NON-LINEAR METHOD OF ESTIMATING A MIXTURE OF SIGNALS

专利摘要:
This method of estimating at most two mixed signals from different sources, whose time / frequency representation shows an unknown non-zero proportion of zero components, by means of a network composed of P> 2 antennas, when the directional vectors U and V of the sources emitting these signals are known or estimated elsewhere, comprises the following steps: a) Calculate the successive Discrete Fourier Transforms of the signal received by the antennas and sampled to obtain a P-vector time-frequency grid of the signal; each element of the grid being called a box and containing a complex vector X forming a measurement; b) For each cell, calculate the estimator of the conditional expectation of the signal, or signals, from the measurement X and a probability density a priori for the signals which is a mixture of Gaussians.
公开号:FR3030807A1
申请号:FR1402981
申请日:2014-12-23
公开日:2016-06-24
发明作者:Meur Anne Le；Jean Yves Delabbaye
申请人:Thales SA；
IPC主号:

专利说明:

[0001] The present invention relates to a method for estimating radio signals from several sources, the time / frequency representation of which shows an unknown non-zero proportion of zero components, by means of a network composed of P> 2 antennas, when the directional vectors U and V of the sources emitting these signals are known or estimated elsewhere. It is common to have to estimate radio signals (denoising) from radars, communications systems, or acoustic signals (audio or sonar), and received by a listening system consisting of a network of antennas. The received signal results from a temporal and spectral mixing of up to 2 sources, which directional vectors are assumed to be known because they are estimated beforehand. The criterion conventionally used is the maximum likelihood (MV), leading to a spatial linear filtering treatment that improves the signal-to-noise ratio by a factor equal to the number of sensors in the single-source case. In the hypotheses in which we place ourselves (known directional vectors), this treatment leads to an unbiased linear estimation with minimal variance of signals for which no prior knowledge is available.
[0002] Other methods whose implementation is more complicated, can be used, such as Capon filtering when the directional vectors are imperfectly or not known (Robust Adaptive Beamforming, Eds P. Stoica and Li J., Wiley, 2006). None of these methods exploits a priori on the signal, and in particular does not allow to correctly delimit the temporal and / or spectral media of the signal since linear (MV) or pseudo linear (Capon) processing always provides a signal in output even if in input the measurement is composed only of noise. The problem is to access the finer knowledge of the signal. The object of the invention is to propose a method making it possible to determine more finely the components of the signal. For this purpose, the subject of the invention is a method comprising the following steps: a) calculating the successive Discrete Fourier Transforms of the signal received by the antennas and sampled to obtain a P-vector time-frequency grid of the signal; each element of the grid being called a box and containing a complex vector X forming a measurement; b) For each cell, calculate the estimator of the conditional expectation of the signal, or signals, from the measurement X and a probability density a priori for the signals which is a mixture of Gaussians. The method thus makes it possible to answer the following questions: for each of the signals present (their number being assumed to be limited to 2 locally), what are the temporal and spectral supports of the supposed signal described by components obtained by means of a time / time analysis frequency And what is the value of each component when it is non-zero Answering these questions improves signal awareness.
