METHOD FOR GEOLOCATING MULTIPLE EMITTERS BY SPACE-TIME PROCESSING

The invention relates to a method for geolocating multiple emitters of position Em on the basis of signals received on a number of remote receiving stations Sk which are made up of a number of sensors (multiple sensors).

It is notably applicable in the technical field of antenna processing which deals with the signals from a number of emitting sources on the basis of the signals received by a number of sensors. A set of sensors on a station is hereinafter called an array of antennas or array of sensors and a set of stations is called a network of stations.

This method involves the field of goniometry, the estimatioh of the angle of arrival (or of incidence) of an emitter located at the point Em on the basis of the signals from a multi-sensor receiving station Sk- The coordinates of the point Em are the components of the vector pm.

As is indicated in Figure 1, the aim of geolocation is to estimate the coordinates pm of the emitters in the plane or in space, these coordinates correspond to those of the points Em represented in Figure 1. The estimation of these coordinates is done either directly or by the use of location parameters such as the angles of arrival from an emitter on each of the stations.

One known geolocation technique is triangulation which consists in estimating the coordinates of an emitter on the basis of the knowledge of the angles of arrival (or incidences) of this emitter on each of the receiving stations.

In an electromagnetic context, the sensors are antennas and the radiofrequency sources are propagated according to a polarization dependent on the emitting antenna. In an acoustic context, the sensors are, for example, microphones and the sources are sound sources.

Figure 2 shows an example of an antenna processing system 10 in which an array 11 of sensors receives the signals from a number of incidence sources 0m. One of the objectives of the antenna processing techniques is to separate or to extract information (signal, parameters, etc.) from each of the sources by exploiting the spatial diversity dependent on the geometry of the antenna array of a station and on the incidence &m of the sources.

The individual sensors of an array of a receiving station located at Sk receive the sources with a phase and an amplitude which depend in particular on the incidences of the paths and on the position of the sensors.

According to Figure 3, the incidence of a path is defined by direction parameters ©m={0m and Am } in which 6m is the azimuth and Am the elevation angle.

The technical problem that will be treated in the present patent application is that of the geolocation of emitters on the basis of signals recorded on a number of multisensor stations through the estimation of different location parameters, which may be the angle of arrival on a station (AOA: Angle Of Arrival), the time of arrival (TOA: Time Of Arrival) on a station or the time difference of arrival (TDOA: Time Difference Of Arrival) between two stations.

The aim of the method is, notably, to geolocate a number of emitters of unknown bandwidths on the basis of the signals received on each of the stations and therefore to resolve one or more of the following technical problems:

• unambiguously geolocating a number of emitters. For this, the technical problem consists in associating with one and the same emitter the AOAs obtained on each of the stations by an antenna processing approach. This association is made blind without a priori knowledge of the signals emitted (binary sequence or pilot signal, bit rate, waveform, etc.)

• optimal recognition of the bandwidth of the signals in the geolocation algorithms which are of the MUSIC algorithm type known to those skilled in the art:

■ without a priori studying the spectral occupancy of the emitted signals,

■ by unambiguously processing the wideband signals in the direction of the network of stations;

• optimizing the cost functions of the geolocation algorithms with a computation cost that is as low as possible.

The method is applied, for example, to the blind (or passive) geolocation techniques, that is to say, techniques in which no a priori information on the emitted signal is available unlike the cases of positioning systems of GPS (Global Positioning System) or GALILEO type.

Most of the geolocation methods are applied in three major steps: a step of estimating the location parameters performed independently on each of the receiving stations then a step of associating the parameters of one and the same emitter and finally a geolocation step that makes it possible to estimate the position of each emitter on the basis of its set of parameters which may be the angles of arrival on each of the stations.

