Method for determining the direction of arrival of HF ionospheric signal paths on an array of N sensors, computer program and associated device

Abstract

The invention relates to a method for determining the direction of arrival of the paths of High Frequency ionospheric signals on a network (2) of N sensors (3), comprising: estimation, by sparse goniometry, of the vector satisfying where σ2 is the noise level and R x is the vectorized covariance matrix of the signal x(t) considered at the output of the sensor network, where the vector a (θ, Δ) of dimension Nx1 is the known response of the sensor network to a received signal of arrival direction (θ, Δ), deduction, as a function of the index qm of each non-zero component of said estimate, of the bearing of paths from a respective transmitter m; for each bearing deduced, given that , the non-zero components of type des are then determined: the elevation of index qp associated with each of these non-zero components , is selected as equal to an elevation of a path from the mth transmitter. Figure for the abridged version: Fig. 1

Description

Title of the invention: Method for determining the direction of arrival of HF ionospheric 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. We are more specifically interested in these HF communications. Prior art

[0003] For HF correlated multi-paths, 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 for the transmitter), as illustrated in [Fig.2]: 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.

[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 difference in propagation time between two paths is inversely proportional to the bandwidth of the transmitter. This is why paths from an HF transmitter are often correlated with each other. On the other hand, conventional direction finding techniques require the construction of interceptors 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 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 the paths of High Frequency ionospheric signals on a network of N sensors, with N > 2 and according to which said method is implemented by an electronic device for determining the direction of arrival of the paths and is characterized in that it comprises the following steps: - i. estimation, by sparse goniometry, of the vector ❖verifying the equation: vec (Rx) - a2vec (IN) = Cp

[0010] 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, si is the signal at the output of the nth sensor: j h

[0011] where

[0012]

[0013] where the vector a (0,^A) of dimension Axl is the known response of the sensor network to a signal received with the direction of arrival (0,^A), ❖and

[0014] Q is the number of potential bearings considered for 1 q < Q and Q' is the number of potential elevations per bearing, A q>, for 1 < q ' < Q' in the discretized incidence space of the sensor network according to a 2D grid of bearings 0q and elevations A q', for 1 q' Q' with 0< ^<360° andO< A q <90°,

[0015] where

[0016] ïj ' Y = : yQ. - ii. identification of the non-zero components, among the components ÿp ..., Pq of said estimate, and deduction, as a function of the index qm of each of said non-zero components Pq, of the source of signal paths from a respective transmitter m; - iii. for each deduced deposit, given that , the non-zero components of type des are then determined: the index elevation qp associated with each of these non-zero components , is selected as equal to an elevation of a path of the mth transmitter.

[0017] The invention thus makes it possible to determine the incidences in situations of HF ionospheric propagation channels with correlated multi-paths, 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 calculation time and calculation power.

[0018] 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.

[0019] The proposed solution also makes it possible to determine the directions of arrival of paths coming from non-controlled transmitters, i.e. for which the standard of the transmitted signal is not known, or at best imperfectly known.

[0020] In embodiments, such a method will further comprise at least one of the following features:

[0021] - the estimation of the direction of arrival comprises the estimation of an elevation angle and a bearing angle;

[0022] - the method comprises at least one of the following provisions:

[0023] the number of paths is greater than the number N of sensors;

[0024] paths are temporally correlated with each other.

[0025] 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 steps i, ii, iii and iv 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.

[0026] The invention also describes a non-transitory computer-readable medium storing such a computer program.

[0027] According to another aspect, the invention describes a device for determining the direction of arrival of the paths of High Frequency ionospheric signals on a network of N sensors, with N > 2, said electronic device for determining the direction of arrival of the paths being adapted to estimate by sparse goniometry, the vector ❖ verifying the equation:

[0028] vec(Rx) -c^vec(IN) = Cy

[0029] 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, si is the signal at the output of the nth sensor: ; P

[0030] where

[0031]

[0032] where the vector a (0,^A) of dimension Axl is the known response of the sensor network to a signal received with the direction of arrival (0,^A), ❖and

[0033] Q is the number of potential deposits considered for 1 4 q 4 Q and Q1 is the number of potential elevations per deposit, A for 1 4 q' 4 Q' in the discretized incidence space of the sensor network according to a 2D grid of deposits and elevations A q>, for 1 4 q' 4 Q* with 0< 09<36OO and 0 4 A / <90°,

[0034] where

[0035] Vj1 ; Y= : yQ,

[0036]

[0037] said device being further adapted to identify the non-zero components, among the components ■ ■■, Pq of said estimate, and to deduce, as a function of the index qm of each of said non-zero components ÿg, the range of signal paths from a respective transmitter m;

[0038] said device being further adapted, for each deduced deposit, given that , to determine the non-zero components of type deet to select the index elevation qp associated with each of these non-zero components, as equal to an elevation of a path of the mth transmitter.

