k . Thus, generally, the probability p(x k [[ID=2⑧]]|θ) of the intersection position x k is

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[0042] As described above, the goal is to fit the probability distribution p(x|y i ) to the set of points obtained when firing rays by the Monte Carlo method. Thus, since AoD is sampled according to p(θ|y i ), the above equation (1) becomes

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[0043] One possibility for performing the fitting is to use a Gaussian mixture model (GMM), although other distributions may also be considered. As mentioned earlier, Figure 9 shows an example of a fitted GMM for a set of points. The weighting described above ("one ray crosses the xy plane several times") can be readily taken into account in the GMM fitting algorithm as needed.

[0044] This process of fitting the distribution is repeated for each BS. As a result, the measurement y performed on each of the n BS is i There are n p(x|y) values, one for each. i ) Obtain the distribution.

[0045] Use a fitted distribution for positioning. The following paragraphs demonstrate that the location probability estimate can actually be obtained by using the product of fitted density functions, as shown by equation (3.5) below. A common method of positioning is to marginalize with respect to θ to obtain a probability

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[0046] Alternatively, the following:

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[0047] Similarly,

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[0048] As a result, the distribution p(x|y i ) If so all y i By multiplying by the probability density function

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[0049] This results in two main implementation modes, which are described below. If p(x|y), the positioning problem can be derived from maximum posterior (MAP) estimation as follows:

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[0050] Using fitted distributions in data fusion If additional data is available, data fusion can be used to obtain better positioning accuracy. Assume that in addition to the calculated data y above, there is additional data z. Fusion can be considered as follows:

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[0051] Based on the mathematical explanation above, two implementation modes of the proposed method can be derived. The first mode is a fully online mode, where, unlike existing methods, the number of rays fired must be limited. The second mode is a partially offline mode, where some calculations are performed offline to prepare some of the results available in the database during the online portion (database retrieval). In both cases, the amount of resources used online is limited, improving the accuracy of the method.

[0052] First implementation mode In this first implementation mode (10, Figure 8), position estimation is achieved as follows:

[0053] AoA measurement error σ 2 This is estimated offline by each BS. Then, in the online phase, S01. Uplink AoA measurement y i This is performed by each BS, and therefore the 3D angle ([y1,...,y N The vector (v) of ]) is delivered. S02. The step of obtaining the corresponding set (spdd) of probability distributions is: S021. Each BS is p(θ|y i Using the AoD angles sampled according to ), a ray is emitted using the Monte Carlo method (or the central device emits a ray for each BS), For each S022.BS, a map is constructed of points where the ray crosses the xy plane. S023. For each map, a parametric distribution (such as GMM) p(x|y i This includes the calculation of ). S03. The step of calculating the position of the user equipment (S03) is: S031.Distribution

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[0054] Figure 10 shows the positioning accuracy obtained in both cases: when the number of rays emitted per BS is small (100) and when the number of rays emitted per BS is large (10,000). A cumulative distribution function of positioning error is used. Regarding the GMM fitting algorithm, for example, a standard GMM fitting algorithm with several modes (clusters) is implemented, and the model with the lowest Akaike information criterion is retained. Note that in both cases (100 rays and 10,000 rays), there is no significant difference in the positioning accuracy of the UE. The distribution fitting method makes it possible to maintain performance with a reduced number of rays. Therefore, this method makes it possible to reduce the resources required to obtain the UE's position while maintaining the same accuracy of the results.

[0055] Second implementation mode The first implementation mode is robust to a reduced number of rays, but still requires ray firing and distribution fitting during the online phase. This still induces very high computational complexity and potential latency, although these can be reduced.

[0056] This problem can be addressed by the following second implementation mode. In short, the main step is to measure the possible AoAy during the offline phase. i The distribution is calculated and saved for each. Then, in the online phase, each BS is angle y i Measure the corresponding conserved distribution p(x|y i ) is recovered. Then, step S03 is performed, which includes steps S031 and S032 of the first implementation mode. The method is also described in relation to Figure 8, and the method includes the following:

[0057] In the offline phase, AoA measurement error σ 2 These are estimated offline by each BS or system. Next, the offline preparation (S00) of the set of probability distributions is performed as follows: For S001 3D angles, the possible 3D angles [0, 2π[ × [0, π[] are discretized. This discretization step may be optimized as a function of impossible reception angles, taking into account the positioning of the BS, for example, by not considering angles where reception is impossible (e.g., behind the BS if the BS is fixed to a wall). The discretization step is to divide the interval into degrees, and for example, [0,π[ can be divided into 180-degree intervals. Thus, for a perfect [0,2π[×[0,π[, 360*180=64800 possible 3D angles are obtained. S002 For each BS, and the discretized angle y i For each, p(θ|y i Using the AoD angles sampled according to ( ), a ray is fired using the Monte Carlo method, and a map of the points where the ray crosses the xy plane is obtained. S003 For each map of acquired points, the distribution p(x|y) such as GMM is used. i ) is fitted, and the distribution parameters are stored in the data structure.

[0058] During the online phase, S01. Uplink AoA measurement y i This is performed by each BS, and therefore the 3D angle ([y1,...,y N The vector (v) of ]) is delivered. S02. Distribution p(x k |y i The parameters of ) are restored from the data structure. The vector angle (v) allows the corresponding pre-calculated distribution to be reconstructed from a conserved set of probability distributions prepared in step S00; that is, the entry for obtaining one corresponding probability distribution for a given BS is the measured 3D angle of this BS. S03. The step of calculating the position of the user equipment (S03) is: S031.Distribution

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[0059] As mentioned above, the main advantage of this second implementation mode is that it avoids ray firing and distribution fitting during the online phase. Nevertheless, it is necessary to store the distribution parameters for each possible angle and each possible BS. The estimate of the number of values ​​to be stored is based on several parameters.