• Estimating the location parameters on a station

There is a huge abundance of literature on the problem of estimating the AOA or TOA location parameters. These estimation methods are applied to one or 2 receiving stations (for the TDOA) and do not make it possible to work directly up to the position of the emitters, because the number of coordinates to be estimated is greater than the number of location parameters estimated (in the case of the AOA on a) station, a single location parameter is estimated). Consequently, to geolocate an emitter, it is necessary to use a number of receiving stations to estimate all the coordinates of the emitter. For example, it is possible to estimate the position of an emitter in the plane on the basis of the AOAs obtained on at least 2 separate stations (triangulation). The traditional geolocation techniques estimate the location parameters (AOA, TDOA, TOA) separately on each of the receiving stations. When there are multiple emitters, this generally entails using a priori information on the signals emitted to associate the location parameters of one and the same emitter.

• Locating the emitters on the basis of the location parameters

Generally, the geolocation techniques are above all used for wireless digital communications; the case covered is then that of a source (portable telephone) for which a number of items of a priori information are available, such as a reference signal or a spreading sequence, which make it possible to identify one and the same emitter on remote receiving stations. When there are multiple sources, it is necessary to associate the parameters of each of the emitters (same reference signal, spreading sequence, bit rate, etc.) before performing the geolocation step on the basis of the location parameters estimated on a number of stations.

• Estimating and associating the location parameters

The Applicant's patent application WO2009/065943 deals with the entire blind (or passive) source geolocation processing system when there are multiple paths, on the basis of a coupled estimation of the angles of arrival (AOA) and of the time differences of arrival (TDOA) of the paths from one and the same source between two separate stations. However, the coupled estimation of the location parameters (AOA-TDOA) does not simultaneously use all the signals received by the remote stations. In particular, the method does not use the AOA of the second station and the method is degraded (or even no longer works) when there are narrowband sources.

• Estimating the position of the emitters directly on the basis of all the received signals

Few works have proposed geolocation algorithms that perform a joint estimation of the geolocation parameters directly on the basis of the signals received on all the stations and supply as output, either directly the position of the emitters, or the location parameters of the emitters jointly estimated. These works have the drawback of not optimally exploiting the band of the signals. In practice, these methods have in common that they implement the high-resolution methods used in goniometry which require a particular modelling of the signals received. More particularly, in goniometry, it is conventionally assumed that the delay induced by the propagation of a signal from one sensor to another in the network of the station can be modelled by a phase shift: this is called the narrowband hypothesis. This hypothesis which is routinely borne out for a typical array of sensors in goniometry is behind the high-resolution algorithms which work on the basis of a linear mix of sources. On the other hand, this hypothesis is rarely borne out for the signals from multiple remote multi-channel stations in which the model is no longer linear, but convolutional because the signals received on the stations are delayed replicas of the signal emitted. In this context, most of the location algorithms directly estimating the position of the known emitters boil down to the price of a suboptimal solution to a narrowband situation in the network of stations sense.

In other implementations, the narrowband hypothesis is arrived at at the level of the network of stations by dividing the received signal into a number of narrow subbands. This has the drawback of considerably reducing the processing band times observation time product in each subband, which has the effect of reducing the accuracy and the resolution. Also, the method does not use all of the information from all the frequency channels by not taking into account, for example, the intercorrelations of the signals from two distinct frequency channels.

It is also possible to resolve the problem of the narrowband hypothesis at the level of the stations, partially, by modelling a wideband signal as a number of narrowband composite signals (components) at the level of the network of stations. This presents the drawback of very quickly saturating, in terms of number of components, the algorithms of MUSIC type, an algorithm known to those skilled in the art. As it happens, the maximum number of components from geolocatable sources must be strictly less than the number of sensors of all the stations.

To sum up, the above mentioned methods and systems of the prior art do not make it possible to coherently process all the band of the signal by using all the available information and to directly locate the sources in the plane or in space.

