Method for determining the direction of arrival of signal paths on a network of N sensors, computer program and associated device

Abstract

The invention relates to a method for determining the arrival direction of signal paths on an array (2) of N sensors (3), comprising a first estimation, by sparse goniometry, of the vector γ satisfying the equation: where σ2 is the noise level, Rx is the vectorized covariance matrix of the signal x(t) considered at the output of the sensor array, and B is the calibration table of the array, and a deduction of the arrival directions of the paths based on this first estimation; then a second estimation of the vector γ satisfying with with composed of crossed terms, for arrival directions defined as a function of the deduced arrival directions, a second estimation of the arrival directions of the paths as a function of this second estimation of the vector γ. Figure for the abstract: Fig. 1

Description

Title of the invention: Method for determining the direction of arrival of signal paths on a network of N sensors, associated computer program and device Technical field

[0001] The invention lies in the field of goniometry, which is the determination of the direction of arrival of electromagnetic signals (radio-electric or sound). It relates more specifically to the estimation of the direction of arrival of incident signals on a network of several sensors (when the signals are radio-electric for example, the sensors are antennas) whose characteristics are known. The incident signals can come from one or more transmitters. For the same transmitter, the transmitted signal can be received along several propagation paths, giving rise to several incident signals on the network of sensors.The invention aims to carry out this estimation even when the incident signals have the characteristic of being temporally correlated (which may be the case when the signals are multi-paths from the same transmitter) and when the transmitters, for example in large numbers, generate in total a number of paths potentially greater than the number of sensors in the sensor network.

[0002] Multi-path situations giving rise to the presence of correlated paths are encountered for example in urban environments in GSM (Global System for Mobile Communications) or LTE (Long Term Evolution) networks, due to reflections on buildings, or in the context of HF (High Frequency) ionospheric communications. Prior art

[0003] For correlated multipaths in the HF case for example, the signals from each of the transmitters propagate along several paths reflected on the ionospheric layers (at a point RI on the E layer and at a point R2 on the F layer), as illustrated in [Fig.2]. In the particular HF case, the different paths from a transmitter of position E generally arrive at a receiver R with the same bearing 0m and different elevation angles Amp. In the multipaths of the GSM or LTE cases for example, the different paths from a transmitter of position E generally arrive at a receiver R with different bearings 0mp and different elevation angles Amp.

[0004] In [Fig.2], the number of paths represented between the transmitter E and the receiver R is equal to 2: p = 1.2.

[0005] Paths arrive at the receiver R with different propagation times which are proportional to the distance traveled. We will thus have correlated paths when the The difference in propagation time between two paths is inversely proportional to the transmitter bandwidth. This is why paths from an HF transmitter are often correlated with each other. On the other hand, conventional direction finding techniques require interceptors to be made with relatively small sub-bands so that the number of incident paths per sub-band is much lower than the number of antennas in the antenna array.

[0006] Some 1D sparse goniometry techniques (i.e. estimation of the bearing only, assuming zero elevation) make it possible to estimate (or "goniometer") the impact of potentially more paths than antennas in the network. With these techniques, an interceptor could thus be implemented with significantly fewer sub-bands and therefore with much wider instantaneous processing bands. However, they do not address the problem of 2D goniometry (with joint estimation of the bearing and the elevation) for any network geometry and they are only suitable for the case of decorrelated paths.

[0007] The MUSIC algorithm, for its part, makes it possible to estimate the direction of arrival of several correlated paths provided that they are not coherent (paths whose arrival time difference is almost zero, being much lower than the inverse of the signal bandwidth) and that they do not exceed the number of antennas in the network. On the other hand, the algorithm requires a significant signal observation time to properly estimate the directions of the correlated paths. This necessary observation time increases with the correlation rate of the paths.