[0003] According to particular embodiments, the method comprises one or more of the following characteristics: said method comprises a step of estimating the parameters necessary to establish the conditional expectation by the method of the moments operating on the cells of a window cut in the time / frequency grid; - the calculation of the conditional expectation estimator is approximated by a Conditional Expectancy with 4 Linear Filters obtained by a four-hypothesis decision process involving four Hermitian forms of the X-measure, followed by a linear filtering controlled by the outcome of the decision; - the calculation of the Conditional Expectancy estimator at 4 Linear Filters is approximated by a Conditional Expectation with Independent Decisions obtained by a two-hypothesis decision process concerning U * X and V * X, followed by a linear filtering ordered by the result of the decision; - depending on the outcome of the decision, the linear filtering treatment giving the Estimator of Conditional Expectation with Independent Decisions, is either: - the maximum likelihood estimator bisources for each source; - the single-source likelihood estimator for the first source, 0 for the second source; - 0 for the first source, the single-source maximum likelihood estimator for the second source; - 0 for each source. - the calculation of the Independent Decisions Conditional Expectancy estimator is approximated by a Maximum Maximum Likelihood obtained by estimating the signal (s) by the maximum likelihood method followed by the comparison of each estimate with a threshold; the threshold or each decision threshold is chosen to respect a so-called false alarm probability of declaring the signal non-zero while it is zero; said method comprises: a first estimation of the signals carried out by the method of Conditional Expectation with Independent Decisions or Maximum Maximum Likelihood, - an estimate of parameters made from the signal components obtained in the preceding step, second estimation of the signals carried out by the Conditional Hope method or by the Conditional Expectancy method with 4 Linear Filters, informed of the values of the parameters obtained in the previous step. The invention will be better understood on reading the following description, made with reference to the accompanying drawings: FIG. 1 is a schematic view illustrating signal sources and an installation for estimating radio signals originating from these sources; according to the invention, given solely for information purposes and without the intention of representing reality; FIG. 2 is a flowchart of one of the methods as implemented in the invention in the single source case; FIG. 3 is a flowchart of one of the methods as implemented in the invention in the case of bisources. The device 8 for estimating a mixture of signals from several sources 12 according to the invention illustrated in FIG. 1 comprises an antenna array composed of a plurality of antenna elements 10 or sensors. Each antenna element is coupled to a reception channel for, in particular, digitizing the analog signal received by each sensor. The invention is suitable both for monopolarization antennal networks and for bipolarization antennal networks. The device further comprises calculation modules. In various alternative embodiments of the signal estimation device according to the invention, the calculation modules can be arranged according to different architectures, in particular each step of the method can be implemented by a separate module or, on the contrary, all the steps can The calculation unit or units are connected to the sensors by any means adapted to transmit the received signals.
[0004] The computing unit or units comprise information storage means, as well as calculation means making it possible to implement the algorithms of FIGS. 2 and 3, depending on whether one is in the monosource or bisources case. Advantageously, the reception is done on a space diversity network (interferometric network) and the demodulation of the signal allowing the "baseband descent" is performed by the same local oscillator for all the antennas to ensure coherence. The received signal is sampled in real or complex (dual quadrature demodulation or other process) on each channel. The received signal, filtered in a band of typically several hundred MHz, is modeled by: s 0 (t) el2n1 ° '. This model does not make assumptions about the type of modulation. This signal is sampled at a rate Te such that 1 / Te >> 2 x band of the wanted signal. The weighted and overlapping Discrete Fourier Transforms (DFTs) of this signal are calculated on NTFD points. The role of weighting is to reduce the sidelobes. As this weighting induces a variation of the contribution of the data to the DFT (the data at the center of the temporal support of the DFT being assigned a weight much larger than the data on the edges of the support), which can go up to loss of short signals, we assume the recovery of temporal supports. The measurements collected are therefore the results of the DFTs. They constitute a time-frequency grid, whose boxes are called time-frequency boxes. Each box in the grid contains a complex vector that is the result of Discrete Fourier Transforms for all channels, for a given time interval and frequency interval. For signal frequencies and distances involved here, the wavefront is considered to be plane. So the antennas receive the signal with a phase difference function of the two angles between the wave plane and the plane of the antennas. In the monosource case, the measurements collected on the complete network are thus written as: X '= snU + Wn - Xr, represents the measurements: Xn is a complex column vector of dimension P, where P is the number of channels and n = 1,2, ... N is a double index (I, c) traversing the space of time (index of the Fourier transform) and frequencies (channel number for a Fourier transform). More precisely, the index n traverses the boxes of a rectangular time window x frequency of size N. The indices I and c correspond to the row and column numbers of the cells of the window. - s ,, is a complex number representing the signal after TFD - Wn is the thermal noise in the time / frequency box of index n. 1fn is a column vector of dimension P. Tfn is Gaussian on its real and imaginary components, independent from one time / frequency box to another and independent of one antennal channel to another. In other words, Wn is white spatially, frequently and temporally. The standard deviation of the noise counted on each real or imaginary component, at a time / frequency box, is equal to a. For the assumption of noise independence from one box to another is verified, it limits the recovery of DFT to 50%. In the case of a monopolarization interferometric network, U is written in the form: where u is a complex scalar dependent on the polarization of the incident wave and its direction of arrival, and where the u are complex numbers of module 1 representing the geometrical phase shifts associated with the direction of the incident wave. One of the antennas of the receiver can be chosen as phase reference. In the case of an interferometric bipolarization network, U is written in the form: U = hH + vV, where h and 2 are complex scalars such that lh -F 2ly = 1 which express the polarization of the incident wave, and where H (resp V) is the response of the lattice to a horizontally polarized wave (resp vertically). H and V depend only on the direction and frequency of the incident wave.