To avoid saturation in terms of number of composite sources at the level of the network of stations, the method according to the invention relies on a space-time approach which makes it possible to increase the size of the observation vector, consisting of the signals received on each sensor, by constructing a larger observation consisting of a number of time shifts of the observations of the sensor signals observed on all the stations. This approach, without, however, proposing any algorithm for location in the plane or in space, has been used in goniometry in order to be able to estimate the angles of arrival of a larger number of sources by using their spectral diversity in terms of bandwidth, carrier frequency and multi-path channel. For example, with such an approach, the space-time processing makes it possible to process a number of emitters strictly less than the number of sensors when there are multiple paths and when the emitters occupy all the reception band. Also, when the emitters do not occupy all the reception band, the capacity of the space-time processing in terms of number of sources exceeds the number of sensors.

The approach proposed in this patent is based on a space-time processing of the signals received on the antennas or sensors of the stations which makes it possible to coherently and adaptively process all the frequency channels of the sources without, however, saturating the network of stations in terms of number of frequency components. As indicated in the preceding paragraphs, the method consists in simultaneously using all the signals received on the stations with the help of a parametric model naturally associating the parameters of one and the same emitter. This makes it possible to avoid a step of estimating the separate location parameters on each of the stations (suboptimal in terms of performance) which requires a step of associating the parameters of one and the same emitter in order to perform an unambiguous estimation of the position of the emitters.

The invention relates to a method for geolocating M incident emitters with a network of K stations Sk each consisting of Nk individual sensors and signal processing means, characterized in that it comprises at
least:

a) a step during which the observation vector is extended by integrating the sampling period Te in the observation vector as follows:

corresponding to the band of the receivers according to Shannon's theorem, x(t) = [ xi(t)... XK(t)]T corresponds to the expression of the signal received on all the K stations, the signal on the k-th station is written:

• xkn(t) is the t-th sample of the signal output from the n-th sensor of the k-th station, sampled by the frequency Fe =1/Te

• sm(t) corresponds to the m-th time signal emitted by the source at the instant f, said signals from the emitters are considered to be independent of one another,

• pk,m and ®km are respectively the complex amplitude and the parameter-of-interest vector of the m-th source on the k-th station, the vector ®km is the direction of arrival on the station k, which can
be seen as a function of the position in the plane or in space,

• Tk,m 's the me °f travel between the m-th source and the station k,

• ak(O) is the response of the k-th network of sensors to a narrowband source of frequency fa at the station k which depends on the parameter 0, said carrier /b corresponding to the central frequency of the receivers,

• nk(/) is the additive noise present on the k-th station at the instant f.

b) a step of jointly estimating the angles of arrival or the positions of the emitters on each of said stations using the following linear model direct geolocation by the joint estimation of the coordinates of the emitters in the plane or in space, sm(f, t) corresponding to the signal from a filter of band 1/LTe centred around the frequency f,

c) a step of geolocating the sources on the basis of the K-uplets of incidence when a joint estimation of the angles is performed.

The space-time approach makes it possible to process a larger number of narrowband composite sources and thus correctly process the wideband sources in the sense of the network of stations.

Other features and advantages of the present patent application will become more apparent on reading the illustrative and nonlimiting examples with appended figures which represent:

• Figure 1, an emitter being propagated towards a network of stations,

• Figure 2, two emitters being propagated towards an array of sensors of a station,

• Figure 3, an incident from a source 0m= {6m, A m} or k(0m) the wave vector.

The following description is given as an example in relation to a system such as that schematically represented in Figure 2, consisting of a signal processing system 10, a number of sensors C1 associated with a station Sk receiving the signals. The processing system 10 is provided with a processor suitable for executing the steps of the various implementations of the method according to the invention which will be described hereinbelow. The system comprises K stations each consisting of Nk individual sensors.

Modelling and formulating the problem Modelling

The method as mentioned above relates to the geolocation of M incident emitters with a network of K stations each consisting of Nk individual sensors. The term source or emitter is used interchangeably in this description to designate one and the same object. When there are M incident sources, the expression of the signal received on this k-th station is written:

• xkn{t) is the t-th sample of the signal output from the n-th sensor of the k-th station, sampled at the frequency Fe =1/re

• sm(t) corresponds to the m-th time signal emitted by the source at the instant t. The signals from the emitters are considered to be independent of one another.