[0039] In embodiments, such a device will further comprise at least one of the following features:

[0040] - the estimation of the direction of arrival comprises the estimation of an elevation angle and a bearing angle;

[0041] - the method comprises at least one of the following provisions:

[0042] the number of paths is greater than the number N of sensors;

[0043] paths are temporally correlated with each other.

[0044] Brief description of the drawings

[0045] 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.

[0046] [Fig-1] [Fig.l] schematically represents a goniometry system 1 in a embodiment of the invention;

[0047] [Fig.2] [Fig.2] illustrates an example of a multi-path propagation channel in HF;

[0048] [Fig.3] [Fig.3] illustrates one of the models used in a goniometry process in one embodiment of the invention;

[0049] [Fig.4] [Fig.4] represents steps of a goniometry method in a mode of carrying out the invention.

[0050] Identical references may be used in different figures when they designate identical or comparable elements. Description of the embodiments

[0051] [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.

[0052] 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).

[0053] 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].

[0054] The bearing Omp 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.

[0055] 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].

[0056] 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.

[0057] We consider that we are in the presence a priori of paths temporally correlated with each other.

[0058] Modeling of the signal received on the direction finding network and deduction of the structure of the vectorized covariance matrix:

[0059] 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: ( equation 1 )

[0060] where is the output signal of the nth antenna, 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 , of dimension Nx 1, characterizes the relationship between the signal measured by the antenna array x( t) and the unit incident signal s( t -t) with arrival direction 0. It is called the response of the goniometry network 2 to a signal received at incidence ©❖❖where 0 = (❖O^A), 0 being the bearing and A the elevation. This response is known; it has by example was determined in a preliminary phase, either by calculation or by calibration experimental, for any continuous value of 0 or for a set predetermined incidence values. For example, for a network where the response depends only on the position of the sensors, the vector a(0) established by calculation is written: a / 0) with an(0) = exp(-j kT(where k(0) is the a(0) - aN(0). wave direction vector and Dn the position of the nth sensor.

[0062] The pth path of the mth transmitter 4 is characterized by its incidence &mp = (^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 routes).

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

[0064]

[0065] The correlation rate between two paths (of indices p, q) of the mth transmitter 4 can be approximated by: (equation 2)

[0066] where Bm is the bandwidth of this transmitter, E\ ] is the mathematical expectation and * denotes the conjugate.

[0067] Thus, we consider that two paths, with indices p, q, of the mth transmitter 4 are correlated if: (equation 3)

[0069] In the particular case, which we are particularly interested in here, of HF ionosopheric signals, 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 is the power of the p&me path such that .

[0070] The model of equation (1) can be rewritten as follows (equation 4)

[0071] Assuming that the noise is decorrelated from the signals of the transmitters 4 and that it is spatially white with where identity matrix of size NxN andH defines the operator of transposed and conjugated (o2 is therefore the noise level), the covariance matrix of the received signals is then written: (equation 5)

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] In practice the covariance matrix is ​​estimated from K time samples as follows: 1. (equation 6) 1. In the following, the vectorized covariance matrix is ​​used: 2. (equation 7) From equations (4)(5) we can show that: 1. (equation 8) where denotes the Kronecker product. This last expression can be rewritten as follows: 1. 1. (equation 9) where the magnitude of the vector e depends on the level of correlation between the paths. It is recalled here that the vectorization of a matrix, for example the matrix R, named vec(R,) is a vector in which the columns of said matrix are arranged one below the other. From equation 9 and for the example of a(0) given previously, we deduce that in this configuration, b(0) is a vector of dimension / V2 whose (n)th component is expressed bn( 0) = exp(- / kT( 0)Z>M) with D„, = Dn-Dk^ where n = n mod N and k — [n]N]. The vector b(0) therefore corresponds to the response of a virtual network where the antennas would be positioned at positions Dn,, 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 < Qtor with $ ~ ° ct $ “ q < • 1. For example, we can take a fixed grid step of 4° according to each of the angles; Q is then equal to 90x22. 2. We then denote by B the following calibration table: 3- B = [ b(0}) ■■■ b(0QrJ ^(equation 10) 4. As a first approximation, we assume that for each path incidence ®mP received by the antenna array, there exists an index q between 1 and Q such that 0»? / > = 0g; it is these incidences, among the Q possible incidences, that we will need to identify. We will denote these indices qmp in equations 10 and 11: In practice, 0g will be the incidence closest to &mP in the grid of Q possible incidences. 1. „ „ emp= ®g,„p for 1 22 P - rm 1. We deduce that (equation 11) 1. 1. We obtain a parsimonious model of the perturbed vectorized covariance matrix by a noise e + a2vec( I v ) depending on the correlation levels between the paths of each of the transmitters 4 as well as the level o2 of the noise. 2.The vectorized covariance matrix could be written as follows: L wc(R,) -ZX,(Ai®A.) Y„, + a2i«jl,v) av“ = (equation 12) 1. Taking into account the particular characteristic of the incidences of multi-paths of HF ionospheric signals where , we define the following calibration table: . (equation 13) 1.