[0008] There is therefore a need for a solution for determining 2D incidences in situations of correlated multi-path propagation channels, such as those encountered in particular in communications in urban environments, in the VHF / UHF bands in particular, or in HF ionospheric type communications, with a number of incident paths greater than the number of antennas in the antenna array, and which do not have the drawbacks of the prior art. Summary of the invention

[0009] To this end, according to a first aspect, the present invention describes a method for determining the direction of arrival of signal paths on a network of N sensors, with N > 2 and according to which:

[0010] said method is implemented by an electronic device for determining the direction of arrival of the paths and comprises the following steps, in a first phase: - i. 1 / first estimate, by sparse goniometry, of the vector y verifying the equation: vec ( R v ) - o2 vec ( ) = By

[0011]

[0012]

[0013]

[0014] where ly is the identity matrix of size NxN, o2 is the noise level and Rx is the vectorized covariance matrix of the signal x(t) considered at the output of the sensor network, with, if xn(t) is the signal at the output of the nth sensor: | ; W? M ; h and B is the calibration table of the network, such that, the vector 3(0), of dimension N xl, being the known response of the sensor network to a signal received with arrival direction 0 and Q being the maximum number of possible distinct arrival directions considered: with - i.2 / in a first estimate of the directions of arrival of the journeys, if the qth component of the first estimate of the vector y is non-zero, then the direction of arrival ®q corresponding to the qth component of B is estimated as the direction of arrival of a received path; said method being characterized in that it further comprises, in a second phase, the following steps: - j. 1 / second estimate of the vector y by determining by sparse goniometry, this time verifying the equation: vec(Rx) - (J2vec(IN) = By with AB] «y AB = [ a*(0i) 0a(0J) ... ], composed of the cross terms a*(0j 0a(Oj), with ij, for a set of arrival directions selectively defined as a function of the arrival directions estimated, in step i.2, as the arrival direction of a received path; - j.2 / in a second estimate of the arrival directions of the journeys, for each non-zero component of the second estimate of the vector y a direction of arrival of paths is determined as follows: if the qth component of the second estimate of y is non-zero, then the incidence ®q corresponding to the qth component of B, is estimated as the direction of arrival of a received path. The invention thus makes it possible to determine the incidences in canal situations

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] correlated multi-path propagation, and this with a number of incident paths lower or higher than the number of sensors (for example antennas) in the sensor network, the solution also requiring reduced computing time and computing power. The first phase using the calibration table B and assuming that the received paths are decorrelated makes it possible to know approximately the directions of the latter and thus to reduce in the second phase, the necessary size of the extended calibration table [B AB] of the parsimonious model in the presence of correlated paths, to estimate their directions more precisely. The proposed solution makes it possible to exploit the advantages of the vectorized covariance matrix model in the presence of correlated paths which make it possible to: - potentially handle more paths than antennas in the direction-finding network - work with direction-finding networks having a lower number of antennas; and - does not require detection of the number of trips. The proposed solution also makes it possible to determine the directions of arrival of paths coming from non-controlled transmitters, i.e. where the standard of the emitted signal is not known, or at best imperfectly known. In embodiments, such a method will further comprise at least one of the following features: - AB= [ a*(0j) ... J is composed of the crossed terms y*(0.) 0a(0j' with î For a set of arrival directions selectively defined according to a predefined neighborhood of the estimated arrival directions, in step i.2, as the arrival direction of a received path; - it is determined at the end of step j.2 of the current iteration if: the value of the constant r) being predefined and if this condition is not verified, a new iteration of steps jl and j.2 is carried out, taking as the first estimate of the arrival directions of the new iteration the second estimate of the arrival directions determined at the current iteration; - the estimation of the direction of arrival includes the estimation of an elevation angle and a bearing angle; - said method comprises at least one of the following provisions: - the number of paths is greater than the number N of sensors; - journeys are temporally correlated with each other. According to another aspect, the invention describes a computer program intended to be stored in the memory of an electronic processing unit and further comprising a microcomputer, said computer program comprising instructions which, when executed on the microcomputer, implement the steps of a method for determining the direction of arrival of signal paths on a network of N sensors according to the first aspect of the invention.

[0027] The invention also describes a non-transitory computer-readable medium storing such a computer program.

[0028] According to another aspect, the invention describes an electronic device for determining the direction of arrival of the paths on a network of N sensors, with N > 2, said device being adapted, in a first phase, to determine a first estimate, by sparse goniometry, of the vector y verifying the equation:

[0029] where I,v is the identity matrix of size NxN, o2 is the noise level and Rx is the vectorized covariance matrix of the signal x(t) considered at the output of the sensor network, with, if x^f) is the signal at the output of the nth sensor:

[0030] and B is the calibration table of the network, such that, the vector a(0), of dimension N xl, being the known response of the sensor network to a signal received with arrival direction 0 and Q being the maximum number of possible distinct arrival directions considered:

[0031] with ~ a' (GQ)

