FR2862137A1 - Transmitters locating method for aircraft, involves associating incidence guide vectors, which are associated with response of sensors, with transmitters at respective instants, and locating transmitters using associated guide vectors - Google Patents

Abstract

The method involves separating transmitters to identify incidence guide vectors associated with a response of sensors. The guide vectors are respectively associated with the transmitters at respective instants. The transmitters are located using the associated guide vectors, by maximizing a normalized vectorial correlation criterion in positioning spaces (x, y, z) of the transmitters.

Description

The invention relates to a method for locating one or

several transmitters.

  It applies in particular to the location of transmitters on the ground from a mobile machine without having knowledge a priori on the signals emitted.

  The technical field is in particular that of the passive location of transmitters.

  Figure 1 illustrates an airborne location. The transmitter is at the position (xo, yo, zo). The bearer at instant tk is at the position (xk, yk, zk) and sees the emitter under the incidence (O (tk, xo, yo, zo), d (tk, xo, yo, zo)) . The angles B (t, xo, yo, zo) and d (t, xo, yo, zo) evolve over time and depend on the position of the transmitter and the trajectory of the carrier.

  The angles B (t, xo, yo, zo) and d (t, xo, yo, zo) are identified with respect to a network of N antennas which can be fixed under the carrier as shown in FIG.

  There are currently several techniques for determining the position (xm, ym, zm) of a transmitter. These localization techniques differ in particular in the parameters that are estimated instantaneously at the level of the sensor network. They can be classified as follows: Use of direction finding, These techniques are known and used in the prior art. In most cases, they are based on a 1D azimuth direction finding. The azimuths Bkm pVtk, xm, ym, zm) associated with the m issuer are measured for different times tk. Using the position (xk, yk, zk) of the carrier at the corresponding instant k, a position (xmk, ymk, zmk) of the transmitter m is estimated by a ground intersection. The position (xk, yk, zk) of the carrier is given by a GPS, its orientation is obtained by a compass in the case of a land carrier and by a navigation unit in the case of an aircraft.

  From all positions (Xmk, Ymk, zmk), the method performs a data extraction to determine the M dominant positions (xm, ym, zm) of the incident transmitters. The location is obtained by triangulation or by ground intersection (2D direction finding). The disadvantage of triangulation techniques is that they require a large amount of scrolling. On the other hand, direction finding techniques must use an unambiguous sensor array to provide the bearings. This has the disadvantage of requiring a calibration table and limit the size of the sensor array and therefore provide limited impact accuracy.

  Using the phase difference between 2 remote sensors, the phase difference Aço (tk, xo, yo, zo) between sensors depends on the positions of the 2 sensors as well as the incidence (B (tk, xo, yo, zo ), d (tk, xo, Yo, zo)) of the transmitter. This time-dependent phase is directly related to the position (xo, yo, zo) of the transmitter. Consequently, by studying the function of the time dgp (t, xo, yo, zo) it is possible to deduce the position (xo, yo, zo) of the emitter. In this family of application the 2 sensors are distant to increase the precision of the measurement of the phase. This has the drawback of varying the phase difference dcp (t, xo, yo, zo) as a function of time over more than 2n and the technique then requires a step allowing the phase to be unrolled over more than 2n. On the other hand, in this technique, the phase is measured by directly performing an intercorrelation between two sensors, which does not make it possible to deal with the multi-transmitter case.

  These techniques take advantage of the fact that the estimated carrier frequency is the sum of the carrier frequency of the transmitter and the Doppler shift due to the traveling speed of the carrier. Doppler shift has the advantage of depending on the position (xo, yo, zo) of the transmitter and also being a function of time Af (t, xo, yo, zo). Consequently, by studying the function of time Af (t, xo, yo, zo) it is possible to deduce the position (xo, yo, zo) of the emitter. However, the measurement of this Doppler shift has the drawback of requiring emitters having particular waveforms. This frequency measurement can be done by cyclic techniques assuming that the transmitted signal is non-circular.

