CN111323744A - Target number and target angle estimation method based on MDL (minimization drive language) criterion - Google Patents

Target number and target angle estimation method based on MDL (minimization drive language) criterion Download PDF

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CN111323744A
CN111323744A CN202010198101.XA CN202010198101A CN111323744A CN 111323744 A CN111323744 A CN 111323744A CN 202010198101 A CN202010198101 A CN 202010198101A CN 111323744 A CN111323744 A CN 111323744A
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target
whitening
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CN111323744B (en
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柳艾飞
郭韩俊
杨德森
莫世奇
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Harbin Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/78—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using electromagnetic waves other than radio waves
    • G01S3/782—Systems for determining direction or deviation from predetermined direction
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
    • G01S3/802—Systems for determining direction or deviation from predetermined direction
    • G01S3/8027—By vectorial composition of signals received by plural, differently-oriented transducers

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Abstract

The invention provides a method for estimating the number of targets and the target angle based on an MDL (minimization drive language) criterion, belonging to the field of array signal processing. The method has the advantage that the correct estimation of the target number and the target angle can be realized under the condition of non-uniform noise. The method mainly comprises the following steps: firstly, establishing an objective function with a Minimum Description Length (MDL) as a criterion by taking the target number and a whitening vector as unknown parameters; solving the minimum value of the MDL objective function by using a genetic algorithm so as to obtain an estimated value of the number of the targets and an estimated value of the whitening vector; then, whitening a covariance matrix of the received signal by utilizing an estimated value of the whitening vector; and finally, realizing accurate estimation of the target angle according to the whitened covariance matrix, the estimated value of the whitened vector and the estimated value of the target number.

Description

Target number and target angle estimation method based on MDL (minimization drive language) criterion
Technical Field
The invention relates to a method for estimating the number and angle of targets based on an MDL (minimization drive language) criterion under a non-uniform noise background, belonging to the technical field of array signal processing.
Background
The target number estimation and the target angle estimation give main information of the target, which is the main content in the array signal processing.
Schmidt, in the literature, "Multiple event location and signal parameter [ J ]. IEEE
Trans. antennas propag, 1988, vol.36, No.4, pp.532-544 "proposes a classical MUSIC high-resolution target angle estimation method, but the MUSIC method requires the assumption of a known target number. Akaike proposes a target number estimation method based on AIC (AIC, Akaike Information Criterion) Criterion in the document "A newboot at the statistical model identification [ J ]. IEEE Trans. Rissane proposes the Minimum Description Length (MDL) criterion in the document "Modeling by short data Description [ J ]. Automatica,1978, vol.14, No.5, pp.465-471", and methods based on the MDL criterion are consistent estimates in the case of uniform noise (equal noise power of different array elements). However, under the condition of non-uniform noise (noise power among array elements is not equal), the method based on the MDL criterion fails, and an over-estimation phenomenon exists. The Diagonal Loading (DL) based MDL criterion method (DLMDL) can solve the target number estimation problem in the case of non-uniform noise to some extent. Zhangjie et al, in the document "improvement of signal source number detection performance by diagonal loading [ J ]. electronic newspaper, vol.32, No.12,2004, pp.2094-2097", propose to use the minimum eigenvalue of the covariance matrix of the received signals multiplied by a constant as the loading amount of the DLMDL method. Shejingling et al propose in "covariance matrix diagonal loading based source number estimation method [ J ]. systematic engineering and electronics, 2008, vol.30, No.1, pp.46-49" to use the square root of the sum of all eigenvalues of the covariance matrix of the received signal as the loading of the DLMDL method. The selection of the optimal diagonal loading amount in the DLMDL method is difficult to determine; in addition, the DLMDL method sacrifices the signal-to-noise ratio. The method of SORTE of amendment proposed by the inventor in the document 'estimation algorithm of information source number [ J ] signal processing under non-uniform noise background, vol.34, No.2,2018, pp.135-138' can solve the problem of target number estimation under the conditions of non-uniform noise and irrelevant information source. But the performance of the modified SORTE method degrades severely in the case of correlated sources.
In terms of target angle estimation, the MUSIC method is derived in a uniform noise background. Therefore, even if the number of targets can be accurately known, the MUSIC method cannot accurately estimate the target angle under the non-uniform noise background, and cannot exert the high-resolution and high-precision performance.