[0032] said device then being adapted for, in said first phase, in a first estimation of the directions of arrival of the paths, if the qth component of the first estimation of the vector y is non-zero, then estimating the direction of arrival corresponding to the qth component, b(0^, of B as the direction of arrival of a received path;

[0033] said device being characterized in that it is adapted to, in a second phase, determine a second estimate of the vector y by sparse goniometry, this time verifying the equation:

[0034] vec ( R, ) - a2vec ( IN ) = Bp with

[0035] AB= [ a*(©i) ®a(0j) ... ], composed of the cross terms a*^) 0a(®j} with ij, for a set of arrival directions selectively defined as a function of the arrival directions estimated, in the first phase, as the arrival direction of a received path;

[0036] said device is adapted to, in said second phase, determine, in a second estimate of the directions of arrival of the paths, for each non-zero component of the second estimate of the vector y, a direction of arrival of paths in the following manner:

[0037] if the qth component of the second estimate of y is non-zero, then the incidence 0q corresponding to the qth component of B, is estimated as the direction of arrival of a received path.

[0038] In embodiments, such a device will further comprise at least one of the following features:

[0039] - AB = [ a*(®i) ... j is composed of the crossed terms 0 a(0j)' with i 1 for a set of arrival directions selectively defined according to a predefined neighborhood of the estimated arrival directions, in said first estimation of the arrival directions of the paths in said first phase, as the arrival direction of a received path;

[0040] - said device is adapted to determine at the end of said second estimation arrival directions of the paths of the current iteration if:

[0041] ..

[0042] the value of the constant q being predefined and if this condition is not verified, the device carries out a new iteration of the second phase, taking as first estimation of the directions of arrival of the new iteration the second estimation of the directions of arrival determined at the current iteration;

[0043] - the estimation of the direction of arrival by said device comprises the estimation of a elevation angle and a bearing angle. Brief description of the drawings

[0044] The invention will be better understood and other characteristics, details and advantages will appear more clearly on reading the following description, given without limitation, and thanks to the appended figures, given by way of example.

[0045] [Fig.l] [Fig.l] schematically represents a goniometry system 1 in one embodiment of the invention;

[0046] [Fig.2] [Fig.2] illustrates an example of a multi-path propagation channel in HF;

[0047] [Fig.3] [Fig.3] illustrates one of the models used in a goniometry process in one embodiment of the invention;

[0048] [Fig.4] [Fig.4] represents steps of a goniometry method in one embodiment of the invention.

[0049] Identical references may be used in different figures when they designate identical or comparable elements. Description of the embodiments

[0050] [Fig.l] schematically represents a goniometry system 1 in one embodiment of the invention, comprising a goniometry network 2 and an electronic processing block 50.

[0051] The direction-finding network 2 is a network of sensors for electromagnetic signals, typically radiofrequency (RF) or sound signals. In the example considered here, the signals are radiofrequencies and the direction-finding network 2 is an antenna network which comprises N receiving antennas 3 (N>2 for operation in 1 dimension (1D) and N>3 for operation in 2 dimensions (2D) >) arranged on a support, here on the ground. Each antenna 3 is adapted to receive incident radiofrequency signals (the paths) at the position of the antenna and convert them into electrical signals representative of the incident signals received. The relative arrangements of the antennas 3 depend on the type of RF signals. Each incident RF signal is a signal whose emission source is a radiofrequency transmitter 4 (for example a mobile telephone).

[0052] The processing block 50 is adapted to receive the electrical signals coming from the different antennas 3 of the antenna array 2, to carry out signal processing on these signals and to determine the directions of arrival, also called “incidences”), defined by the bearing and elevation of the path, of each of the paths received by the antennas 3, by implementing the steps described below with reference to [Fig.4].

[0053] The bearing 6mp corresponds to the angle of the direction of arrival projected in the horizontal plane (the horizontal plane is the plane tangent to the surface of the Earth at the location of the antenna array) relative to a reference axis of the sensor array. The elevation A mp corresponds to the angle formed between the horizontal plane and the direction of arrival. The elevation can also be called the site angle.

[0054] In one embodiment, the processing block 50 comprises a memory 51 and a microprocessor 52, and the memory 51 has software instructions which, when executed by the microprocessor 52, implement the steps incumbent on the processing block 50 and described below with reference to [Fig.4].