  Use of propagation times, These techniques exploit the differences in air travel time (TDOA or Time difference of arrival) which are directly related to the respective distances of the transmitter to different air and therefore to the position (xo, yo, zo ) of the transmitter. By using at least three sufficiently spaced aerials, it is possible to deduce the position (xo, yo, zo) of the transmitter by hyperbolic location. The disadvantage of these techniques is that they can not be implemented in a single carrier context because of the considerable spacings required between air. On the other hand, in these techniques, the difference in time is measured by directly performing an intercorrelation between two sensors, which does not make it possible to deal with the multi-transmitter case.

  The method according to the invention is based in particular on a new direct estimation approach of the positions (xm, ym, zm) of each of the emitters from a parametric analysis of the multi-channel signal at various times tk over a duration Dt. Another function of parametric analysis is to separate the different transmitters at each instant tk. We then associate the parameters of the same transmitter from different times tk to finally locate each of the transmitters.

  The invention relates to a method for locating one or more sources, the source or sources being in motion with respect to a sensor array, the method comprising a step of separating the sources in order to identify the direction vectors associated with the source. sensor response to a given incidence source. It is characterized in that it comprises at least the following steps: E associating the direction vectors alm ... aKm of the mth emitter obtained respectively at the instants É locate the mth emitter from the vectors ai ... aKm associated.

  The method according to the invention has the following advantages in particular: E it makes it possible to locate in addition to the position in (x, y, z) of a transmitter its speed vector, E applies when one is in the presence of one or more transmitters 10 incidents, E implementation does not require any particular knowledge of the transmitted signal, it allows to use an ambiguous array of sensors that is to say several incidences are associated with the same response of the which have the advantage of being large and thus of being more robust to the phenomena of coupling between air or, more generally, to modeling errors of the air network, and it can be implemented on networks calibrated in (04 ).

  It can be implemented on antennas networks with diversity of amplitude such as co-located antennas: network with dipoles of the same phase center and having different orientations.

  Other characteristics and advantages of the subject of the present invention will appear better on reading the description which follows given by way of illustration and in no way limiting on reading the appended figures which represent: FIG. 1 the schematic diagram of the location of a ground position transmitter by means of an aircraft; and FIG. 2 the relationship between an antenna array and the incidence of an emitter. FIG. 3 is a general diagram explaining the operation of the method. according to the invention, FIGS. 4, 5 and 6 show examples of implementation of the process according to the invention.

  In order to better understand the object of the present invention, the following description is given by way of illustration and in no way limiting to locate several transmitters disposed on the ground by means of an array of sensors equipping a moving aircraft. Such a system is for example described in Figure 1. The aircraft is equipped with a processor adapted to implement the steps of the method according to the invention.

  The method can also be implemented in the context of vehicle moving on the ground.

  FIG. 3 represents, in a time-amplitude diagram of the signal, the signal x (t) composed of a combination of the signals of the emitters at different times t1, t2, ... tK. In this figure, the various steps implemented, namely the separation of the emitters SE and the parametric estimate EP, the association of the parameters of each emitter, the location of an emitter are summarized.

  In the presence of M transmitters, the method has, at the instant t at the output of the N network sensors, the vector x (t) representative of the mixture of the signals of the M transmitters. Around the instant tk, the vector x (t + tk) of dimension Nxl, representing the mixture of the signals of the M transmitters, is expressed as follows:

M

  X (t + tk) = E a (ekm, Akm) Sm (t + tk) + b (t + tk) = Ak S (t + tk) + b (t + tk) for ItI <At / 2 m = 1 where b (t) is the supposed Gaussian noise vector, a (04) is the response of the sensor array to an incident source (04), Ak = [a (Okl, Akl) ... a (OkM, Akm)], s (t) = [s1 (t) ... sM (t)] T, ekm = e (tk, xm, Ym, Zm) and Akm = 4 (tk, xm, Ym, zm). In this model the mixing matrix Ak depends on the instant tk of observation. (1)

  The direction vector of the incidence corresponding to the m issuer at the instant tk akm = a (Okm, 0km) = a (tk, xm, ym, zm) of the third emitter (2) is a known function of tk and the transmitter position (xm, ym, zm).

