CN111474526A - Rapid reconstruction method of airborne STAP clutter covariance matrix - Google Patents

Rapid reconstruction method of airborne STAP clutter covariance matrix Download PDF

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CN111474526A
CN111474526A CN202010332592.2A CN202010332592A CN111474526A CN 111474526 A CN111474526 A CN 111474526A CN 202010332592 A CN202010332592 A CN 202010332592A CN 111474526 A CN111474526 A CN 111474526A
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covariance matrix
matrix
clutter
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CN111474526B (en
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刘明鑫
冯文英
杜英杰
房梦旭
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Chengdu Aeronautic Polytechnic
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures

Abstract

The invention provides a method for quickly reconstructing an airborne STAP clutter covariance matrix, which comprises the following steps: s1, receiving an echo signal by using a pulse array radar; s2, obtaining a clutter covariance matrix estimation value according to the echo signal; s3, obtaining an error variable according to the clutter covariance matrix estimation value, and obtaining a covariance matrix low-rank matrix recovery model according to the error statistical characteristics; and S4, according to the covariance matrix low-rank matrix recovery model, rapidly completing reconstruction of the airborne STAP clutter covariance matrix by using a covariance matrix Toeplitz structure and a Coulter-Council condition. The method solves the problems that the clutter and noise covariance matrix CNCM is difficult to accurately estimate in a small sample and the target detection is seriously influenced. The method and the device have high estimation accuracy and calculation efficiency, especially under the condition of small samples.

Description

Rapid reconstruction method of airborne STAP clutter covariance matrix
Technical Field
The invention belongs to the field of airborne radar clutter suppression, and particularly relates to a method for quickly reconstructing an airborne STAP clutter covariance matrix.
Background
Space-time adaptive processing (STAP) with excellent performance in clutter suppression and target detection plays an important role in airborne radar. In the practical application of STAP, the system can calculate an ideal weight vector and then obtain the optimal filter output response according to the clutter and noise covariance matrix estimated by the snapshot of the adjacent distance units. In practice, in order to make the performance degradation from the estimation not exceed the theoretical optimum of 3dB, the number of training snapshots should be at least twice the system freedom, which is difficult for the radar to meet in non-homogeneous environments, especially in small samples.
In view of the above problems, scholars at home and abroad propose corresponding solutions based on different angles. The dimension reduction algorithm reduces the degree of freedom of the system and the required training sample amount by designing a fixed dimension reduction structure, and improves the calculation speed. However, the rank reduction algorithm estimates clutter subspace from a feature space classification and analysis method according to the low-rank characteristic of clutter, so that performance loss caused by insufficient sample number is reduced, an accurate estimation of a clutter covariance matrix can be given from priori knowledge in a heterogeneous environment based on a knowledge-assisted method, the uneven distribution of the clutter can be essentially overcome by a direct data domain method, and space-time aperture loss and slow-moving target detection performance degradation can be generated. The sample selection method removes non-uniform samples to reduce performance loss, which makes training sample starvation more severe.
Disclosure of Invention
Aiming at the defects in the prior art, the rapid reconstruction method of the airborne STAP clutter covariance matrix provided by the invention solves the problems that the clutter and noise covariance matrix is difficult to accurately estimate in a small sample and the target estimation is seriously influenced.
In order to achieve the above purpose, the invention adopts the technical scheme that:
the scheme provides a method for quickly reconstructing an airborne STAP clutter covariance matrix, which comprises the following steps:
s1, receiving an echo signal by using a pulse array radar;
s2, obtaining a clutter covariance matrix estimation value according to the echo signal;
s3, obtaining an error variable according to the clutter covariance matrix estimation value, and obtaining a covariance matrix low-rank matrix recovery model according to error statistical characteristics;
and S4, according to the covariance matrix low-rank matrix recovery model, rapidly completing reconstruction of the airborne STAP clutter covariance matrix by using a covariance matrix Toeplitz structure and a Coulter-Council condition.