Disclosure of Invention
The invention aims to provide a method for estimating the number of targets and the target angles based on a minimum length description (MDL) criterion aiming at the problem that the existing method cannot accurately estimate the number of the targets and the target angles under the non-uniform noise condition, so that the accurate estimation of the number of the targets and the target angles under the non-uniform noise background is realized.
The purpose of the invention is realized as follows: the method comprises the following steps:
acquiring N times of sampling data by an array consisting of M sensors, and acquiring a signal vector r (N) with M × 1 dimensions by nth sampling, wherein N is 1,2, … and N;
step (2): estimating a covariance matrix according to N sampling data r (N), N is 1,2, …, N
Figure BDA0002418358880000021
And (3): defining w and k as a search whitening vector and the number of search targets respectively, wherein each element in w is a positive real number, and k belongs to {0,1,2, …, M-1 }; determining the objective function as:
Figure BDA0002418358880000022
wherein the content of the first and second substances,
Figure BDA0002418358880000023
representing the (w, k) value at which the function takes the minimum value, i.e.
Figure BDA0002418358880000024
MDL (w, k) is an MDL function with (w, k) as the parameter to be estimated, and the expression is:
Figure BDA0002418358880000025
wherein λ isi(w) is the matrix diag (w)
Figure BDA0002418358880000026
The ith eigenvalue arranged from large to small of (1), diag (w) represents a diagonal matrix, and diagonal elements are vectors w;
and (4): solving the objective function in the step (3) by using a genetic algorithm to obtain a whitening vector estimation value
Figure BDA0002418358880000027
And target number estimation value
Figure BDA0002418358880000028
And (5): based on whitening vector estimation
Figure BDA0002418358880000029
For covariance matrix
Figure BDA00024183588800000210
Whitening to obtain
Figure BDA00024183588800000211
And (6): according to the covariance matrix after whitening
Figure BDA00024183588800000212
Whitening vector
Figure BDA00024183588800000213
And the estimated value of the target number
Figure BDA00024183588800000214
Estimating to obtain a target angle
Figure BDA00024183588800000215
The invention also includes such structural features:
1. covariance matrix in step (2)
Figure BDA00024183588800000216
The expression is as follows:
Figure BDA00024183588800000217
wherein, (.)HRepresents a conjugate transpose operation;
covariance matrix estimate as the number of samples approaches infinity
Figure BDA00024183588800000218
Approaching the desired value R, the expression is:
R＝ARsAH+Rn，
wherein a ═ a (θ)1),…,a(θk)]，a(θk) Is the steering vector of the kth target, θkIs the incoming wave direction of the kth target, Rs＝E[s(t)sH(t)]，s(t)＝[s1(t),…,sk(t)]，sk(t) is the waveform of the kth source, RnThe expression of (a) is as follows:
Figure BDA0002418358880000031
wherein the content of the first and second substances,
Figure BDA0002418358880000032
the noise power of the mth array element, M is 1,2, …, M,
Figure BDA0002418358880000033
not exactly equal, in which case the array noise is non-uniform noise.
2. The concrete implementation steps of the step (5) comprise:
(5.1) estimating a value from the whitening vector
Figure BDA0002418358880000034
Get whitening matrix as W, expressThe formula is as follows:
Figure BDA0002418358880000035
wherein the content of the first and second substances,
Figure BDA0002418358880000036
representing a diagonal matrix with diagonal elements as vectors
Figure BDA0002418358880000037
(5.2) use of whitening matrix W vs. covariance matrix
Figure BDA0002418358880000038
Whitening to obtain
Figure BDA0002418358880000039
The expression is as follows:
Figure BDA00024183588800000310
3. the concrete implementation steps of the step (6) comprise:
(6.1) pairs
Figure BDA00024183588800000311
Performing characteristic decomposition to obtain characteristic values lambda ranging from large to smalli(w), and its corresponding feature vector ui，i＝1,2,…,M；
(6.2) estimating the value according to the number of targets
Figure BDA00024183588800000312
And a feature vector uiTo obtain a noise characteristic matrix UnThe expression is:
Figure BDA00024183588800000313
(6.3) based on the whitening matrix W and the noise feature matrix UnConstruction of the spatial spectrum P (θ):
Figure BDA00024183588800000314
wherein theta is a search angle, and a (theta) is a guide vector corresponding to the angle theta;
(6.4) searching a peak value of the spatial spectrum P (theta), wherein the position of the peak value is the target angle estimated value, namely:
Figure BDA00024183588800000315
wherein the content of the first and second substances,
Figure BDA0002418358880000041
is an estimate of the jth target angle,
Figure BDA0002418358880000042
representing the value of theta at which the function takes the maximum value.