[0060] Let N be the number of BS. In the simulation example, N=4. The number of values ​​used to discretize the possible 3D angles is...

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[0061] In the case of a 3D positioning problem (i.e., the user device needs to be positioned in 3D), the proposed method can be repeated for multiple XY diagrams. The objective is then to find the correct XY diagram that gives the Z coordinate. For example, in a modified or feature, one XY diagram can be selected in which one (x,y) position has a higher probability compared to other positions (i.e., an XY diagram in which one cluster is very likely and has low variance). Many techniques for selecting one XY diagram from several available diagrams can be assumed or derived from the proposed method.

[0062] In another variation or feature, the proposed method can also be extended to a 3D positioning problem, as follows: The 3D set of possible locations of the UE may be divided into small cubes, where it is checked whether the cubes intersect with the rays to construct an equivalent map of points. In other words, instead of slicing the 3D environment in several drawings, the environment is sliced ​​into a set of cubes of a predetermined size. The other steps of the method remain unchanged.

[0063] According to another feature or variation, if the antenna diagram / beamforming of the UE is non-uniform, its orientation can be taken into account favorably. As a result, when constructing a map of points via ray tracing, the AoA of the rays at the intersections can be taken into account. In other words, one map is constructed for one orientation of the UE, in which case only points corresponding to rays arriving in the expected orientation are retained. Thus, measurement y i Several maps need to be constructed, one for each orientation of the UE. Then, at least one of the two implementation modes (online only / partially offline) is implemented for each possible orientation, and the model that produces the best likelihood is held. Note that only fitted distributions corresponding to the same orientation should be combined. Combining distributions associated with different orientations is wasteful.

[0064] According to the embodiments described above, each receiver can determine all or part of the location of the user equipment based on the configuration of its own receiver. Furthermore, the determination of the user equipment location may also be performed by a centralized device (which may be one of the receivers Rx) that calculates the location by acquiring the necessary data from the receivers, as described in this disclosure. As shown in Figure 11, the configuration of the device DV affecting the measurement may be an antenna system (AS) coupled to a processing circuit including a processor (PROC) and memory (MEM) via an interface (IN), as described above. Alternatively, supplementarily, or as a variation, the necessary data (e.g., AoA) may also be received via a communication link CL, which enables the device to perform the location determination of this disclosure. The memory stores at least the instructions of the computer program according to this disclosure.

Claims

1. A method for determining data representing the location of a user device in an environment including a collection of base stations, N reception angles ([y １ , . . . , y Ｎ Step (S01) of obtaining a vector of ]), wherein each angle of the vector corresponds to the reception angle of the signal at a given base station of the set of base stations, Step (S02) of obtaining N probability distributions, wherein each probability distribution is obtained from the result of ray emission in a 3D representation of the environment, A method comprising the step (S03) of calculating at least one probability of the position of the user device as a function of the N probability distributions and the N angle vectors.

2. The method according to claim 1, wherein the step of obtaining N probability distributions (S02) includes the step of loading probability distributions from a data structure.

3. The step of obtaining the N probability distributions (S02) is to select from the probability distributions the receiving angle of the signal [y ｉ The method according to claim 2, further comprising the step of selecting one probability distribution for each of the following:

4. The method according to claim 1, wherein the step of obtaining the N probability distributions (S02) includes the step of calculating the probability distribution as a function of the virtual reception angle for each base station.

5. For each base station, the step of calculating the set of probability distribution densities as a function of the virtual reception angle includes at least one iteration consisting of the following steps: The steps include determining a virtual reception angle for one of the multiple possible reception angles for the signal, The steps include: calculating a probability distribution as a function of the virtual reception angle; The method according to claim 4, comprising at least one iteration of the step of storing the probability distribution associated with the virtual angle in a data structure.

6. The step of calculating the probability distribution as a function of the virtual reception angle is, A step of using a Monte Carlo algorithm to emit at least one ray in the 3D representation of the environment, wherein the AoD of the at least one ray is sampled as a function of the virtual angle, The steps of constructing a map of points in the 3D representation of the environment where the at least one ray is emitted and intersects a plane at a predetermined height in the 3D representation of the environment, The method according to claim 5, comprising the steps of calculating the parametric distribution of the points in the map of the points and distributing the probability distribution associated with the virtual angle.

7. Step (S03) of calculating the position of the user device as a function of the N probability distributions and the N angle vectors, The steps include: (S031) calculating the global probability distribution by multiplying the N probability distributions mentioned above; The method according to claim 1, comprising the step (S032) of determining the maximum value representing the most likely location of the user device from the global probability distribution.

8. Step (S02) to obtain the probability distribution of N sets of angles ([y １ , . . . , y Ｎ The angle (y) of the aforementioned vector ｉ ]) each, A step of using a Monte Carlo algorithm to fire at least one ray in the 3D representation of the environment, wherein the AoD of the at least one ray is the angle ([y ｉ The firing step is sampled as a function of ]), The steps include:

1. At least one ray is emitted in the 3D representation of the environment, and a map is constructed of points where the at least one ray intersects a plane at a predetermined height in the 3D representation of the environment; The parametric distribution of the points in the map of the points is calculated, and the angle ([y ｉ The method according to claim 1, comprising the step of distributing the probability distribution associated with ]).

9. A computer program comprising an instruction, when executed by a processor, causing the processor to implement the method according to any one of claims 1 to 8.

10. An apparatus for determining the position of a transmitter in an environment comprising a plurality of receivers, each having a known position, wherein the apparatus comprises an interface for receiving measurements performed by the receivers, and a processor for implementing the method according to any one of claims 1 to 8.

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