• pk.m and are respectively the complex amplitude and the parameter-of-interest vector of the m-th source on the k-th station. The vector &t „ is the direction of arrival on the station k, which can
be seen as a function of the position in the plane or in space.

• T. is the time of travel between the m-th source and the station k.

• ak(0) is the response of the k-th array of sensors to a narrowband

source of frequency fo at the level of the station k which depends on the parameter The carrier f0 corresponds to the central frequency of the receivers, the carrier frequency corresponds to the central frequency of the analogue filters of the receivers.

• nk(f) is the additive noise present on the k-th station at the instant t.

The observation vector x(t) consisting of the signals received on all the stations is written according to (1):

A single observation according to the equation (2) therefore contains the signals received on the different sensors, the sensors of a given station being able to have different geometries from one station to another. In which n'(f) is the following multi-station noise vector:

(3).

The observation vector is then constructed by extending the observation which corresponds to obtaining the following space-time observation:

y(0 = : (4).

*(t-LT,)_

In which Te=\lFe is the sampling period. This amounts to subdividing the incident signals into components of band BL=1/(LTe) whose width can be adjusted by the number of shifts L. By then assuming that LT. » max i\t m -1. m I}, that is to say, that the product (band x time) (band = BL) of passage of the source through the network should be very much less than 1, it is possible to bear out the narrowband hypothesis (expression known to those skilled in the art) and to write:

(5).

in which ® designates the Kronecker product, a complex gain which now depends on the frequency f,=(l/L)Fe, and on the position pm of the source.

(6).

in which the signal sm(ft,t) is the output of a filter of band l/LTe centred around the frequency f, of the signal received by the first station In the case of a narrowband hypothesis, the observation can be written linearly; L is an adjustment factor, which corresponds to a breakdown of the signal into narrow subbands of band 1/(LTe), in this example into L narrow subbands. The noise vector is Written:

The equation (5) can be rewritten as follows:

the m-th source on all the stations and in which (9).

(10)

The vector b(/,p,u(p/m, φ m) .

Consequently, by using a MUSIC-type approach with the 2nd-order statistics, the multi-station directing vectors generate the signal space of the covariance matrix Ryy of the observation y(t). Knowing that b(/,p, φ )=U( φ p,/)p, a MUSIC-type approach then consists in minimizing i the following criterion:

parameter containing the complex amplitudes, IL is the identity matrix of dimension LxL and diag(A) the block-diagonal matrix consisting of the columns of the matrix A. The following matrix nA is the MUSIC noise projector obtained on the basis of the specific elements of Rw (15) in which is the signal space such that ud is the specific vector associated with the d-th greatest specific value of the estimate Rw of the covariance matrix of the observation y(r) knowing that the rank of R^-R^ is D, the integer D then corresponding to the i number of narrowband components observed (or detected) in the vector y(t) in which det(M) designates the determinant of the matrix M.

In the method, the multidimensional criterion C( φ f ,/,p) is optimized, for example, in two different ways.
A first MUSIC-type approach consists in estimating the set 0 = { φ 1 ■ • ■ φ M } of the location parameters, then deducing the frequency components of each of the sources.

The components (all the directions of arrival on each of the stations or position of the emitter):

(16)

For each minimum φ m of the criterion (16), the criterion that makes it possible to estimate the frequencies fi of the corresponding source is written

(17)

The second approach consists in estimating the set of the frequency components r = {f ••• f1 } then deducing the set *,={ φ 1 ■■• yMi] of the location parameters at each of the frequencies ff.