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] with Q the number of potential bearings considered and Q' the number of potential elevations per bearing, in the discretized incidence space of the antenna network according to a 2D grid of bearings and elevations A for 1 < q < Q, for 1 < q' < Q' with 0< ^<360° andO< A q <90° and we deduce the following second parsimonious model: vec ( RÀ ) = C xy + o2 vecfXv) with 'Y]' (equation 14) where each vector Yç of size ( Q x Q ' ) represents, relative to the path deposit 0q associated with it, the vectorization of the covariance matrix of the potentials journeys and where yg contains non-zero components only when the index q corresponds to a path deposit corresponding to a transmitter of index m from which come signals received by the sensor network; in this case q is noted qm: , where the matrices Rm are of dimension Q'xQ' ​​and where the component Rm(i,j) of Rm is non-zero only when there exists either a path k if i = J, or two paths (path k and path / of transmitter m) otherwise, from said transmitter of index m, of elevations associated with the indices i, j; in this case i (elevation index relative to path k) and j (elevation index relative to path / ) are noted respectively qk and q^ and ~ ^kl Rm (4. / )-0 otherwise (in the case of a single path k, 1 is taken equal to k in the previous formula. 1. 1. Considering the model of equation (12), - the vector is composed of at most N2- N+l independent components with a network of N antennas; - the matrix is ​​composed of (Pm)2 columns because it is of dimension NxPm. The number of non-zero components contained in the vectors {yi,...,^yM} is then equal to . 1. We then deduce that the condition of identifiability of the paths is as follows: 1. (equation 15) 2. Assuming that the number of paths per transmitter verifies , the capacity in number of transmitters then becomes: 1. Principle of sparse goniometry

[0086] 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.

[0087] The objective of sparse goniometry, in a configuration of uncorrelated paths, is to solve the system of equations 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 to be used to approximate the covariance matrix) then correspond to the non-zero components of the vector y ❖where , and therefore we can deduce that the incidence corresponding to the qmpth component of B is an incidence of a received path at time t, i.e. 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 received paths among the set of potential incidences.

[0088] In other words: if the qth component of y, i.e., component ❖(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(6V), is determined as the incidence of a received path.

[0089] However, we are in the presence of a system of equations with 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 a regularization or penalty to the classic least squares criterion <e>(X,y) which aims to promote the parsimony of the solution which must contain many zero components. The criterion to minimize following the vector x has the following form: 1. (equation 17)

[0090] The relative weight of the two terms is adjusted by a regularization parameter X in order to guarantee the relationship 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 of response b(0). The penalty <b(x,x) a pour expression : 1. (equation 18) 2. The CELO penalties and the Zo penalty (the l0 penalty being defined as the lo norm multiplied by 2) used in the thesis indicated above have in common that they verify . In the case of / 0, the value of e tends towards 0 whereas, 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.

[0091] 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: 1. (equation 19)

[0092] where is the proximal of the penalty.

[0093] In the case of l0 and CELO, the proximal operator verifies:

[0094] case of l0.

[0095] CELO case:

[0096] with (.)+=max(0,.).

[0097] The steps for estimating the sparse vector are summarized below:

[0098] Step AO: Initialization by the vector x* and z=0

[0099] Step Al: Calculation of (corresponding to a gradient descent on the least squares)

[0100] Step A.2: Updating the vector with the proximal:

[0101] Step A.3: If return to step A1 with i= i +1. Otherwise, the sparse vector V is estimated equal to xW.

[0102] The value of corresponds to the desired estimation accuracy. 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.

[0103] The CELO penalty allows to initialize with x*=0 unlike l0 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.

[0104] Sparse goniometry process in the presence of correlated paths

[0105] 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 (12)-(14) exploiting the bearing and elevation modeling of the multipaths of the HF ionospheric signals.

[0106] 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 C0 to C.3 detailed below.

[0107] In a step CO, the processing block calculates Rx as a function of the signals x(t) obtained at the output of the N antennas and deduces y using the following formula:

[0108] .