[0055] The received paths come from a set of M transmitters 4. The number M is a priori unknown, like the number of multi-paths received from the same transmitter.

[0056] We consider that we are in the presence a priori of paths temporally correlated with each other.

[0057] Modeling of the signal received on the direction finding network and deduction of the structure of the vectorized covariance matrix:

[0058] In the presence of M transmitters each having Pm paths, m = 1 to M, the signal at the output of the network 2 of the N antennas 3 of the direction finding network 1 is written as follows:

[0059] [Math.l] F-hiO x(0 = ■MO = XXW ri - ) + n(r) ......!

[0060] where X^.t) is the output signal of the nth antenna, Sn(f) the signal of the mth transmitter 4 and n(t) the noise vector. The signals of each of the transmitters 4 are assumed to be decorrelated (i.e. the signals of any one of the transmitters 4 are assumed to be decorrelated from the signals of any other of the transmitters 4).

[0061] The vector a(0), of dimension AO I, characterizes the relationship between the signal measured by the antenna array x(t) and the unit incident signal s(tr) of arrival direction 0. It is called the response of the goniometry array 2 to a received signal of incidence O, where O = (0, A), 0 being the bearing and A the elevation. This response is known; it has for example been determined in a prior phase, either by calculation or by experimental calibration, for any continuous value of O or for a predetermined set of incidence values. For example, for an array where the response depends only on the position of the sensors, the vector a(0) established by calculation is written: a^©) withan( 0) xexpf-j^f kT(0)D„} where k(0) is the vector a(0) = - wave direction and Dn the position of the nth sensor.

[0062] The pth path of the mth transmitter 4 is characterized by its incidence Qmp = (0mp, Amp), its propagation delay xmp and its amplitude pmp (in the particular HF case, we recall that the bearing of the different paths of the transmitter is the same for the different paths).

[0063] The radio signal sm(t) of complex amplitude, band Bm and central frequency fm is expressed for example in the form:

[0065] The correlation rate between two paths (of indices p, q) of the mth transmitter 4 can be approximated by:

[0066] [Math.2] ms VI ^P^ -—7--- LJ ftn [ T — T ni i ,w mp !

[0067] where Bm is the bandwidth of this transmitter, E\ ] is the mathematical expectation and * denotes the conjugate.

[0068] Thus, we consider that two paths, with indices p, q, of the mth transmitter 4 are correlated if:

[0069] [Math.3]

[0070] In HF, where the bandwidth is often of the order of 3kHz, the paths are then correlated when the arrival time difference is less than 0.33ms. We also note that y'a is the power of the pth path such that vm _ I n i2. f PP Irmpl

[0071] The model of equation (1) can be rewritten as follows

[0072] [Math.4] Aw-| 3(0^' 3(¾ p) + n( / j with < i Pmi s pp [p,.-

[0073] Assuming that the noise is decorrelated from the signals of the transmitters 4 and that it is spatially white with E [ ] = rr-I yOÙ identity matrix of size NxN and" defines the transpose and conjugate operator (o2 is therefore the noise level), the covariance matrix of the received signals is then written:

[0074] [Math.5] with Rx,„ - E\ SptjSp (!)

[0075] In practice the covariance matrix is ​​estimated from K time samples in the following manner:

[0076] [Math.6] has tr

[0077] In the following, the vectorized covariance matrix is ​​used:

[0078] [Math.7]

[0079] From equations (4)(5) it can be shown that:

[0080] [Math. 8] J = È +aW(Iv) w---l

[0081] where denotes the Kronecker product. This last expression can be rewritten as follows:

[0082] [Math.9] b(0mP) +e + aW(l:V) with J h(®) - a (®)®a(0)

[0083] where the amplitude of the vector e depends on the level of correlation between the paths.

[0084] According to equation 9 and for the example of a(0) given previously, we deduce that in this configuration, b(®) is a vector of dimension N1 whose (n)th component is expressed bn(0) = exp(-j“ kT(O)Dw) with DtP = Dn-Dk+^ where n = ri mod N and k — [riIN] • The vector b(®) therefore corresponds to the response of a virtual network where the antennas would be positioned at positions Dn,_

[0085] We consider a sampling of the incidence space of the antenna network according to a 2D grid of bearings 0q and elevations A q containing Q potential incidences noted ®q for 1 < q < Q, with 0 < 3q < 360 ° and 0 < A q < 90 °.