[0005] In all cases, U is of dimension P, where P is the number of antennas used.
[0006] We can consider that U is normed, and that sn carries the signal power and the average gain of the network. U is conserved by the DFT, which is a linear transformation, and is found on the signal at the output of TFD.
[0007] In the general case there may be a mixture of K signals (K being possibly greater than the resolution of the network). The signal is written as follows: = E (n) U k + W; n = 1, 2,. . .N k = 1 Equation 1 Expression of a Signal Mix The fundamental assumption is that when the set of N time / frequency fields is restricted to a rectangular area or window of index j, the complexity of the environment is as in such a window, the mixing of the signals is limited to two signals.
[0008] Then the model becomes: = s1 (n) U11 + s12 (n) U 2 + T Equation 2 Expression of a signal mixture in a window Windows of a predetermined size are defined to cover the time-frequency grid. All these windows form a cutting of the grid. The size of the windows is chosen so that at most two signals from two sources are present in each window. The vector U or the vectors U and V designating the unitary directional vector or vectors formed by the incident signal or the incident signals with respect to the network are then extracted (or estimated) by any suitable known means. A loop is made to go through all the windows defining the cutting of the grid. For each window, a step of estimation of (the) signal (signals) is implemented by means of the conditional expectation and approximations that can be made for the specific model of the signals. The final processing breaks down into: a non-linear decision-making step of the situation in each time / frequency box: source 1 present and source 2 present, or: source 1 present and source 2 absent, or: source 1 absent and source 2 present , or: source 1 absent and source 2 absent, then a linear filtering step specific to the situation. The obtained treatment is unbiased, almost optimal in the sense of the mean squared error, and delimits in time / frequency the support of the signal to be estimated. The estimation of the signal is done on a window where the situation is monosource or bisources. In monosource, the measured vector signal for the box of index n is X ,, = snU + Wn, n = 1,2, ... Equation 3 Expression of the measured signal (monosource case) In bisources, we have: = snU + +, n = 1,2, ... Equation 4 Expression of the measured signal (case bisources) In the writings of Equation 3 and Equation 4, U and V are unitary directional vectors of a monopolarization network or bipolarization, sn and c ,, are complex signals that must be estimated; W 'is the noise which is spatially white and in n, Gaussian, centered and of covariance: E (WnW, 1 = 20-2 / p where ip is the unit matrix of CP (P being the number of reception channels). * denotes the conjugated transpose.
[0009] In the following, it will be assumed that U or V are estimated by Û and T2 for example using a method of the MUSIC type, and that this estimate having been made on a number of boxes N >> 1, it is possible to approximation U = 0, V = e. To take into account that s ,, (or c ,,) can be zero for some n, without knowing the modulation of the signal in advance, we model sn (or c ,,) as independent samples in n d a random variable whose probability density is a mixture (q, 1-q, q <1) of two Gaussian centers with respective variance 217, (j = 1 for s' and j = 2 for c ,,), and 2r2 , where r2 <a2 <2crj2 is the power of the useful signal if it is present when r2 is neglected in the expression (1- q) 2r2 + q2crj2 of the mean power. r is a model regularization parameter that makes it possible to apply the Bayes formula for probability laws that admit probability densities with respect to the Lebesgue measure; however, the physical reality is that there is no signal when modeling it by means of the centered Gaussian of variance 2r2 (power2r2). That is why, at the end of the calculations, we keep only the limit of the expressions when r 0. s' and c ,, are considered independent. The measured signal is written in both cases, monosource or bisources, in the unique form: X ,, = MS ,, + W ,,, n = 1,2, N Equation 5 Matrix form of the measured signal (, T where M = U and Sn = s, 'in monosource, and M = (UV), S' = s 'c' in bisources, with M known and cr2 known In the rest of the document, to lighten the notations, being understood that the processing operates on each box of index n independently, one omits the net index one notes X the measurement in a box time / frequency, s the signal monosource and S = SC the signal bisources in a box time / frequency. A priori knowledge about S is given by a probability density In the single-source case: 2 " p (s) = 1- q exp exp 27ro-215'2 Drz-2) 2r2 (1s 2" Equation 6 Probability Density of the signal (monosource case) In the bisources case: J p (S) = y detC exp (-, Equation 7 Signal probability density (case bisources) where q1 = q2, q2 = q3 = q (1- q), q4 = (1- q) 2 if the sources are considered independent and equiprobable (in the following we generalize to a distribution, q2, q3, q4 of the 4 situations not bound by the expressions above), and C1 = (20.12 0 "(2o-12 0, C 3 (222 0 ( 2r2 0 "0 20-22) 0" 0 2o-2 0 2r21 2) Equation 8 Covariance matrices of the signal are the covariance matrices of S for the four possible cases.
