Sign In to Follow Application
View All Documents & Correspondence

Method For Estimating The Number Of Incident Sources In A Sensor Array By Means Of Estimating Noise Statistics

Abstract: The invention relates to a method and system for determining the number of incident sources in an array that comprises C sensors receiving N observations, said method comprising at least the following steps: calculating the matrix B and the eigenvalues {λ1,…, λN} thereof obtained from a signal received on C sensors; classifying the eigenvalues {λ1,…, λN} so as to obtain λ1≥… ≥ λN; initializing from i to i= M + 1 and i = i - 1; calculating the mean and the standard deviation of the noise eigenvalues; calculating the mean of the N - i lowest eigenvalues of the matrix B; and calculating the standard deviation of the N - i lowest eigenvalues of the matrix B. If λ1 > λmoy + ησ, then said eigenvalue belongs to the signal space, and the number of sources present in the mixture is equal to i, where η is a threshold that makes it possible to monitor the probability of a false alarm. If λ1 > λmoy + ησ, said eigenvalue belongs to the noise space, and the steps are repeated.

Get Free WhatsApp Updates!
Notices, Deadlines & Correspondence

Patent Information

Application #
Filing Date
27 June 2012
Publication Number
10/2014
Publication Type
INA
Invention Field
PHYSICS
Status
Email
remfry-sagar@remfry.com
Parent Application

Applicants

THALES
45 rue de Villiers F 92200 Neuilly sur Seine
FERREOL Anne
130 Boulevard de Valmy F 92700 Colombes