[0086] For example, we can take a fixed grid step of 4° according to each of the angles; Q is then equal to 90x22.

[0087] We then note B the following calibration table:

[0088] [Math. 10] B = [ 6(0^ ■■■ b(®Q) ] with,

[0089] - as a first approximation, we assume that for each incidence ®mp of path received by the antenna network, there is an index q between 1 and Q such that ®mP = 0^ ; these are the incidences, among the Q possible incidences, that will need to be identified. We will note these indices qmp in equations 10 and 11:

[0090] ®mp= O^for 1 <n<p l 1 ” P ~ 1 m

[0091] In practice, 0^ will be the incidence closest to ®mp in the grid of Q possible incidences.

[0092] We deduce that

[0093] [Math. 11] For vec ( RT ) - By + e+rr vec ( I v ) with s [ 1 p S i ... 11( / / ) = 0 otherwise

[0094] We obtain a parsimonious model of the vectorized covariance matrix perturbed by a noise e + 02vec( ) depending on the levels Yi™ of correlation between the paths of each of the transmitters 4 as well as the level o2 of the noise.

[0095] The vectorized covariance matrix vec(Rx) could be written as follows:

[0096] [Math. 12] HAS / ' vec(R;< ) = £( A,; ® Am )ym + cri. with ym = yœ(R5w ) m=l

[0097] Principle of parsimonious goniometry

[0098] The field of parsimonious estimation from an observation model brings together the mathematical principles allowing the resolution of a system of equations having more unknowns than equations knowing that most of the unknowns are zero.

[0099] The objective of sparse goniometry, in a configuration of uncorrelated paths, is to solve the system of equations y — vec(Rx) -02vec(lp) to estimate the sparse vector y. According to equations (10)(11), the incidences of the received paths corresponding to the vector x(t) (as considered, therefore, at the K sampling instants at Ir used to approximate the covariance matrix) then correspond to the non-zero components of the vector y where j _ vm, and therefore ' yimp) Y pp we can deduce that the incidence corresponding to the qmpth component of Best is an incidence of a path received at time t, i.e. 0^ = Qmp- This is illustrated in [Fig.3] which illustrates how the estimation of the sparse spectrum y makes it possible to determine which are the incidences of the paths received among the set of potential incidences.

[0100] In other words: if the qth component of y, i.e., component Y(q), is determined, at the end of the sparse goniometry processing, as non-zero, then the incidence ®q, corresponding to the qth column of B, b(©t?), is determined as the incidence of a received path.

[0101] However, we are in the presence of a system of equations having more unknowns than equations. To solve this system of equations, it is then necessary to exploit the parsimony of the vector y. To do this, we add to the classic criterion of least squares a regularization or penalty <1> (X, y) which aims to promote the parsimony of the solution which must contain many zero components. The criterion to be minimized according to the vector x has the following form:

[0102] [Math. 17] J* (A x)=| ||y - Bxf +$ (X x)

[0103] The relative weight of the two terms is adjusted by a regularization parameter X in order to guarantee the relation J x) > J¢(2, y) for all vectors x. According to the results presented in “Sparse goniometry of radio-electric sources: models, algorithms and robust implementations”, Alice Delmer, doctoral thesis, Université Paris-Saclay, December 2021, this weight can be fixed a priori from the resolution limit of the virtual sensor network with response b(0). The penalty <b(X,x) a pour expression :

[0104] [Math. 18] y . ... W;,o)=o <b(z.x)=> (p(Â.xLyl) with < v ^(Zr^0)>0

[0105] The CELO penalties and the Zo penalty (the l0 penalty being defined as the l0 norm multiplied by 2) used in the thesis indicated above have in common the verification that ç>(2, > £) - À- In the case of Zo, the value of e tends towards 0 whereas, in In the case of CELO, the function is wider in the vicinity of 0. Other penalties with the same properties have been proposed in the literature.

[0106] The algorithm for estimating the vector y is iterative with an initialization with the vector x°. The recurrence relationship between two steps of the algorithm is as follows:

[0107] [Math. 19] x1'' = with / 3 < 1 / ||b"b||

[0108] where prox j is the proximal of the penalty.

[0109] In the case of Zo and CELO, the proximal operator verifies:

[0110] case of Zo: (x) = xa if |x„| > 0 otherwise [YES] CELO case

[0112] with (.)+=max(0,.).