[0010] S is estimated using conditional expectation using the monosource and bisources models (Equation 5, Equation 6 and Equation 5, Equation 7). Conditional Expectancy (CI) is the estimator i§ that minimizes the mean squared difference E (12) s -. It is moreover unbiased, and gives an explicit solution for. It is constructed in the following way: Let X be the measure; its probability density, which depends on the parameter to be estimated S, is interpreted as the conditional probability density of X knowing S. We therefore have p (XIS) and p (S) coming from the prior knowledge of S. is given by the explicit formula: = iSp (S 1 X) dS domS Equation 9 Estimate of S p (SIX), the conditional probability density of S knowing X, is obtained by the Bayes formula. p (X 1 S) .p (S) p (SIX) = p (X) Equation 10 General writing of the conditional probability density of S knowing X With p (X) = fp (XIS) .p (S) dS domS Equation 11 General writing of the probability density of X In the case where X = MS + V and p (S) is Gaussian, centered on covariance C, we can find analytically, which is not the case in general. It is a linear function of X. Indeed (in dimension 2): 1 X - MS 2 p (XIS) = exp 7r24o-4 20-2 p (S) = 1 exp (- S * CS) det C r 2 1 X * MS S * M * XS * M * MS p (XIS) p (S) = exp g4 4cr4 detC 202 2cr2 2o-2 2 (72 m * m Let E- = + C-1 2o-2 Completing the "square" in S, we have: I 2 p (XIS) p (S) = K2 exp ((S12M * Xj E- 1 Mj V2 + X11MX det C 2cs 2o- 2o-2 4cr4) where K2 is a constant (= 1 / rt-44a4) in dimension 2. / is a positive definite Hermitian matrix, from which we deduce: K rt-2 detE exp (11X X * MY-M * X fp (XIS) p (S ) dS = det C 20.2 40-4 domS Equation 12 Probability Density of the Sp (X 1 S) p (S) dS 2 exp (1rt-2 = K f det C domS 42 X * MEMsX 4 20- 2 MX 20-2 40- Equation 13 Conditional probability density of S knowing X in bisources The complete expressions of Equation 12 will be used to find the estimator sought for our problem In the case where S is a Gaussian sample, the Equations 9, Equation 10, Equation 11, Equation 12, and Equation 13 d equation: = MX 20-2 Equation 14 Estimate of S in bisources (case where S is Gaussian) that one can also write: = (2o-2Z-1) 1M X = (M * M + 2o-2C-1) 1M X It is concluded that if 2c72C-1 «M * M, reduces to the maximum likelihood estimator of S using the model of Equation 5 without prior knowledge of S: = (/ 1/1 * M) 1 M * X .MV The condition 211-2C-1 "M * M as matrices, is also expressed by C >> 2172 (M * M) which means that the prior on S which is defined by C does not bring any real information about S.