[0109] Then, in a step C1, estimation of the vector by a parsimonious processing process as set out in steps A0 to A.3 (by replacing the matrix B by the matrix C defined by equation (13) and by replacing y^ by ).

[0110] Step C.2: of , identification of vectors with non-zero components (or in other words, of non-zero norm), among the sub-vectors ..., Ÿq of thus estimated (reminder: is a non-zero vector only when the index q corresponds to a bearing of the paths of a transmitter of index m from which come signals received by the sensor network; in this case q is noted qm ) and deduction of the bearings of the incident transmitters, these bearings being those associated with the only non-nuisance vectors, ie for q = qm (the number of vectors having non-zero components also provides the value of M, the number of transmitters at the origin of the signals received).

[0111] Step C.3: for each deposit deduced from step C.2 (and therefore for each emitter m), m = 1 to M, identified in step C.2, given that: the non-zero components of type des are then identified: each of these non-zero components is associated with an index elevation qp and this is selected as corresponding to the elevation of a path of the mth emitter associated with the deduced deposit.

[0112] The estimate obtained by steps CO to C.3 takes into account both the correlation between the paths and the particularity of the HF paths. The estimate is much more precise than the estimate obtained by steps AO to A.3 with dictionary B where the correlation of the paths significantly increases the noise level. Taking into account the correlation between the paths without taking into account the specificity of the HF paths would involve extending dictionary B by a dictionary AB which contains all the cross terms n(®mp) 0 a(®„;) and whose size would be prohibitive.

[0113] These estimated arrival directions {} 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.).

[0114] 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). < / e>

Claims

1. Claims Method for determining the direction of arrival of the paths of high-frequency ionospheric signals 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 is characterized in that it comprises the following steps: - i. estimation, by sparse goniometry, of the vector ❖ verifying the equation: vec(Rx) -a2vec(IN) = Cy 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, si is the signal at the output of the nth sensor: Or where the vector a (0,^A) of dimension Axl is the known response of the sensor network to a signal received with the direction of arrival (0,^A), ❖and Q is the number of potential bearings considered 0q for 1 q Q and Q' is the number of potential elevations per bearing, A q>, for 1 < q' < Q' in the discretized incidence space of the sensor network according to a 2D grid of bearings 0q and elevations A q-, for l <q'<Q’avec Os ^<360° etO< <90°, où V = ii. identification of non-zero components, among the components p], ■ ,Yq of said estimate, and deduction, as a function of the index qm of each of said non-zero components yq, of the source of signal paths from a respective transmitter m; iii. for each deduced deposit, given that , the non-zero components of type des are then determined: the index elevation qp associated with each of these non-zero components , is selected as equal to an elevation of a path of the mth transmitter. ^Claim 2] Method for determining the direction of arrival of signal paths on an array (2) of N sensors (3) according to claim 1, wherein the estimation of the direction of arrival comprises the estimation of an elevation angle and a bearing angle. ^Claim 3] Method for determining the direction of arrival of signal paths on an array (2) of N sensors (3) 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 4] 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 steps i, ii, iii and iv 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 5] Device (50) for determining the direction of arrival of the paths of High Frequency ionospheric signals on a network of N sensors, with N > 2, said electronic device for determining the direction of arrival of the paths being adapted to estimate by sparse goniometry, the vector ❖verifying the equation: vec(Rx) -<72vec(IN) = Cy 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, si is the signal at the output of the nth sensor: i xif); ih where where the vector a (0,^A) of dimension Axl is the known response of the sensor network to a signal received from the direction of arrival (0,^A), ❖and Q is the number of potential bearings considered 0q for 1 < q < Q and Q' is the number of potential elevations per bearing, A for 1 < q' < Q' in the discretized incidence space of the sensor network. according to a 2D grid of bearings Oq and elevations A for l^q'^Q'with 0< ^<360° and 0 A q' <90°, where ; y Q . said device (50) being further adapted to identify the non-zero components, among the components of said estimate, and to deduce, as a function of the index qm of each of said components y^ non-zero, the field of signal paths from a respective transmitter m; said device being further adapted, for each deduced deposit, given that , to determine the non-zero components of type deet select the index elevation qp associated with each of these non-zero components, as equal to an elevation of a path of the mth transmitter.

6.

7. Device (50) for determining the direction of arrival of the paths according to claim 5, in which the estimation of the direction of arrival comprises the estimation of an elevation angle and a bearing angle. Device (50) for determining the direction of arrival of the paths according to claim 5 or 6, where at least one of the following two provisions is verified: the number of paths is greater than the number N of sensors; paths are temporally correlated with each other.

Images