  The method according to the invention comprises at least the following steps: 1. estimating one or more parameters associated with the position of the source, for example the direction vectors, the bearings, the position, etc. and separating the M transmitters for the different instants tk, which consists in identifying the incidence direction vectors akm for (1 <m <M). This first step is for example performed by source separation techniques known to those skilled in the art, 2. Associate the estimated parameters for the mth transmitter, for example by associating the different incidence vectors, a1 m akm respectively obtained at times tl, ... tk, 3. locate the emitter from the associated vectors.

  Step of association In the presence of M transmitters and after separation of sources, the method has at time tk the M signatures akm for (1 <m <M). At time tk + 1 the source separation gives the M vectors b; for (1 <i <M). The objective of this monitoring is to determine for the m issuer, the index i (m) which minimizes the difference between akm and bi (m). In this case we deduce that ak + 1, m = b; (m). To perform this association we define for example the distance between two vectors u and v by: ld (u, v) = 1 uxe (uHu) vHv) where u "is the conjugate transpose of the vector u. i (m) verifies: (3) d (akm, bi (m)) = lmin [d (akm, bi)] so

H

  a bi (m) d (akm, bi (m)) = min [1- H x 1SiSm km akm i (m) bi (m) In this association we consider a function [3m associated with the mth emitter: Rm (tk) = d (akm, aom) (5) Over the association we obtain for each emitter m and for 1 <m <M, the function pm (t). This function aims in particular to eliminate the instants tk whose value [3m (tk) seems too far from an interpolation of the function f3m (t), that is to say that we eliminate the aberrant times which may be associated with other transmitters. A tolerance zone +/- A is defined around the curve defined by the function [3m (tk). This tolerance zone will depend on the estimation accuracy of the akm vectors. In particular in the presence of M = 1 source the zone will be of the order of A = 3 / -iBAt (where At is the elementary time of parametric estimation illustrated fig.3 and B is the instantaneous band of the signal x (t) ).

  The steps of this association for K instants tk are for example the following: Step ASE 1: Initialization of the process at k = 2. The initial number M of emitters is for example determined by a detection test of the number of sources at the moment known to those skilled in the art, Step ASE 2: For 1 <m <M determination of the indices i (m) applying equation (4) and using the vector ak, m with 1 <m <M and the bi vectors identified at time tk + 1 for (1 <i <M), Step ASE 3: For 1 < m <M perform the operation ak + T m = bi (m), Step ASE 4: Incrementation k4-k + l and if k <K return to step ASE-1, Step ASE 5: From the family of instants and = {t1 <... <tK}, eliminate the 1 (4) instants te J such that the coefficients (3m (t;) do not belong to the zone delimited by the interpolation curve of ( 3m (tk) and the tolerance zone A. We will also eliminate the instants tk Oë I (3m (tk) - Rm (tk-1) I <A. After this sorting, the new family of instants is cD = {ti < ... <t,} and we put K = 1.

  At the end of these steps, the method determined the atm vectors aKm associated with the same emitter.

  Locating an Emitter The method determines the position of the emitter emitter from the components of the atm vectors up to akm. These vectors akm have the particularity of depending on the instant tk and especially on the position (xm, ym, zm) of the transmitter. In particular for a network composed of N = 2 sensors spaced by a distance of d in the axis of the carrier, the vector satisfies akm: exp j2rt -d cos (e (tk, xm, Ym Zm)) cos (A (k , xm, Ym, Zm) _ 2 _ The value 1 of the first component corresponds to the reference sensor.From Figure 1, the incidence (6 (tk, xm, ym, zm), d (tk, xm , ym, zm)) can be directly calculated from the carrier position (xk, yk, zk) at time tk and the position (xm, ym, zm) of the transmitter.