The invention has the beneficial effects that: the invention provides a new clutter and noise covariance matrix reconstruction method, which provides a low-rank matrix recovery model according to the covariance matrix estimation error statistical property. A closed form expression of the clutter and noise covariance matrix is estimated by using a Toeplitz structure and a Coueta-k condition, a fast solving method of the clutter and noise covariance matrix is given, and finally, a weight vector is established, so that detection and analysis of a target signal are facilitated.
Further, the expression of the clutter covariance matrix estimate in step S2 is as follows:
Figure BDA0002465491200000021
Figure BDA0002465491200000022
wherein the content of the first and second substances,
Figure BDA0002465491200000023
representing clutter covariance matrix estimate, NtrDenotes the number of samples, XtrA matrix of training samples is represented that is,
Figure BDA0002465491200000024
represents XtrConjugate transpose of (1), xtr,iRepresenting the ith training sample.
The beneficial effects of the further scheme are as follows: the clutter covariance matrix estimation value is obtained by using the training sample mean value, and conditions are provided for constructing an error variable model in the following scheme.
Still further, the expression of the covariance matrix low-rank matrix recovery model in step S3 is as follows:
Figure BDA0002465491200000031
Figure BDA0002465491200000032
wherein, min rank [ R ]c]Representing the taking matrix RcS.t. represents the min rank Rc]The value of the expression is satisfying
Figure BDA0002465491200000033
Under the conditions of (a) to (b),
Figure BDA0002465491200000034
presentation pair
Figure BDA0002465491200000035
The expression is inverse and squared, E denotes the covariance matrix estimation error, η denotes the noise error margin, Rc denotes the clutter covariance matrix, Ntr denotes the number of samples,
Figure BDA0002465491200000036
an estimate of the clutter covariance matrix is represented,
Figure BDA0002465491200000037
to represent
Figure BDA0002465491200000038
Transpose of, σn 2Representing noise power, I representing identity matrix, N representing number of array elements, M representing number of pulses, RuRepresenting the actual values of the clutter covariance matrix.
The beneficial effects of the further scheme are as follows: according to the method, a clutter covariance matrix reconstruction model is constructed by using error statistical characteristics according to a low-rank matrix recovery theory.
Still further, the expression of reconstructing the clutter covariance matrix in step S4 is as follows:
Figure BDA0002465491200000039
Figure BDA00024654912000000310
Figure BDA00024654912000000311
Figure BDA00024654912000000312
wherein the content of the first and second substances,
Figure BDA00024654912000000313
representing the real and imaginary parts of h,
Figure BDA00024654912000000314
and
Figure BDA00024654912000000315
respectively representing the real and imaginary parts of a complex variable,
Figure BDA00024654912000000316
represents the pseudo inverse, Z1And Z2Respectively, sub-matrices of the same dimension divided by matrix Z, and h by h(i)A matrix of components, h(i)Represents the intermediate variable, and i ═ 1,2 … N, N represents the corresponding dimension of the uniform linear array, GNNRepresentation matrix
Figure BDA00024654912000000317
The matrix of block elements of (a) is,
Figure BDA00024654912000000318
the estimated value of R (G) is shown,
Figure BDA00024654912000000319
representing the estimated value of R, G representing an intermediate matrix, Rc(u, v) represents a clutter covariance matrix.
The beneficial effects of the further scheme are as follows: the method provides a fast and effective closed solution of a model by using a covariance matrix Toeplitz structure.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram illustrating the estimated covariance matrix eigenvalue spectrum in the present embodiment.
Fig. 3 is a comparison diagram of the angular doppler beams in this embodiment.
Fig. 4 is a graph comparing the loss of signal to noise ratio in the present embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Examples
The clutter plus noise covariance matrix (CNCM) usually estimated by training the snapshot is the key to obtain the weight vector in space-time adaptive processing (STAP), however, the clutter plus noise covariance matrix CNCM is difficult to estimate accurately in a small sample, and the target estimation is seriously affected. In order to solve the problem, the application provides a new clutter and noise covariance matrix CNCM reconstruction method, the method reconstructs a clutter and noise covariance matrix CNCM by using a Toeplitz structure, then a closed form expression of the estimated clutter and noise covariance matrix CNCM is derived, finally, a weight vector is established, the detection and analysis of a target signal are facilitated, and the simulation result shows the effectiveness of the method.