Compared with the prior art, the invention has the beneficial effects that: the method has the advantage that the correct estimation of the target number and the target angle can be realized under the condition of non-uniform noise. The target number and the target angle under the non-uniform noise condition can be accurately estimated. The method can still realize accurate estimation of the target number and the target angle under the conditions of related information sources and low signal-to-noise ratio, and compared with the existing method, the target number estimation performance is improved by 10dB, and the target angle estimation performance is improved by 5 dB.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention.
FIG. 2 shows the variation of the success rate of target number estimation with the signal-to-noise ratio under the conditions of non-uniform noise and uncorrelated signal sources in the method of the present invention, the MDL method, the modified SORTE method, and the DLMDL method.
FIG. 3 shows the variation of Root Mean Square Error (RMSE) of target angle estimation with signal-to-noise ratio under the condition of non-uniform noise and uncorrelated signal sources by the SORTE MUSIC method.
FIG. 4 shows the variation of the success rate of target number estimation with the signal-to-noise ratio under the conditions of non-uniform noise and related information sources in the method of the present invention, the MDL method, the modified SORTE method and the DLMDL method.
FIG. 5 shows the variation of the Root Mean Square Error (RMSE) of the target angle estimation with the signal-to-noise ratio in the case of non-uniform noise and correlated sources by the DLMDL MUSIC method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The technical idea of the invention is as follows: establishing a minimum length description criterion target function MDL (w, k) by taking a whitening vector w and a target number k as unknown parameters, solving the minimum value of the target function MDL (w, k) by utilizing a genetic algorithm to obtain a whitening vector estimated value
Figure BDA0002418358880000043
And target number estimation value
Figure BDA0002418358880000044
Using whitening vector estimates
Figure BDA0002418358880000045
To the covariance matrix of the received signal
Figure BDA0002418358880000046
Performing whitening treatment to obtain
Figure BDA0002418358880000047
According to the covariance matrix after whitening
Figure BDA0002418358880000048
Whitening vector estimation
Figure BDA0002418358880000049
And target number estimation value
Figure BDA00024183588800000410
Calculating to obtain a target angle estimation value
Figure BDA00024183588800000411
Referring to fig. 1, the implementation steps of the invention are as follows:
acquiring N times of sampling data by an array consisting of M sensors, and acquiring a signal vector r (N) with M × 1 dimensions by nth sampling, wherein N is 1,2, … and N;
step (2): estimating a covariance matrix according to N sampling data r (N), N is 1,2, …, N
Figure BDA00024183588800000412
The expression is as follows:
Figure BDA00024183588800000413
wherein, (.)HRepresents a conjugate transpose operation;
covariance matrix estimate as the number of samples approaches infinity
Figure BDA0002418358880000051
Approaching the desired value R, the expression is:
R＝ARsAH+Rn，
wherein a ═ a (θ)1),…,a(θk)]，a(θk) Is the steering vector of the kth target, θkIs the incoming wave direction of the kth target, Rs＝E[s(t)sH(t)]，s(t)＝[s1(t),…sk(t)]，sk(t) is the waveform of the kth source, RnThe expression of (a) is as follows:
Figure BDA0002418358880000052
wherein the content of the first and second substances,
Figure BDA0002418358880000053
the noise power of the mth array element, M is 1,2, …, M,
Figure BDA0002418358880000054
not exactly equal, in which case the array noise is non-uniform noise.
Defining w and k as a search whitening vector and the number of search targets respectively, wherein each element in w is a positive real number, and k belongs to {0,1,2, …, M-1 }; determining the objective function as:
Figure BDA0002418358880000055
wherein the content of the first and second substances,
Figure BDA0002418358880000056
representing the (w, k) value at which the function takes the minimum value, i.e.