[0113] The steps for estimating the sparse vector are summarized below:

[0114] Step AO: Initialization by the vector x° and z=0

[0115] Step A. 1: Calculation of u = x d-0 - ( y^'0-Bx ) (corresponding to a descent of gradient on least squares)

[0116]

[0117] Step A.2: Updating the vector with the proximal ^z) _ prox Step A.3: If || y-Bx® || > S return to step Al with i= i +1.

[0118] The value of s corresponds to the desired estimation precision. It can be linked to an average noise level if it is known. Other stopping criteria are also possible, such as a maximum number of iterations or the decrease in the criterion between two iterations.

[0119] The CELO penalty allows initialization with x°=0 unlike lQ in the general case because of the presence of local minima. The steps of estimating the sparse vector y can be carried out with other penalties from the literature such as MCP. It is also possible to use more complex schemes based on these simple steps: time-varying penalty or proximal, iteration-dependent parameters, vector averaging over several iterations, etc.

[0120] Sparse goniometry process in the presence of correlated paths

[0121] Now considering that paths coming from the same transmitter 4 are correlated with each other, the approach proposed by the invention is to use the model coming from equations (9)-(11):

[0122] [Math.20] y “ vcc(R j-crvec'^ -le m with e = ŸX?™* )® a(0OT ) m=l

[0123] where the observation V is tainted by the noise vector e whose level depends on the intercorrelation terms of the paths. With the model of equation (20), in one embodiment of the invention, the steps Ai, i = 0 to 3, of the algorithm presented above are applied to estimate the vector V with the calibration table B (therefore assuming that the paths are decorrelated). We thus obtain an erroneous vector y allowing us to deduce according to (10)(11) a first estimate of the incidences of the paths for 1 < m < M and 1 p Pm. A complement of calibration table AB is then constructed, containing the crossed terms ( ©j ) 0 a(®j)' with For a set

[0124]

[0125]

[0126] of incidences selected according to the estimated incidences @ . for example those of the incidences located in a predefined neighborhood of said estimated incidences . The dimensions of the neighborhood according to a compromise retained between complexity of the calculations and performance. In one embodiment, AB is constructed only the incidences estimated previously, the precision of the final estimates then being degraded compared to the embodiments taking into account the neighborhoods. The predefined neighborhood is expressed for example in terms of the number of points in the direction in the 3dB lobe of the virtual response network a*(0 ) 0a(0j)' The model of equation (20) then becomes [Math.21] y = Bÿ with = [B AB] and y = Y _P_

[0127] where y is a sparse vector having as non-zero components the power terms ypp of the paths with indices corresponding to the presence of sources, and nuis terms otherwise and P is also a sparse vector, having as only non-zero components the intercorrelation terms y1^ of the paths (pq).

[0128] In a second step, the vector F is estimated this time with the extended calibration table B to extract a better estimate of y and it is determined according to equations (10)(11) a better estimate of the incidences for 1 < m < M and 1 p Pm. (the total number of paths estimated can indeed change in the case where there are sources or paths close (in terms of incidence) which are not initially resolved and which we then manage to separate by having improved the model. M and Pm not being known a priori, the number of non-zero components detected can therefore vary).

[0129] Without this two-step process, the AB calibration table complement would have to contain the cross products for all incidences, i.e., a number of / Q \ columns. For Q — 22*90, i.e., a grid step of 4° along both \ 2 / angles, this then represents nearly 2 million columns. If we choose only the neighborhood of the incidences estimated in step 1, for example the estimated incidences and their 8 nearest neighbors, we will have at most a calibration table complement with / 9 x Pm \, or a little more than 20,000 columns if we \ 2 / consider the maximum number p / n — 23: we then divided the number of columns to add by 100.

[0130] Additional assumptions, considering for example the HF propagation model, can be added to further reduce the number of cross products, such as for example a maximum bearing difference between the two directions considered.

[0131] In an embodiment of the invention illustrated in [Fig.4], a method 100 using this approach is implemented by the processing block 50; this method 100 thus comprises the steps BO to B.6 detailed below.