  Step of transformation of the vector According to an alternative embodiment, the method comprises a step of transforming the vector akm into a vector bkm whose components are formed from the components of the vector akm. In particular, the method constructs, for example, the vector bkm of dimension (N-1) x1 by choosing a reference sensor in n = i: akm = (6) = a (tk, xm, ym, zm) a (1) / ak ,,, (i) (7) = b (tk, Xm, ym, Zm) OR akm (i) is the / th bkm akm (i 1) / akm (l) ah (i + 1)! akm (i) akm (N) / akm (i) component of akm The components of bkm correspond in this case to the ratios of the components of the vector akm and the vector akm (i).

  Thus in the example of equation (6) by setting i = 1 we get: ((8) bkm = exp j2z cos (9 (k, xmYm, zm)) cos (4k, xm, Ym, zm = akm (2) / akm (1) Knowing that the akm direction vectors are estimated with a certain error ekm such that akm = a (tk, xm, ym, zm) + ekm, we can deduce that it is the same for the transformed vector bkm of (7) Step of maximization of a correlation criterion Knowing that the vector akm is a function of the position (xm, ym, zm) of the transmitter, it is the same for the vector bkm The method comprises a step of maximizing a standard vector correlation criterion LK (x, y, z) in the space (x, y, z) of a transmitter position where

H

  bK H (x, Y, z) LK (xy Z) _ 4 v KHbKΔvK (x, Y, z) HvK (x, Y, z)) (9) With b lm = VK (xm, ym, Zm) + WK, VK (x, y, z) b (t,, x, y, z) b (tK, x, y, z) bK = W lm and wK = W Km The noise vector WK has the covariance matrix R = E [wK WKH]. Assuming that the matrix R is known, the criterion can be envisaged with a bleaching technique. Under these conditions one obtains the following criterion LK '(x, y, z): IbxH R 1 VK (x, Y, z) 2 xxR lbx x (x, Y, z) HR 1Vx (x, Y, z)) (10) With R = E [wK WKH] It should be noted that the criteria of equations (9) and (10) are equal when R = a2l, ie when the errors are considered equal on all sensors and independent between sensors. The criterion LK (x, y, z) of equation (10) is therefore valid for a model noise WK of white statistics.

  The criteria LK (x, y, z) and LK '(x, y, z) are between 0 and 1 and satisfy LK (x, y, z) = LK' (x, y, z) = 1 for the position (xm, ym, zm) of the emitter. This standardization makes it possible to set a threshold of good location r1. Thus all the maxima (xm, ym, zm) of LK (x, y, z) that satisfy LK (xm, ym, zm)> r1 are considered good locations. The threshold can be set according to an approximate knowledge of WK statistics.

  É The criteria LK (x, y, z) and LK '(x, y, z) have the advantage of being able to implement a localization technique in the presence of a network of sensors calibrated in space (04) . Knowing that at instant tk we know the analytic relation linking the incidence (0 (tk, x, y, z), A (tk, x, y, z)) of the emitter at its position (x, y, z), we can deduce from the incidence (0 (tk, x, y, z), A (tk, x, y, z)) the vector a (tk, xm, ym, zm) = a (0 (tk, x, y, z), A (tk, x, y, z)) by interpolating the calibration table (relative to the calibrated antennas). Note, however, that this method is insensitive to phase bias (due to the vector correlation criterion).

  These criteria also make it possible to take into account the phase and the amplitude of the components of a (04). The method can therefore be envisaged with collocated antenna networks with diversity of diagrams.

  It should be noted that in an airborne context the knowledge of the altitude h of the aircraft makes it possible to reduce the calculation of the criterion in the search space (x, y) by posing z = h. In the example of equations (6) and (8) the vector VK (x, y, z) is written as follows: exp (j27 cos (*, x, y, z)) cos (A (, , x, y, z)) 1 exp (j 22 cos (8 (K, x, y, z)) cos (A (tK, x, y, z) 1

J

  In this process it is possible to consider initializing the algorithm at K = Ko and then recursively calculating the criterion LK (x, y, z). Under these conditions LK (x, y, z) is computed recursively as follows: LK + 1 (X, Y, z) = 1% 1-1 (x, y, z) 12