Figure BDA0002418358880000057
MDL (w, k) is an MDL function with (w, k) as the parameter to be estimated, and the expression is:
Figure BDA0002418358880000058
wherein λ isi(w) is the matrix diag (w)
Figure BDA0002418358880000059
The ith eigenvalue arranged from large to small of (1), diag (w) represents a diagonal matrix, and diagonal elements are vectors w;
and (4): solving the objective function in the step (3) by using a genetic algorithm to obtain a whitening vector estimation value
Figure BDA00024183588800000510
And target number estimation value
Figure BDA00024183588800000511
And (5): based on whitening vector estimation
Figure BDA00024183588800000512
For covariance matrix
Figure BDA00024183588800000513
Whitening to obtain
Figure BDA00024183588800000514
The concrete implementation steps comprise:
(5.1) according to
Figure BDA00024183588800000515
Obtaining a whitening matrix W, wherein the expression is as follows:
Figure BDA00024183588800000516
wherein the content of the first and second substances,
Figure BDA00024183588800000517
representing a diagonal matrix with diagonal elements as vectors
Figure BDA00024183588800000518
(5.2) use of whitening matrix W vs. covariance matrix
Figure BDA0002418358880000061
Whitening to obtain
Figure BDA0002418358880000062
The expression is as follows:
Figure BDA0002418358880000063
and (6): according to the covariance matrix after whitening
Figure BDA0002418358880000064
Whitening vector estimation
Figure BDA0002418358880000065
And the estimated value of the target number
Figure BDA0002418358880000066
Estimating to obtain a target angle
Figure BDA0002418358880000067
The concrete implementation steps comprise:
(6.1) pairs
Figure BDA0002418358880000068
Decomposing the eigenvalue to obtain the eigenvalue lambda arranged from large to smalli(w) and its corresponding feature vector ui,i＝1,2,…,M；
(6.2) estimating the value according to the number of targets
Figure BDA0002418358880000069
And a feature vector uiTo obtain a noise characteristic matrix UnThe expression is:
Figure BDA00024183588800000610
(6.3) based on the whitening matrix W and the noise feature matrix UnConstruction of the spatial spectrum P (θ):
Figure BDA00024183588800000611
wherein theta is a search angle, and a (theta) is a guide vector corresponding to the angle theta;
(6.4) searching a peak value of the spatial spectrum P (theta), wherein the position of the peak value is the target angle estimated value, namely:
Figure BDA00024183588800000612
wherein the content of the first and second substances,
Figure BDA00024183588800000613
is an estimate of the jth target angle,
Figure BDA00024183588800000614
representing the value of theta at which the function takes the maximum value.
The present invention is further described below in conjunction with simulation experiments.
Simulation conditions
In the simulation experiment, a software simulation platform is MATLAB R2014a, a genetic algorithm carried by MATLAB R2014a is used, parameters of the genetic algorithm are set as default values, 5 times of genetic algorithm are used in each experiment to obtain 5 estimated values, and the estimated values are averaged to be output so as to improve the estimation accuracy of whitening vectors and target numbers. The array is a uniform linear array consisting of 5 array elements, and the spacing between the array elements is half wavelength; the target signal is a far-field narrow-band signal, and the incoming wave directions are respectively 30 degrees and 50 degrees; the noise is white gaussian noise, and the target signal is uncorrelated with the noise; the noise power of 5 array elements is respectively
Figure BDA00024183588800000615
The power of different target signals is equal, and the signal-to-noise ratio is defined as
Figure BDA00024183588800000616
Wherein the content of the first and second substances,
Figure BDA00024183588800000617
in order to target the power of the signal,
Figure BDA00024183588800000618
for noise average power, the expression is
Figure BDA00024183588800000619
Figure BDA00024183588800000620
The noise power of the m array element; the sampling number is 1000; the Monte-Carlo frequency is 100; the diagonal loading of the diagonal loading based MDL algorithm (DLMDL) is taken as
Figure BDA0002418358880000071
Wherein λ ismIs a covariance matrix
Figure BDA0002418358880000072
The mth eigenvalue of (1).