[0132] In a step BO, the processing block calculates Rx as a function of the signals x(t) at the output of the N antennas and deduces y using the following formula:

[0133] y = m?(Rv) - o2vec(M •

[0134] Then, in a step Bl, a first estimate of the vector T is carried out by solving y — vec ( Rv ) - (With ( ) = By by sparse goniometry, in ap for example, replicating the process comprising the steps described above A.0, A1, A.2 and A.3, with the calibration table B to obtain this first estimate, named y

[0135] In a step B.2, a first estimate of the incidences {q} of the received paths (corresponding to %(t) for the K sampling instants considered) is deduced, from the vector y, and according to the equations (10)(11): the incidences of the received paths are determined as those corresponding only to the non-zero components of y, i.e. if the qth component of y is non-zero (named qmp), then the incidence 0mp corresponding to the qth column of B, = 0mp) is estimated as the incidence of a received path. Conversely, the incidences corresponding to the zero components of y are not part of the incidences of the received paths.

[0136] In a step B.3, the following complementary calibration table is constructed:

[0137] AB — [ a*(0j) ® a(0j) ... ], containing only the cross terms a*(0i) 0a(0j)' with z À For a set of incidences in the predefined neighborhood of the estimated incidences q .

[0138] Taking into account in AB only the estimated incidences and the incidences in their vicinity only (possibly of size 0) makes it possible to reduce the number of potential incidences to be considered, by only considering a subset of thus very reduced size.

[0139] In a step B.4, a second estimation of the vector F is carried out by solving by sparse goniometry, which vector P verifies:

[0140] ~ ri M y By with |B = [B AB] and y =

[0141] where y was calculated in BO; the sparse resolution is for example carried out by applying the process comprising the steps described above A.0, A1, A.2 and A.3.

[0142] This allows us to obtain the vector R tP. and to extract a second estimate of the vector y.

[0143] In a step B.5 and similarly to step B.2, a second estimate of the incidences {©} of the received paths is deduced, as a function of the second estimate of the vector Y, and according to equations (10)(11).

[0144] In a step B.6, if || y-By || > 77 then return to step B.3 (taking as first estimates of the incidences of this new iteration of B.3 and B.4, the second estimates of the incidences determined at the current iteration); otherwise the incidences of the paths estimated in B.5 are considered as final estimates. The value of the threshold / / is predefined according to a compromise between estimation precision / volume and speed of the calculations executed. For example, the threshold / / is linked to an average noise level.

[0145] These estimated arrival directions {0} are then used, for example to locate the transmitters 4, which is used by the processing block 50 or another electronic device, in spectrum control, telecommunications management, tracking of transmitter carriers (search for buried victims after natural disasters, protection of animal species, etc.).

[0146] The method may be implemented by executing software instructions on a processor as described above by way of example. Alternatively, it may be implemented by dedicated hardware, typically a digital integrated circuit, either specific (ASIC) or based on programmable logic (e.g. FPGA / Field Programmable Gate Array).

Claims

Claims

1. Method for determining the direction of arrival of signal paths on a network (2) of N sensors (3), with N > 2 and according to which: said method is implemented by an electronic device (50) for determining the direction of arrival of the paths and comprises the following steps, in a first phase: - i. 1 / first estimate, by sparse goniometry, of the vector y verifying the equation: ) ••• By where Ijv is the identity matrix of size NxN, o2 is the noise level and Rx is the vectorized covariance matrix of the signal x(t) considered at the output of the sensor network, with, if xn(t) is the signal at the output of the nth sensor: M ; P and B is the network calibration table, such that, the vector a(0), of dimension iVxl, being the known response of the sensor network to a signal received with arrival direction 0 and Q being the maximum number of possible distinct arrival directions considered: with b ( ® to (@$( ® | - i.2 / in a first estimate of the directions of arrival of the paths, if the qth component of the first estimate of the vector y is non-zero, then the direction of arrival ®q corresponding to the qth component, / 7(6^), of B is estimated as the direction of arrival of a received path; said method being characterized in that it further comprises, in a second phase, the following steps: - j. 1 / second estimate by parsimonious goniometry of the vector y this time verifying the equation: vec ( Rx ) - a2vec ( IN ) = By with AB= [ a*(0j) ® a(ôj) ... ], composed of the crossed terms a*( ®i) ® a(0j)' with i J, for a set of arrival directions selectively defined as a function of the arrival directions estimated, in step i.2, as the arrival direction of a received path; - j.2 / in a second estimation of the arrival directions of the paths, for each non-zero component of the second estimation of the vector y, a direction of arrival of paths is determined in the following way: if the qth component of the second estimation of y is non-zero, then the incidence &q corresponding to the qth component of B, b(&q), is estimated as the arrival direction of a received path.