As shown in fig. 1, the present invention provides a method for rapidly reconstructing an airborne STAP clutter covariance matrix, which includes the following steps:
s1, receiving an echo signal by using a pulse array radar;
s2, obtaining a clutter covariance matrix estimation value according to the echo signal;
s3, obtaining an error variable according to the clutter covariance matrix estimation value, and obtaining a covariance matrix low-rank matrix recovery model according to error statistical characteristics;
and S4, according to the covariance matrix low-rank matrix recovery model, rapidly completing reconstruction of the airborne STAP clutter covariance matrix by using a covariance matrix Toeplitz structure and a Coulter-Council condition.
In this embodiment, assume a side view airborne phased array radar with a uniform linear array of N array elements with a cell spacing d in the Coherent Processing Interval (CPI) and with a fixed Pulse Repetition Interval (PRI) TrWhere d is λ/2, λ is the radar wavelength. In the absence of range ambiguity, the space-time snapshots received from a range ring are:
Figure BDA0002465491200000051
where at represents the target power. Target space-time pilot vector of
Figure BDA0002465491200000052
Figure BDA0002465491200000053
And v (f)t) The spatial and temporal steering vectors of real objects are defined as:
Figure BDA0002465491200000054
Figure BDA0002465491200000055
wherein f ist＝2vrTrcos(θ)/λ，
Figure BDA0002465491200000056
vrIs the radar speed, θ is the direction of the target, xuIs clutter plus noise data, which can be expressed as:
Figure BDA0002465491200000057
where n is a Gaussian white noise vector with a power of
Figure BDA0002465491200000058
NcIs the number of independent clutter blocks in the azimuth domain, fc,iAnd
Figure BDA0002465491200000059
normalized Doppler and spatial frequency, a, respectively, of the clutter block ic,iIs the complex gain of the i-th clutter block, the time and space steering vectors corresponding to the i-th clutter slice are expressed by the following equations (5) and (6), respectively:
Figure BDA00024654912000000510
Figure BDA00024654912000000511
corresponding space-time steering vector:
Figure BDA00024654912000000512
wherein the content of the first and second substances,
Figure BDA00024654912000000513
l＝0,…,N-1,r＝1,…,M,i＝1,…,Nc. Assuming that the different clutter blocks are independent, the clutter plus noise covariance matrix (CNCM) based on equation (4) can be modeled as follows:
Figure BDA0002465491200000061
wherein the content of the first and second substances,
Figure BDA0002465491200000062
is a clutter space-time steering matrix with a clutter power matrix P ═ diag ([ P ═ diag)1,p2,...,pNc]T),pk＝E(|ac,k|2)。
In this embodiment, according to the minimum variance distortion response criterion, the optimal STAP weight vector may be calculated as:
Figure BDA0002465491200000063
in fact, Ru is typically estimated from training samples and can be calculated as:
Figure BDA0002465491200000064
wherein the content of the first and second substances,
Figure BDA0002465491200000065
is a training sample matrix, NtrRepresenting the number of samples.
In this embodiment, R in the covariance matrix is expressed by equation (7)c∈CNM×NMIs a nested Toeplize matrix and is represented by the vector u ═ u(1)T；…；u(N)T]TAnd the first row v ═ v(1)T；…；v(N)T]TIs determined wherein
Figure BDA0002465491200000066
And
Figure BDA0002465491200000067
then R iscThe structure of the (u, v) is specifically as follows:
Figure BDA0002465491200000068
wherein R is(n)∈CN×NIs a non-Schmitt Toeplize matrix composed of u(n)And v(n)The specific form is determined as follows:
Figure BDA0002465491200000069
in fact, clutter RuThe estimation using equation (9) is defined as:
Figure BDA00024654912000000610
where E consists of signal to signal and signal to noise correlation terms, the vector form of E satisfies an asymptotic normal distribution since the finite samples have values other than 0:
Figure BDA0002465491200000071
the following can be obtained:
Figure BDA0002465491200000072
in the formula (I), the compound is shown in the specification,
Figure BDA0002465491200000073
can be used
Figure BDA0002465491200000074
Estimate W, As%2(N2M2) Representing chi-square distribution with a degree of freedom N2M2The parameter η is introduced here to define a confidence interval [0, η ]]The probability that the true solution falls within this interval is 1-p, making 1-p as large as possible.