(II) simulation content and results
First, the experiment is used to compare uncorrelated signal sources and non-uniform noise conditions, and the target number estimation success rates of the method, DLMDL, modified SORTE, MDL methods of the present invention vary with SNR, as shown in fig. 2.
Referring to fig. 2, at-5 dB, the estimation success rate of the method of the present invention is still 1, and the number of targets can be correctly estimated; however, when the signal-to-noise ratio is less than 5dB, the performance of the DLMDL method is rapidly reduced, and the target number cannot be successfully estimated. It can be seen that compared with DLMDL, the performance of the method of the invention is improved by 10 dB. Compared with the modified SORTE method, the method has slightly lower estimation success rate when the signal-to-noise ratio is-10 dB. Finally, the MDL method still fails no matter how high the signal-to-noise ratio is.
And secondly, estimating the target number by using a corrected SORTE method, and then estimating the target azimuth by using a MUSIC method according to the estimated value, wherein the method is marked as the SORTE MUSIC method. This experiment was used to compare the target angle estimate Root Mean Square Error (RMSE) with SNR for uncorrelated target signals and non-uniform noise, as shown in fig. 3.
Referring to fig. 3, the method of the present invention cannot estimate the target angle when the signal-to-noise ratio is less than-5 dB, and cannot estimate the target angle when the signal-to-noise ratio of the SORTE MUSIC is less than 0 dB; therefore, compared with the SORTE MUSIC method, the method disclosed by the invention has the advantage that the performance is improved by 5 dB.
And thirdly, the experiment is used for comparing the target number estimation success rate of the method, the DLMDL method, the modified SORTE method and the MDL method with the change of the SNR under the condition that the correlation coefficient of two information sources is 0.6 and the non-uniform noise is caused, as shown in figure 4.
Referring to fig. 4, at this time, neither the modified sotte method nor the MDL method can estimate the target number. Compared with DLMDL, the performance of the method is still improved by 10 dB.
And fourthly, firstly estimating the target number by using a DLMDL method, and estimating the target azimuth by using an MUSIC method according to the estimated value, wherein the method is marked as the DLMDL MUSIC method. The experiment was used to compare the variation curves of target angle estimation Root Mean Square Error (RMSE) with SNR for the method of the invention and the DLMDL MUSIC method under non-uniform conditions with a correlation coefficient of two sources of 0.6, as shown in fig. 5.
Referring to fig. 5, the method of the present invention cannot estimate the target angle when the signal-to-noise ratio is less than 0dB, and cannot estimate the target angle when the signal-to-noise ratio of DLMDL MUSIC is less than 5 dB; therefore, compared with the DLMDL MUSIC method, the performance of the method is improved by 5 dB.
From fig. 2 to fig. 5, it can be seen that the method of the present invention can achieve accurate target number estimation and target angle estimation under the condition of non-uniform noise. In addition, the method can still realize accurate estimation of the target number and the target angle under the conditions of related information sources and low signal-to-noise ratio, and compared with the existing method, the target number estimation performance is improved by 10dB, and the target angle estimation performance is improved by 5 dB.
In summary, the invention discloses a method for estimating the number of targets and the target angle based on an MDL criterion under a non-uniform noise background, and belongs to the field of array signal processing. The method has the advantage that the correct estimation of the target number and the target angle can be realized under the condition of non-uniform noise. The method mainly comprises the following steps: firstly, establishing an objective function with a Minimum Description Length (MDL) as a criterion by taking the target number and a whitening vector as unknown parameters; solving the minimum value of the MDL objective function by using a genetic algorithm so as to obtain an estimated value of the number of the targets and an estimated value of the whitening vector; then, whitening a covariance matrix of the received signal by utilizing an estimated value of the whitening vector; and finally, realizing accurate estimation of the target angle according to the whitened covariance matrix, the estimated value of the whitened vector and the estimated value of the target number.

Claims (4)

1. A target number and target angle estimation method based on MDL criterion is characterized in that: the method comprises the following steps:
acquiring N times of sampling data by an array consisting of M sensors, and acquiring a signal vector r (N) with M × 1 dimensions by nth sampling, wherein N is 1,2, … and N;
step (2): estimating the covariance according to N sampling data r (N), N is 1,2, …, NVariance matrix
Figure FDA0002418358870000011
And (3): defining w and k as a search whitening vector and the number of search targets respectively, wherein each element in w is a positive real number, and k belongs to {0,1,2, …, M-1 }; determining the objective function as:
Figure FDA0002418358870000012
wherein the content of the first and second substances,
Figure FDA0002418358870000013
representing the (w, k) value at which the function takes the minimum value, i.e.