Inventors

Specification

METHOD AND SYSTEM FOR ESTIMATING THE NUMBER OF SOURCES INCIDENT ON AN ARRAY OF SENSORS BY ESTIMATING THE NOISE STATISTICS The invention relates notably to a method and its associated system for estimating the number of incident sources in an array comprising C sensors or antennas on which N observations are processed. For the description below, the following notation will be used: • C is the number of reception sensors, • N is the number of nonredundant observations processed; for example, N=C if only the 2^^ order statistics of the received signal are taken into consideration, and N=f(C*') where f(.) is a polynomial function of N of order lnt(q/2) if the q*"^ order statistics are taken into consideration, • K is the number of signal samples for each observation, • M is the number of sources to be estimated, • x(t) is the signal received by the array of sensors, and is a vector of size C. The problem of estimating the number of sources present in a mixture constitutes a crucial step in passive listening systems before carrying out operations of high-resolution localization, separation techniques or joint demodulation. It involves detecting (M) sources with M lying between 0 and N-1, where N is the number of nonredundant observations processed by the C sensors of the reception antenna. In an electromagnetic context, the sensors are antennas and the radio sources propagate with a polarization. In an acoustic context, the sensors are microphones and the sources are sounds. Conventional methods for estimating the number of sources present in a mixture rely, for example, on statistical tests based on the eigenvalues (EV) of the covariance matrix of the signal received by the sensors of the reception antenna. These tests are based on knowledge of the probability law of the fluctuation of the noise eigenvalues, given that the 2 covariance matrix of the signal is estimated using K statistically independent samples and that the noise is assumed to be white and Gaussian. The strongest eigenvalues of the covariance matrix correspond to the signal eigenvalues, while the weakest values of the matrix generally correspond to the noise. Asymptotically (K tending to infinity) and in the presence of white noise, the noise eigenvalues are all identical. For a finite number K of samples, fluctuations are observed which make separation of the signal eigenvalues from the noise eigenvalues not straightforward. For dealing with these statistical fluctuations, the most conventional tests are the chi-square, AlC and MDL tests, which will be described below and which use the assumedly Gaussian statistics of white noise. Chi-Square Test This test consists in estimating the likelihood ratio of the noise eigenvalues and in increasingly testing various hypotheses about the number N-M of noise eigenvalues RV{M) = 2K{N-M)\og[^^^~^ {a{N-M)J where g{N-M) and a{N-M) represent the geometric and arithmetic means of the (N-M) smallest eigenvalues of the covariance matrix B of the observation, K being the number of samples observed. The likelihood ratio asymptotically follows a chi-square law with (N-M)^-1 degrees of freedom because the noise is assumed to be white and Gaussian, which makes it possible to set a detection threshold when the number of samples K is high (K>30). AlC (Akaike Information Criterion) and IVIDL (Minimum Distance Length) Tests This criterion was initially developed by H. Akaike in order to determine the order of a model [1]. It is based on calculating the likelihood ratio of the noise eigenvalues, with the addition of a corrective term which makes it possible to take account of situations in which the value of K is low (for example K<30). The number of sources is then determined as being the integer which minimizes the following quantity: 3 AICiM) = -K(N- M) log I ^^ \ + mi2N-m) \a{m)) where g(m) and a{m) represent the geometric and arithmetic means of the m=N-M smallest eigenvalues of the covariance matrix B of an observation, K being the number of samples observed. Another test has been proposed in order to confront the consistency problem of the AlC test; this involves the minimum distance length or MDL criterion, which introduces a modified corrective term. A prior art method [2] is proposed for detecting the number of sources in the presence of colored noise. This method relies on the assumptions of a linear array and uncorrelated signals. Empirical Threshold Criteria The preceding statistical criteria are based on a white structure of additive Gaussian noise. In practice, the noise is neither white nor Gaussian. Under these conditions, the noise eigenvalues are no longer all identical when the number of observations K tends to infinity. This is why purely empirical criteria aiming to classify the "small" and "large" eigenvalues have been proposed. These methods notably have the drawback of making strong assumptions either about the structure of the covariance matrix, about that of the covariance matrix of the noise or about that of the covariance matrix of the signal without noise. Decrease of the Eigenvalue Spectrum When incident signals have strong correlations or small angle differences, certain eigenvalues of the signal space become close to those of the noise, which leads to underestimation of the number of sources. Methods have been developed for overcoming this problem, by postulating an empirical distribution law of the eigenvalues in the noise space. The modeling of the decrease may be linear or exponential. The estimation of the number of sources then relies on searching for a significant jump in the decrease of the eigenvalues. It is, however, necessary to adjust a detection threshold value which relies on the assumption of circular additive Gaussian noise. Neural Networks 4 Other methods have been developed around neural networks in order to estimate a small number of sources present. These methods impose a structure on the covariance matrix of the noise and have fairly significant implementation complexity. Wiener Filtering Methods which are based on the multistage Wiener filter [3] have also been proposed. They make it possible to obviate the phase of calculating the covariance matrix of the signal as well as the decomposition into eigenvalues. It is assumed that the additive noise is white noise and that the sources are generated by a filter with 3 coefficients and are incident on an equally spaced linear array. The test for detecting the number of sources then utilizes this structure. In practice, the temporal spread of the sources is not known and the noise does not necessarily have a white structure. Other methods assume that the noise is Gaussian and spatially correlated, two assumptions which are not necessarily satisfied in a real situation. The empirical method described in [4] relies on modeling the exponential decrease of the noise eigenvalues, i.e. r{p) = exp - /Y with -T^ = ^{P) where p is the number of noise eigenvalues, (>^>-->/l^) are the eigenvalues of the covariance matrix and K is the number of observations used to estimate the covariance matrix. The noise or signal decision test is then as follows Noise Hypotfiesis Vp - V;- ^ —^ With X = " ■ Signsi Hypothesis ^ M. / Despite its effectiveness, this method has the drawback of not working when the number of observations used to estimate the covariance matrix tends to infinity. It assumes a white structure of the noise and therefore does not work in the presence of correlated and colored noise. 