Figure BDA0002465491200000075
Then we can build the following low rank matrix recovery model pair RcEstimating:
Figure BDA0002465491200000076
however, equation (16) remains an NP-hard problem, and to avoid non-convexity, we replace the pseudo-rank norm with the tracking norm using convex relaxation, so equation (16) can be rewritten as:
Figure BDA0002465491200000077
ignore RcAnd (3) introducing a Lagrangian operator to reconstruct the formula (17):
Figure BDA0002465491200000078
according to the principle of extended invariance, R is obtained by solving the following optimization problemcMaximum sample maximum likelihood estimation of (2):
Figure BDA0002465491200000079
this problem can be solved with CVX, but this is time consuming, so the present application proposes an efficient solution by deriving a closed expression. From the Countake condition, the solution that can be obtained for the model (19) satisfies the following equation:
Figure BDA00024654912000000710
in the formula (I), the compound is shown in the specification,
Figure BDA00024654912000000711
Figure BDA00024654912000000712
let matrix G have the following structure, defined as follows:
Figure BDA0002465491200000081
in the formula, Gmn∈CM×MLet D be [ D ]NM-1；…；D-(NM-1)]Wherein D isnFor the matrix G with a sub-matrix GnnIs the sum of the sub-matrices on the nth diagonal of the unit. Definitions of the present application
Figure BDA0002465491200000082
To find u and v from equation (20), we convert the right part of equation (20) equal sign into:
Figure BDA0002465491200000083
wherein:
Figure BDA0002465491200000084
Figure BDA0002465491200000085
wherein:
Figure BDA0002465491200000086
Figure BDA0002465491200000087
Figure BDA0002465491200000088
wherein the content of the first and second substances,
Figure BDA0002465491200000089
represents a vector h(i)And i is 1,2 … N.
We can obtain from the matrix transformations of equations (20) and (22):
Figure BDA00024654912000000810
it is possible to obtain:
Figure BDA0002465491200000091
it is possible to obtain:
Figure BDA0002465491200000092
wherein the content of the first and second substances,
Figure BDA0002465491200000093
and
Figure BDA0002465491200000094
representing the real and imaginary parts of the complex variable respectively,
Figure BDA0002465491200000095
the pseudo-inverse is represented. Can easily be obtained from the above formula
Figure BDA0002465491200000096
And (6) estimating the value.
In this example, we compared the conventional STAP and the proposed method comprehensively by numerical experiments. Consider the airborne radar parameters of one side as N-10, M-10, λ -0.03M, TrAssuming normalized spatial frequency and doppler frequency of the target to be 0.1 and-0.2, clutter to noise ratio to 40db, and signal to noise ratio to 10 db. to highlight the feasibility and efficiency of the proposed method in small samples, simulation verification of the estimated covariance matrix eigenvalues, beam pattern and signal to noise interference ratio SCINR penalty was performed, STAP performance was generally measured by the estimated covariance matrix eigenvalues as shown in fig. 2, fig. 2 is an estimated covariance matrix eigenvalue spectrum, N in fig. 2(a)tr100, N in fig. 2(b)tr200. STAP performance is usually measured by estimated covariance matrix eigenvalues, and fig. 2 shows a comparison of covariance matrix eigenvalues in the case of sample NM and 2NM, both of which predict the first few dominant eigenvalues well, but the SMI method deviates significantly in small samples, and the proposed method does not.