[0011] The signal estimate in the single source case is as indicated below. In the one-dimensional case for S = s (monosource), we have M = U and therefore M * M = 1; The matrix C is reduced to the constant c; ((2 1 1X-Us12 1 Isl 2 x0 p (X 1 S) p (S) =, ep; p (s) = exp Dru '20r2 Z.0 c' I ^) We deduce E-1 = 1 + 1 or 2, = 20.2C 20'2 c 2c72 + c 2 2cr2 + c 1 U * X p (XIS) p (S) = exp 20.2 + C 2c2c 1 = 'Dro-2 Then comes: doms f sp (XIS) .p (S) = exp K 2c72cc 20.2 + c 2 20.2 + 20.2 (20.2 + c) U * X 20.2 + c le Equation 15 Conditional probability density of S knowing X in monosource doms fp (XIS) p (S) = K 20.2c C 2cr2 + c exp X 2 20.2 20.2 (20.2 + c) 2 U * X Equation 16 Probability Density of Monosource Measurements We obtain the conditional expectation, in the Gaussian case for s, by the quotient of Equation 15 by Equation 16: = c ux 20-2 + c Equation 17 Estimate of s in monosource (where s is Gaussian) If c "20.2, which expresses that we have not A priori information on s: s * is reduced to the maximum likelihood estimator: S-mv = U * X The signal estimate in the bisources case is as indicated below. conditional expectation estimator is obt by Equation 15 and Equation 16 for the mixed density of S given by Equation 7. (1X112 After simplification by the common factor K2rt-2 exp numerator and at the denominator, we obtain: v det (1 * * E * X ME MX 'MX det Ci exp 4u') 20.2 S = Equation 18 Conditional expectation in bisources With E-ri = M * M + CT or E = 2o-2 (M * M + 20-2C71) 20.2 Let ri = 20-2CT1 (dimensionless), Q. = (M * M + 20-2C.71) 1 = (M * M + Fj) = Ej / 202 We have: 262 in all terms at det Eqj exp ME, M * Xj (1 * det 4c74 Eq, det Qi detF exp j = 1 4 Eqj det Q. det F1 exp 13 (X * MQJM * X 2o-2 (X * MQJM * f 20-2 Equation 19 Conditional expectation According to Equation 8, M * M (1 U * V "= = 1 F2 = V * U 0 F3 = (0.2 / 0.2 0.2 / 0.2 F4 = 1 2 0 0 70.2 /0.12 0.2 / r2 ) 0 0 70-2 a-2a-2 / 0.2 0 0 70-2 / 1-2 0.2 /'.2 0 /) QI 7 3 - Q-1 4 - 71+ 62 / e2 V * U ( 1+ 0.2 VsU u * v 1+ 02 /0.2 U * V 1 + 0.2 r2 u * v 1+ 0.2 /0.22, U * V 1 + 0.2 / r2 Q2-1 = We deduce from this: Q1 =, p- 0 -2 / 0-11 (1+ 0-2 / 0-22) - read (1 + 02/0. 2 2 V * U - utv 1+ 0.2 / 02 1) 1 2 Q2 = + 0.2 / 0.12 X1 + 0.2 /1.2 )_ (1 + 0.2 / r2 - U * V - v * u 1+ 0-2 / 0 -12) 1 2 U * V 1 (1 + 62/62 2 Q3 = - u * v 1 + 0.2 R-2) (1+ o-2 11-2) (1+ o-2 lo-22) - 1U * V12 -V * U Q4 =, 0-2 / 1-2 Y Hu * v12 (1 + 0.2 / 2 - t./*V VU 1+ 0-2 / 1-2 1 Equation 20 Matrices Qi L ' expression of the estimate of the signal is approximated to allow its estimation as indicated below in the bisources case. The determinant products in Equation 19 are respectively equal to the following expressions which are given an approximation for a good signal-to-noise ratio (1712/172 »1 and c2r / cr2» 1) and for r o. det det = [(1 0.2 /0.)(1+ (72 / (722) ..... 1u * v 2] -1 -1 4 / Cr 26 2 Cf / i 2 1-1U * V12) 64 ## EQU2 ## a2 1 detQ3 det1 "3 = [(1+ a2 // - 2) (1+ a-2 / cr22) -1U 2] -1 0.4 / c2 / a2 2 detQ4 detr4 = [(1+ cr2 / - U * V a-4 / r4 = 1 Equation 21 Det Qi det n Similarly, we find for Q. when e -> 0: QI is unchanged - (.1 + .72 / .712 + a-2 / a- 22) -1U * v 2 1 V * LI 1 1 Q2 - Mi + 0-2 / 0-12) where 0, o Q3 O 1 / (1+ 0-2 cr22), Q4 0 0 ,, Equation 22 Shape It is observed that the products detQ1 det I- 'have a finite limit in each of the four situations, as do the matrices Qj, which is a satisfactory behavior.