This approach makes it possible to exploit the frequency diversity of the emitters which do not necessarily share the same frequencies. In this case, the vector u(p,,/,p) with u(p, = {φ1 ••• φM}, the following covariance matrix of following dimension NxN is constructed which makes an average of the matrices R, over all the frequencies detected (32)

The MUSIC method for estimating the parameters ^={φ1 ■■• <φM(} consists in minimizing the following criterion:

in which the following matrix IIglobal is the MUSIC noise projector obtained

from the specific elements of R global The criterion is then reduced to the minimization of the following criterion:

A triangulation algorithm is applied for each emitter. This consists in is the position pm of an emitter on the basis of its K-uplet of angle of incidences

All the estimation criteria based on the parameter can

be reduced to the position vector p = (x,y,z)T because the incidence &k of the source on the station k is a nonlinear function of the position p = (x,y,z)T of the source. Consequently, the parameter 9 is also a nonlinear function of p = (x,y,z) because

The relationship linking the incidences 0* to the position is given below and is a triangulation relationship known to those skilled in the art which makes it possible to optimize the criterion in a space of smaller dimension by parameterizing the problem according to the position of the sources. Optimizing the location criteria - mode of operation The preceding problems using a MUSIC-type approach can be resolved in the search for the minima of criteria all written in the following form:

(36)

From an initialization point £m° in the vicinity of a solution C,m, a descent algorithm of Gauss-Newton type known to those skilled in the art is obtained by the following iterative method: on the i-th iteration, a pair £m' is deduced from £m'_1 by the following relationship:

C—H-^CMO+C1 (37)

in which H(Q and V(Q are respectively the Hessian and the gradient of the criterion ./(£) whose elements are given here:

with and in which C, is a vector of dimension P whose elements are denoted and in which \B are the azimuth and the bearing of the source of direction km. When there are two stations located at Si and SK, it can be shown that the coordinates of the point Em:

The value 1 corresponds to the first station and the index k to the k-th station. The operatorH corresponds to the conjugate transpose. In the continuation of the development, the following is assumed:

(47).

By using (4), the wave vector k(0t) associated with the incidence ®t (am,pm) has the following expression:

The expression (6) then gives the relationship between &km and (am,pm). The knowledge of the parameters (αm, β m) of the direct paths will then make it possible to deduce the coordinates of the point Em by the relationship (1).

In the particular case of a triangulation in the plane in which the angles ©. „ are scalars such that 0. =a„,@,„ = Bn, and in which S, = A and

St = B, the expression (4) becomes Knowing that (xm,ym) are the coordinates of the emitter located at Em.

|AB|| corresponds to the distance between the points A and B which is also the norm of the vector AB
Summary of the steps of the geolocation method according to the invention Initial step 0: Construct the space-time observation y(t) with L time shift based on the multistation observation x(t) according to (4).

Step 1: Estimate the covariance matrix of the observations R^ on the basis of the signals according to the equation (13).

Step 2: Estimate the dimension D of the signal space of the matrix R^ on the basis of a conventional test on its specific values according to a method known to those skilled in the art, such as, for example, the MUSIC algorithm.

Step 3: Knowing the dimension D of the signal space of the matrix Rw, estimate its noise projector IIb using the equation (15).

Variant embodiments

Step 4: The context then demands a choice of one or the other pathway: either direct estimation of the positions, or simultaneous estimation of all the angles of arrival φm, or by direct estimation by parameterizing J

is deduced from ;m'_1 by the following relationship:

in which H(Q and V(Q are respectively the Hessian and the gradient of the criterion J(t) whose elements are given here:

with M(Q = TH (S)n6T((;) and in which £ is a vector of dimension P whose elements are denoted £p and in which \) which are the location parameters φm. .

10 - Geolocation method according to Claim 1, characterized in that it secondarily comprises the following additional steps:

a step of estimating the covariance matrix of the observations on the basis of the signals x(t) in which t belongs to the interval {1, T}

in which, knowing that the observation y(t) is modelled according to a finite number of response components that there is a joint estimation of the parameters (f,,p,m,,φ m) by a method of high resolution type known to those skilled in the art using the 2nd-order statistics contained in Ryy and the vector response b(/,p,φ) of a component.

11 - Geolocation method according to Claim 1, characterized in that there is a step of joint estimation of the parameters (f„p,m,) of a component.

12 - Geolocation method according to Claim 10 and 11, characterized in that it includes a step of re-parametrizing