2. Method for determining the direction of arrival of signal paths on a network (2) of N sensors (3) according to claim 1, according to which AB = [ a*(0{) ® a(®j) ... ] is composed of the cross terms a*(0i) 0a(0j), with i for a set of directions of arrival selectively defined according to a predefined neighborhood of the directions of arrival estimated, in step i.2, as the direction of arrival of a received path.

3. Method for determining the direction of arrival of signal paths on a network of N sensors according to claim 1 or 2, according to which it is determined at the end of step j.2 of the current iteration if: v Bf |ç the value of the constant / / being predefined and if this condition is not verified, a new iteration of steps jl and j.2 is carried out, taking as the first estimate of the directions of arrival of the new iteration the second estimate of the directions of arrival determined at the current iteration.

4. Method for determining the direction of arrival of signal paths on a network of N sensors according to any one of the preceding claims, according to which the estimation of the direction of arrival comprises the estimation of an elevation angle and a bearing angle. ^Claim 5] Method for determining the direction of arrival of the signal paths on a network of N sensors according to any one of the preceding claims, comprising at least one of the following provisions: - the number of paths is greater than the number N of sensors; - paths are temporally correlated with each other.^Claim 6] Computer program, intended to be stored in the memory of an electronic processing unit (50) and further comprising a microcomputer, said computer program comprising instructions which, when executed on the microcomputer, implement the steps of a method for determining the direction of arrival of signal paths on a network of N sensors according to one of the preceding claims.^Claim 7] Electronic device (50) for determining the direction of arrival of paths on a network of N sensors, with N > 2, said device being adapted, in a first phase, to determine a first estimate, by sparse goniometry, of the vector y verifying the equation: mt ) — «7 'iw ( I v 1 Bv X > / XZ < where is the identity matrix of size NxN, o2 is the noise level and Rx is the vectorized covariance matrix of the signal x(t) considered at the output of the sensor network, with, if x„(0 is the signal at the output of the nth sensor: « S / } î p Si (?) î and B is the calibration table of the network, such that, the vector a(0), of dimension iVxl, being the known response of the sensor network to a signal received with direction of arrival 0 and Q being the maximum number of possible distinct directions of arrival considered:. with said device (50) then being adapted to, in said first phase, in a first estimation of the directions of arrival of the paths, if the qth component of the first estimation of the vector y is non-zero, then estimate the direction of arrival &q corresponding to the qth component, of B as the direction of arrival of a received path; said device (50) being characterized in that it is adapted to, in a second phase, determine a second estimation of the vector y by sparse goniometry, this time verifying the equation: vec(7?v) -a2vec(IN) -Bÿ with eî vd * [Fj AB-[ a*(0j) ®a(0j) ...], composed of the cross terms a*( ©i ) ® a(©j} with * B for a set of arrival directions selectively defined as a function of the arrival directions estimated, in the first phase, as the arrival direction of a received path; said device (50) is adapted to, in said second phase, determine, in a second estimate of the arrival directions of the paths, for each non-zero component of the second estimate of the vector y, a direction of arrival of paths in the following manner: if the qth component of the second estimate of y is non-zero, then the incidence corresponding to the qth component of B is estimated as the arrival direction of a received path.

8. Device (50) for determining the direction of arrival of the paths according to claim 7, in which AB= [ a*(0;) 0a(0j) ... ] is composed of the crossed terms a*(0j) ® a(0j)' with for a set of directions of arrival selectively defined according to a predefined neighborhood of the directions of arrival estimated, in said first estimation of the directions of arrival of the paths in said first phase, as direction of arrival of a received path.

9. Device (50) for determining the direction of arrival of the signal paths on a network of N sensors according to claim 7 or 8, adapted to determine at the end of said second estimation of the directions of arrival of the paths of the current iteration if: 5 the value of the constant r| being predefined and if this condition is not verified, the device carries out a new iteration of the second phase, taking as first estimate of the directions of arrival of the new iteration the second estimate of the directions of arrival determined at the current iteration.

10. Device (50) for determining the direction of arrival of signal paths on a network of N sensors according to any one of the preceding claims 7 to 9, in which the estimation of the direction of arrival by said device comprises the estimation of an elevation angle and a bearing angle.