[0012] This gives a first expression of the estimator. In reality, only one of the terms in Equation 19 is preponderant for each box, which leads to a first simplification. From this we deduce the new estimation process. = Q joM * X where j 0 = Arg Max {ql detQI derI exp (X * MQ A / 1 * XI 20-2 »i What we simplify in: = QioM * X where jo = Arg Max FI = Arg M ax {ln (qj detQ1 det ri) + X * MQJM * X / 2o-2} Equation 23 Estimation of the signal with decision function M * X is given by: M * X = tU * X V * X Q det Fi are given by Equation 21. The Q's are given by Equation 22, {q2, j = 1 The q's are given for example by q1 = q (1 - q), j = 2,3, (1- q) 2, j = 4 Equation 24 Expression of the parameters qj if there is independence of the 4 situations and equiprobability for s # 0, c # 0. F (j) is given by: 20 F (ji) = ln (qi det Q1 det Fi) + X * MQ1M * X / 20-2 = ln (q2 (1-1U * V 2) 0.4 I 0.120.22) + X * MQ1M * X / 2c2 F (j2) = ln (q2det Q2 det F2) + X * MQ2M * X / 20-2 = 14 (1- q) cr2 / c712) + X * UU * XI 20-2 F (j3) = ln (q3 det Q3 of F3) ± X * MQ3M * X 20-2 = 114 (1- q) o-2 / o-22) + X * VV * X / 2cr2 F (j4) = ln (q4 det Q4 det r4) + X * MQ4M * X / 20-2 = ln ((1- q) 2) For jo = 1, we find the maximum likelihood estimator. Indeed in this case (Cr2 / 0 = ---- 0 and QI =) so that § "= IM * X. On 0 (72 / itf_2 2) finds that if U * V = 0, then the estimates of s and c are completely separated, because then the relation = (M * MrM * X is simplified and decoupled into = U * X, ê = V * X For jo = 2, .§'T = (U * X, 0) (filtering by the directional vector of the source 1) For jo = 3, = (0, T7 * X) (filtering by the directional vector of the source 2) For jo = 4, = (0,0) Where the symbol T designates the transpose, the optimal processing has been "linearized", since four linear filters have been obtained, ordered by the decision on the type of situation for each box: the two sources are present / the source 1 is present / source 2 is present / none of the two sources is present The so-called "Conditional Expectancy at 4 Linear Filters" is called the estimator, so that the optimal estimator has been simplified by decomposing it into two stages: - The detection of The situation - The application of a filtering appropriate to the situation It is satisfactory to note that the estimator is independent of r, which is the expected behavior since r is not a physical parameter, but a device allowing to model the situation "absence of signal" by a very pinched Gaussian. This estimator requires the calculation of three quadratic forms and a test. The hard point remains the calculation of the unknown parameters a hi = 1 4 15e, efr (the power of the noise 25 2o2 is assumed known). In the particular case where the 2 sources are independent, and have the same power and the same presence rate, the parameters can be estimated by calculating the empirical moments of order 2 and 4. If we call 20 -'2 the common value of the variance of the Gaussian 30 representing each source, and q the probability common to both sources, everything happens as if we were in a monosource situation, with a single source of variance 2o - = 2 (72 and probability of presence qm = 2q. '2 0-m and qm are then given by the following equations: {-U 4 = 2qm (2 -Ulxn = 8qm 0-m +0.2 + qm) 20-2 2 (2 0-m +0.2 + 8 (1 qm) 0-4) In the general case (independent sources), the parameters of the model are four in number: a q2 0-12 0-22. One skilled in the art knows how to generalize the method of moments above to higher orders to obtain estimates of these parameters A variant of the estimation process is to simplify the decision previously, as follows: The conditional expectation considers the four possible situations: s 0, c 0; s 0, c = 0; s = 0, c 0; s = 0, c = 0 It would normally be necessary to deal with a decision problem to four hypotheses. For simplicity, we propose to test s # 0 against s = 0 independently of c on the one hand, and to test c # 0 against c = 0 independently of s on the other hand. Thus, two tests are carried out with two hypotheses instead of a test with four hypotheses. These tests will be carried out from the pre-processed measurements U * X, V * X TEST OF s 0 VS s = 0 U * X = s + U * Vc + u H1:, s # 0 V * X = V * U.s + c + v {U * X = U * V.c + u Ho:, s # 0 VX = c + v Equation 25 Simplified hypothesis test: the 2 hypotheses for s where the (.) indicate the scalar product x scalar and where u = U * W, v = V * W: (u, v) is Gaussian, centered and covariant: E {(U * W 18 (W * UW * V)}. 2o-2 ( 1 U * T / V * W y * U 1 and where c is an unknown parameter It is an invariant problem by the group of vector translations (U * V 1) T and a linear hypothesis problem (see "Testing Statistical Hypothesis ", 3rd edition, EL