Figure FDA0002418358870000014
MDL (w, k) is an MDL function with (w, k) as the parameter to be estimated, and the expression is:
Figure FDA0002418358870000015
wherein λ isi(w) is a matrix
Figure FDA0002418358870000016
The ith eigenvalue arranged from large to small of (1), diag (w) represents a diagonal matrix, and diagonal elements are vectors w;
and (4): solving the objective function in the step (3) by using a genetic algorithm to obtain a whitening vector estimation value
Figure FDA0002418358870000017
And target number estimation value
Figure FDA0002418358870000018
And (5): based on whitening vector estimation
Figure FDA0002418358870000019
For covariance matrix
Figure FDA00024183588700000110
Whitening to obtain
Figure FDA00024183588700000111
And (6): according to the covariance matrix after whitening
Figure FDA00024183588700000112
Whitening vector
Figure FDA00024183588700000113
And the estimated value of the target number
Figure FDA00024183588700000114
Estimating to obtain a target angle
Figure FDA00024183588700000115
2. The method of claim 1, wherein the method comprises: covariance matrix in step (2)
Figure FDA00024183588700000116
The expression is as follows:
Figure FDA00024183588700000117
wherein, (.)HRepresents a conjugate transpose operation;
covariance matrix estimate as the number of samples approaches infinity
Figure FDA00024183588700000118
Approaching the desired value R, the expression is:
R＝ARsAH+Rn，
wherein a ═ a (θ)1),…,a(θk)]，a(θk) Is the steering vector of the kth target, θkIs the incoming wave direction of the kth target, Rs＝E[s(t)sH(t)]，s(t)＝[s1(t),…,sk(t)]，sk(t) is the waveform of the kth source, RnThe expression of (a) is as follows:
Figure FDA0002418358870000021
wherein the content of the first and second substances,
Figure FDA0002418358870000022
the noise power of the mth array element, M is 1,2, …, M,
Figure FDA0002418358870000023
not exactly equal, in which case the array noise is non-uniform noise.
3. The method for estimating the number of targets and the target angle based on the MDL criterion as claimed in claim 1 or 2, wherein: the concrete implementation steps of the step (5) comprise:
(5.1) estimating a value from the whitening vector
Figure FDA0002418358870000024
Obtaining a whitening matrix W, wherein the expression is as follows:
Figure FDA0002418358870000025
wherein the content of the first and second substances,
Figure FDA0002418358870000026
representing a diagonal matrix with diagonal elements as vectors
Figure FDA0002418358870000027
(5.2) use of whitening matrix W vs. covariance matrix
Figure FDA0002418358870000028
Whitening to obtain
Figure FDA0002418358870000029
The expression is as follows:
Figure FDA00024183588700000210
4. the method of claim 3, wherein the target number and the target angle are estimated based on MDL criterion, and the method comprises: the concrete implementation steps of the step (6) comprise:
(6.1) pairs
Figure FDA00024183588700000211
Performing characteristic decomposition to obtain characteristic values lambda ranging from large to smalli(w), and its corresponding feature vector ui，i＝1,2,…,M；
(6.2) estimating the value according to the number of targets
Figure FDA00024183588700000212
And a feature vector uiTo obtain a noise characteristic matrix UnThe expression is:
Figure FDA00024183588700000213
(6.3) based on the whitening matrix W and the noise feature matrix UnConstruction of the spatial spectrum P (θ):
Figure FDA00024183588700000214
wherein theta is a search angle, and a (theta) is a guide vector corresponding to the angle theta;
(6.4) searching a peak value of the spatial spectrum P (theta), wherein the position of the peak value is the target angle estimated value, namely:
Figure FDA0002418358870000031
wherein the content of the first and second substances,
Figure FDA0002418358870000032
is an estimate of the jth target angle,
Figure FDA0002418358870000033
representing the value of theta at which the function takes the maximum value.
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