P

  K + 1 YK + 1 (x, y, z) where K + 1 (X, y, Z) = aK (x, @, Z) + bK + 1 ni "b (tKi.1, x, y, z ) 11K + 1 (x, y, Z) = YK (X, y, Z) + b (tK + 1, x, y, Z) H b (tK + 1, x, y, z) I3K + 1 = PK + bK + 1 mH bK + 1 m The coefficients aK + 1 (X, y, Z) = aK (x, y, z) yK + 1 (x, y, Z) = YK (X, y, Z) ), RK + 1 = 3K are intermediate spectra for calculating LK + 1 (x, y, z).

  When the vectors b (tK + 1, x, y, z) and bkm are of norms VK (X, y, Z) = (12) constants equal to p the relation of recurrence of equation (12) becomes: LK +1 (x, y, z) = aK + i (x, y, Z) fit (K + 1) 2 where aK + 1 (x, y, Z) = aK (x, Y, z) + bK + 1 mH b (tK + 1, x, y, Z) The process is described so far assuming that the emitters have fixed positions. It can easily be extended to the case of moving vector velocity targets (vxm, vym, vzm) for which an evolution model is available. Under these conditions the incidence of the same emitter is parameterized as follows: ekm-tf tk, xm Vxm tk, ym-Vym tk, Zm Vzm tk) and Akm = 4 (tk, xm-Vxm tk, ym Vym tk, Zm uzm tk) where (xm, ym, zm) is the position of the emitter at time to and (vxm, vym, vzm) the velocity components of the emitter at moment to. Under these conditions the vector bkm of equation (7) is parameterized by (xm, ym, zm) and (vxm, vym, vzm) in the following way: bkm = b (tk, xm, ym, zm, vxm , vym, vzm,) + Wkm Naturally the location criteria LK and LK 'of equations (9) and (10) are no longer parameterized only by (x, y, z) but also by (vx, vy, vz ). The method therefore consists in maximizing the criterion LK (x, y, z, vx, vy, vz) as a function of the 6 parameters (x, y, z, vx, vy, vz).

  The method can be applied to a very large number of measurements. In this case, the method comprises a step of reducing the numerical computation complexity (which is a function of the number of measurements) by decreasing K. The method provides for performing on the elementary measurements the following processes: decimation of the instants tk, in eliminating the neighboring moments for which the evolution of the curve (3m (tk) is not significant, filtering (smoothing of the measurements which are the guiding vectors) and sub (13) (14) (15) sampling, the measurements are then merged over a defined time (extraction by association of director vector to produce a synthesis measurement) Summary of the steps of the process The method of locating several transmitters using K instants tk can be summarized by the following steps: Step n 1: Identification vectors akm for (1 <m <M) at K instants tk by applying for example a source separation and source identification technique as described in the references [2] [3].

  Step n 2: Association of the atm vectors up to aKm obtained at the respective instants ti ... tK associated with the mth transmitter for 1 <m <M by applying the steps ASE-1 to ASE-5 described above.

  Step # 3: Initialization of the Process at m = 1 Step # 4: Transformation of K vectors akm into bKm vectors as suggested by equation (7).

  Step 5: Calculation and maximization of the criterion LK (x, y, z) of equation (9) to obtain the position (xm, ym, zm) of the emitter.

  Step n 6: Incrementation m - m + 1 and if m <M return to step n 3 In order to refine the estimation of the position (xm, ym, ym) of the emitters, the steps of the process can be carried out from iteratively as follows: Step 7: Identification of the vectors b; for (1 <i <M) at times tK + 1 by applying for example a technique of separation and identification of sources as described in references [2] [3].

  Step # 8: For 1 <m <M determination of the indices i (m) by applying equation (4) and using the vector akm and the vectors b; for (1 <i <M). Step n 9: For 1 <m <M is carried out the operation aK + m = bi (m) Step n 10: For 1 <m <M calculation of the criterion LK + 1 (x, y, z) iteratively using equations (12) and (13) and minimization of LK + 1 (x, y, z) to obtain the position (x ,,,, ym, zm) of the mth emitter.