[0013] Lehmann, J.P. Romano, Springer, 2005). It can be treated by firstly projecting on the orthogonal (U * V 1) T to eliminate c, then testing the presence of s by a chi2 test. The projection is written: U * V u * x - (u * v) v * x = {(1- 2) s (LT) v (H1) u - 14, (H0) The test to be carried out is thus on the measure u * x - (u * v) v * x12: u * x - (u * v) v * x 2> OR <Equation 26 Simplified hypothesis test on s 2 1U * X (U * V) V * X 2> or <2 ', where This is the same as doing the test: g'MV (1- lu * v 2) slmv is the maximum likelihood estimate of s.
[0014] TEST OF c # 0 AGAINST c = 0 In the same way for c, we project M * X on the orthogonal of (1 V * U) T in order to eliminate the terms in s and we obtain the new measure to consider: - (v,) TT * x + v * x = (1- U * V12 + v - (T / (H'1) v - (v * Or Vro We obtain the following test: (T / U) U * X -V * X12> or Equation 27 Simplified hypothesis test on c that can be written bsmv = 19> or <, u '(V * UU * X - V * X (1- U * V 2) WHERE êmv is the estimate of c in the maximum likelihood sense of C. In bisources the proposed estimator consists of performing the following operations: As illustrated in Figure 3, from the calculation of the maximum probability estimator bisources' 'A / y = (3/1 * M) -1M * X performed in step 220, a thresholding of the module of each component of, §'mv is performed in step 320 on each of the components SMV and lêmvl Then, depending on the situation, spatial filtering is applied to steps 331 to 334 under the following conditions, which provides the 'Independent Decisions Conditional Expectancy Estimator' (ECDI): o If 1. juv> threshold and ê mvl> threshold: SECDJ = (MM) 1 M * X (step 331) ',, v1> threshold and g' mvl <threshold and <threshold and lê mv <threshold: SECDI = UX, Cc = (1) (step 332), the Advl> threshold: sECDI = 0, êECDI = V * X (step 333) êmvl <threshold: '. . ## EQU3 ## (step 334) o If o Si o Si Ig.mv 15 In monosource the proposed estimator consists of performing the following operations, as illustrated in FIG. 2: From the calculation of the maximum estimator likelihood SMV = UX performed in step 210, thresholding of the: ssmv module is performed in step 350, then, depending on the situation, spatial filtering is applied to steps 361 or 362 under the following conditions : o If 1mvl> threshold sECDJ = U * X (step 361) <threshold g 'EcDi = 0 (step 362) Advantageously, the threshold for steps 320, 350 is set as follows: Pfa is the probability to decide s # 0 whereas s = 0 and Pd, probability of deciding s # 0 whereas s # 0 O. For example, we propose, in a way that is in no way limitative, to use the Neyman-Pearson criterion which consists in fixing the Pfa (for example a few percent) and in return to maximize Pd, which makes it possible to obtain a threshold over 2 'and, u'. For example, and in no way limiting, one can also adjust the value of 2 '(resp, u') so that 1 - Pd = Pfa around a fixed RSB. A variant close to the Maximum Likelihood Maximum and called the Maximum Likelihood Maximum (MVS) is to perform the following operations: - Calculation of the maximum likelihood estimator, §mv AdrM X - Threshold of the component module of - Depending on the situation, application of spatial filtering o If SMV <threshold: 5MVS = 0, otherwise Ssmvs =. ". smv o If êmvl <threshold: êmvs = 0, otherwise êmvs = êmv Another variant is to use one of the two previous estimators to initialize the unknown parameters q1114, c, a, then apply the Conditional Expectancy estimator or the Conditional Expectancy estimator to 4 Linear Filters.