5 Also known in the prior art is the document: KRITCHIVIAN S ET AL: "Nonparametric detection of the number of signals and random matrix theory", SIGNALS, SYSTEMS AND COIVIPUTERS, 2008 42 ND ASILOMAR CONFERENCE ON, IEEE, PISCATAWAY, NL, USA, October 26, 2008 (2008-10-26), pages 1680-1683, XP031475587 - ISBN 978-1-4244-2940-0, as well as: CHEN W ET AL: "Detection of the number of signals: a predicted eigen-threshold approach", IEEE TRANSACTIONS ON SIGNAL PROCESSING, IEEE SERVICE CENTER, NEW YORK, NY, US LNDK-DOI: 10.1109/78.80959, vol.39, No. 5, May 1, 1991 (1991-05-01), pages 1088-1098; XP002506761 ISSN 1053-587X. From a general point of view, the technical object is to estimate the number M of components of the following linear mixture: where r,,., a vector of dimension Nxl, is a more or less linear transformation of the observation x^, received by the C sensors, n^is an additive noise vector. Each source Sm(k) is associated with the signature a„. If the 2""^ order statistics are taken into consideration, the object is to detect M on the basis of the following covariance matrix: From a very general point of view, the detection of the number M is carried out on the basis of the N eigenvalues ^i of the matrix B. The subject of the present invention relates to a method making it possible notably to take account of mixed signals in the case of correlated and/or colored noise, or noncircular, non-Gaussian noise, without the specificity of a particular sensor array geometry. The method works in the presence of correlated sources and/or sources having a large power gradient. By extension to higher orders, the method can detect a number of sources greater than the number C of sensors of the reception antenna. 6 The invention relates to a metliod for determining the number of incident sources in an array comprising C sensors receiving N observations, characterized in that it comprises at least the following steps: Step 1: Calculating the matrix B of dimension NxN observed over N components and obtained from a signal received by C, sensors, Step 2: Calculating the eigenvalues {A^,...,Jifj]ofthe matrix B, Step 3: Classifying the eigenvalues of the matrix B of the signal in order to obtain A^>...>A^ and initializing the number of received sources to M = Mmax, step 4.0: Initializing i to i=M+1, Step 4.1: i = i-1, step 4.2: Calculating the mean and the standard deviation of the noise eigenvalues -> Calculating the mean of the N-i smallest eigenvalues of the matrix B 1 ^ -> Calculating the standard deviation of the N-i smallest eigenvalues of the matrix B Step 4.3: If A, > ^^^^n^-, then this eigenvalue belongs to the signal space and the number of sources present in the mixture is equal to i, where ;; is a threshold which makes it possible to control the probability of false alarm. The method is terminated. Step 4.4: If z. < -i„e3^+ rja, this eigenvalue belongs to the noise space: return to step 4.1. The invention also relates to a system for determining the number of incident sources in an array comprising C sensors receiving N observations, characterized in that it has at least one receiver comprising a 7 processor adapted for carrying out the steps of the method which have been explained above. Other characteristics and advantages of the method and system according to the invention will become clearer on reading the following description of an exemplary embodiment, given by way of illustration and without any limitation, supplemented with the figures in which: • Figure 1 represents an example of an antenna processing system, and • Figure 2 represents an example of an array of sensors with positions (Xn, yn). Figure 1 shows an example of an antenna processing system, which is composed of an array 1 of sensors or antennas 41 receiving signals coming from various sources with different arrival angles 0/p (/ is the index of the emitter and p that of the path) and a receiver 3. The receiver comprises a processor adapted for carrying out the steps of the method according to the invention. The array may also comprise obstacles 2 at which the signals are reflected before being received by the antennas. The elementary sensors 4i of the array receive the signals emitted by the sources with a phase and amplitude depending in particular by their angles of incidence and the positions of the sensors. The angles of incidence are parameterized in one dimension or 1D by the azimuth Gm, and in two dimensions 2D by the azimuth 0m and the elevation Am- Figure 2 schematizes an example of an array of 6 sensors receiving the signals from P=2 different sources. The method according to the invention notably has the object of determining the number M of incident sources in an array comprising C sensors receiving N observations. To this end, the following steps will be carried out in the receiver 3: Step 1: Calculating the matrix B of dimension NxN observed over N components and obtained from a signal received by C sensors, Step 2: Calculating the eigenvalues {/?,,...,;ijv}of the matrix B, 8 Step 3: Classifying the eigenvalues of the matrix B of the signal in order to obtain /?,>...>A^ and initializing the number of received sources to M = Mmax, Step 4.0: Initializing i to i=M+1, Step4.1: i = i-1, Step 4.2: Calculating the mean and the standard deviation of the noise eigenvalues -^ Calculating the mean of the N-i smallest eigenvalues of the matrix B 1 ^ -> Calculating the standard deviation of the A/-/' smallest eigenvalues of the matrix B Step 4.3: If X^ > K^^'^'^' then this eigenvalue belongs to the signal space and the number of sources present in the mixture is equal to i, where ;; is a threshold which makes it possible to control the probability of false alarm. The method is terminated. Step 4.4: If X^ < ^„e3^+ 7cr, this eigenvalue belongs to the noise space: return to 4.1. The method depends notably on two parameters A^^ax and r). Mmax may typically be equal to N/2 according to one nonlimiting example, ri is a coefficient giving the sensitivity of the method and depending on a probability of false alarm. It may for example be selected such that 2...> X^ and initializing the number of received sources to M = M^ax, Mmax may for example be taken as N/2, Step 4.0: Initializing i to i=M+1, Step4.1: i = i-1. Step 4.2: Calculating the mean and the standard deviation of the noise eigenvalues -^ Calculating the mean of the N-i smallest eigenvalues of the matrix B 1 ^ -^ Calculating the standard deviation of the N-i smallest eigenvalues of the matrix B 15 Step 4.3: If A^ > A„earj+'7*^> then this eigenvalue belongs to the signal space and the number of sources present in the mixture is equal to i, where 77 is a threshold which makes it possible to control the probability of false alarm, Step 4.4: If Z- < ^^^sn+ v^, this eigenvalue belongs to the noise space: return to step 4.1. 2 -The method as claimed in claim 1, characterized in that the eigenvalues of the matrix are organized in decreasing order. 3 - The method as claimed in claim 1, characterized in that the matrix B is the estimated value of the covariance matrix of the observation: x{t) is the signal received by the array of sensors, a vector of size C, and x(tk) is the signal received for the instant tk- 4 - The method as claimed in claim 1, characterized in that the matrix B is the estimated value of the spatiotemporal covariance matrix of the observation: r^=x^(f^) is an observation vector containing L different time offsets of the observation x(t) defined by Equation (3) M x,(0= x(/-r,) =£b(^„,/„K(X„0 + «(0 1 16 where 5,„(0 and s„{f„„t) are the input/output of a finite band filter centered on/m. 5 - The method as claimed in claim 1, characterized in that, in the event that the matrix B is not of full rank, the method takes into consideration the R nonzero eigenvalues of the covariance matrix. 6 - The method as claimed in claim 1, characterized in that the matrix B considered is an estimation of the matrix of the intercumulants of order 2q of the signals for K observations of the vector x(/^.) of dimension Cx1, and in that the method comprises a step of estimating the dimension of the signal space of the statistics matrix considered, which corresponds to the number of sources when they are independent, by using the following signal model: where P is the number of sources present; given that x„ (/) is the n'*^ component of x(/), the intercumulant Is defined by: c«m, (/■,...,i2J = cum(x. {t),...,x. (0,x,^^, {t)',-,x,^ (O'.^v, (O'-'^V. (')'V. i^)''-'\ (0*) for l

Documents