  Step 11: If it is decided to continue to be more precise and less ambiguous the process returns to step # 7.

  Example of implementation of the method The simulations were carried out with an array of N = 2 sensors aligned in the axis of the carrier with d12, = 3. As d / 1 = 3, a method performing a direction finding at times tk would be completely ambiguous and would not allow triangulations to be performed later to locate the transmitter. In FIGS. 5, 6 and 7 corresponding to the location criteria for K = 3, 7 and 16 is plotted the pseudo-spectrum LK (x, y) to be maximized making it possible to determine the position of the transmitter in the space (x , y). Knowing that if the emitter is in (xo, yo) then LK (xo, yo) = 1, we deduce that the iso-level curves LK (x, y) = 0.99 characterize the width of the main lobe. Noting that the location accuracy depends on the width of this lobe, it is deduced from Figures 5, 6 and 7 that the larger K is important and the better the location accuracy.

  References [1l RO.SCHMIDT. A signal subspace approach to multiple emitter location and spectral estimation, November 1981 [2] J. F. CARDOSO, A. SOULOUMIAC, Blind beamforming for non-Gaussian Signais, EE Proceedings-F, Vol.140, N 6, pp. 362-370, Dec. 1993.

  [3] P. COMON, Independent Component Analysis, a new concept, Signal Processing, Elsevier, April 1994, vol 36, no. 3, pp 287-314.

Claims (6)

  1 - Method for locating one or more sources, said source or sources being in motion with respect to a sensor array, the method comprising a step of separating the sources in order to identify the direction vectors associated with the response of the sensors to a given incidence source, characterized in that it comprises at least the following steps: E associating the direction vectors atm.ÉÉKM obtained for the mth transmitter and respectively for the instants é locate the mth transmitter from the vectors ai. ..aKm associated.   2 - Process according to claim 1 characterized in that the association step comprises at least the following steps: Step ASE 1: initialize the process at k = 2, Step ASE 2: for 1 <m <M determine the indices 1 (m) using the relation d (akm, b; (m)) = lmin [d (akm, b1)], the vector ak, m and the vectors b; identified at time tk + 1 for (1 <i <M), establish a function [3m (tk) = d (akm, aom) Step ASE 3: for 1 <m <M perform the operation ak + 1 m = bi (m), Step ASE 4: increment k <k + 1 and if k <K return to step ASE-1, Step ASE 5: from the family of instants (I) = {t1 <.. . <tK}, thus obtained, extract the instants t; which do not belong to a zone defined by the curve [3m (tk) and a zone of tolerance.   3 - Process according to claim 1 characterized in that the locating step comprises at least the following steps: maximizing a standard vector correlation criterion Lk (x, y, z) in the space (x, y, z) of position of an emitter with bKHvK (x, y, z) 2 (bKHbKvK (x, y, z) HVK (x, y, z)) = VK (xm, Ym, Zm) + K, VK (X, Y , Z b Km b (tl, x, y, z) b (tK, x, y, z) wlm and wK = w where wk is the noise vector for all positions (x, y, z) of a transmitter.   4 - Process according to claim 3 characterized in that the vector bK comprises a vector representative of the noise whose components are functions of the vector components atm ... akm.   - Method according to claim 3 characterized in that it comprises a step where the covariance matrix R = E [wK wKH] of the noise vector is determined and in that the criterion bKH R 1 vK (x is maximized , y, Z) 2 (bKHR-1bK) vK (x, y, z) HR-1vK (x, y, z)) LK '(x, y, Z) = 6 Process according to claim 5, characterized in that the evaluation of the criterion LK (x, y, z) and / or the criterion LK '(x, y, z) is recursive.   7 - Method according to one of claims 1 to 6 characterized in that it comprises a step of comparing the maximums with a threshold value.   8 - Method according to one of claims 1 to 7 characterized in that the transmitters to be located are movable and in that the vector is parameterized by the position of the transmitter to locate and the speed vector.