权利要求:
Claims (8)
[0001]
CLAIMS 1. A method for estimating at most two mixed signals coming from different sources, whose representation in time / frequency reveals an unknown non-zero proportion of zero components, by means of a network composed of P> 2 antennas, when the directional vectors U and V of the sources emitting these signals are known or otherwise estimated, comprising the following steps: a) Calculate the successive Discrete Fourier Transforms of the signal received by the antennas and sampled to obtain a P-vector time-grid signal frequency; each element of the grid being called a box and containing a complex vector X forming a measurement; b) For each cell, calculate the estimator of the conditional expectation of the signal, or signals, from the measure X and a density (p (s)) of prior probability for the signals which is a mixture of Gaussians.
[0002]
2.- Method according to claim 1, characterized in that it comprises a step of estimating the parameters (q1,0'12,0'22) necessary to establish the conditional expectation by the method of the moments operating on the boxes a window cut in the time / frequency grid.
[0003]
3- Method according to claim 1 or 2, characterized in that the calculation of the estimator of the conditional expectation is approximated by a Conditional Expectancy at 4 Linear Filters obtained by a decision process with four hypotheses relating to four Hermitian forms of the measure X, followed by a linear filtering controlled by the result of the decision.
[0004]
4- Method according to claim 3, characterized in that the calculation of the estimator of the Conditional Expectancy at 4 Linear Filters is approximated by a Conditional Expectation with Independent Decisions obtained by a decision processing with two hypotheses relating to U * X and V * X, followed by a linear filtering controlled by the result of the decision.
[0005]
5. The method as claimed in claim 4, wherein, according to the result of the decision, the linear filtering treatment giving the Estimator of Conditional Expectation with Independent Decisions is either: the maximum likelihood estimator bi-sources for each source; - the single-source likelihood estimator for the first source, 0 for the second source; - 0 for the first source, the single-source maximum likelihood estimator for the second source; - 0 for each source.
[0006]
6. The method as claimed in claim 5, characterized in that the calculation of the Estimator of Conditional Expectation with Independent Decisions is approximated by a Maximum Likelihood Maximum obtained by the estimate of the signal (s) by the method of maximum likelihood. followed by comparing each estimate to a threshold.
[0007]
7- The method of claim 4 or 6, characterized in that the threshold or each decision threshold is chosen to respect a so-called false alarm probability of declaring the non-zero signal while it is zero.
[0008]
8- Process according to claims 4, 5 or 6, taken in combination with claim 1 or 3, characterized in that it comprises: - a first estimation of the signals carried out by the method of Conditional Hope with Independent Decisions or the Maximum Likelihood Maximum, - An estimate of parameters (qi, o-12, (5-22) made from the signal components obtained in the previous step, - A second estimate of the signals performed by the Conditional Hope method or by the Conditional Expectation method with 4 Linear Filters, informed by the values of the parameters (q1,0-12, cr) obtained in the previous step.

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优先权:

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申请号 | 申请日 | 专利标题

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FR1402981|2014-12-23|

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FR1402981A|FR3030807B1|2014-12-23|2014-12-23|NON-LINEAR METHOD OF ESTIMATING A MIXTURE OF SIGNALS|FR1402981A| FR3030807B1|2014-12-23|2014-12-23|NON-LINEAR METHOD OF ESTIMATING A MIXTURE OF SIGNALS|

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PCT/EP2015/081213| WO2016102697A1|2014-12-23|2015-12-23|Method for the non-linear estimation of a mixture of signals|

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EP15820534.4A| EP3238094A1|2014-12-23|2015-12-23|Method for the non-linear estimation of a mixture of signals|

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US15/539,386| US10560073B2|2014-12-23|2015-12-23|Method for the non-linear estimation of a mixture of signals|