Secondly, both algorithms can detect the target, but the method has better clutter suppression performance in enough training samples. The target cannot be distinguished because SMI cannot effectively estimate CNCM, resulting in the filter containing too much clutter residues when insufficient samples are empty. However, the proposed algorithm detects moving objects in the sample by (30) accurately estimating the CNCM, effectively suppressing clutter, as shown in fig. 3.
Finally, the SCINR penalty of SMI is similar to the algorithm proposed in samples, but not good in small sample cases, as shown in fig. 4, the proposed algorithm is hardly affected by the number of samples. Therefore, SCISNR loss of the algorithm is far better than that of SMI, clutter under the condition of small training samples can be effectively inhibited, and the problem of radar performance reduction caused by sample shortage is solved.
In conclusion, the method is a novel rapid CNCM reconstruction method based on the Toeplitz structure. The algorithm has higher precision, can improve the dynamic detection performance, obtains the reconstructed CNCM by solving the convex optimization problem, and the simulation result shows that the method has higher estimation precision and calculation efficiency.

Claims (4)

1. A method for rapidly reconstructing airborne STAP clutter covariance matrix is characterized by comprising the following steps:
s1, receiving an echo signal by using a pulse array radar;
s2, obtaining a clutter covariance matrix estimation value according to the echo signal;
s3, obtaining an error variable according to the clutter covariance matrix estimation value, and obtaining a covariance matrix low-rank matrix recovery model according to error statistical characteristics;
and S4, according to the covariance matrix low-rank matrix recovery model, rapidly completing reconstruction of the airborne STAP clutter covariance matrix by using a covariance matrix Toeplitz structure and a Coulter-Council condition.
2. The method for fast reconstruction of clutter covariance matrix of an airborne STAP according to claim 1, wherein the expression of clutter covariance matrix estimate in step S2 is as follows:
Figure FDA0002465491190000011
Figure FDA0002465491190000012
wherein the content of the first and second substances,
Figure FDA0002465491190000013
representing clutter covariance matrix estimate, NtrDenotes the number of samples, XtrA matrix of training samples is represented that is,
Figure FDA0002465491190000014
represents XtrConjugate transpose of (1), xtr,iRepresenting the ith training sample.
3. The fast airborne STAP clutter covariance matrix reconstruction method of claim 1, wherein the expression of the covariance matrix low-rank matrix recovery model in step S3 is as follows:
Figure FDA0002465491190000015
Figure FDA0002465491190000016
wherein, min rank [ R ]c]Representing the taking matrix RcS.t. represents the minimum of the rank of (1), and the minrank [ R ] is obtainedc]The value of the expression is satisfying
Figure FDA0002465491190000017
Under the conditions of (a) to (b),
Figure FDA0002465491190000018
presentation pair
Figure FDA0002465491190000019
The expression is inverse and squared, E represents the covariance matrix estimation error, η represents the noise error margin, RcRepresenting clutter covariance matrix, NtrThe number of samples is represented as a function of,
Figure FDA00024654911900000110
an estimate of the clutter covariance matrix is represented,
Figure FDA00024654911900000111
to represent
Figure FDA00024654911900000112
Transpose of, σn 2Representing noise power, I representing identity matrix, N representing number of array elements, M representing number of pulses, RuRepresenting the actual values of the clutter covariance matrix.
4. The fast airborne STAP clutter covariance matrix reconstruction method of claim 1, wherein the expression of clutter covariance matrix reconstruction in step S4 is as follows:
Figure FDA0002465491190000021
Figure FDA0002465491190000022
Figure FDA0002465491190000023
Figure FDA0002465491190000024
wherein，
Figure FDA0002465491190000025
Representing the real and imaginary parts of h,
Figure FDA0002465491190000026
and
Figure FDA0002465491190000027
respectively representing the real and imaginary parts of a complex variable,
Figure FDA0002465491190000028
represents the pseudo inverse, Z1And Z2Respectively, sub-matrices of the same dimension divided by matrix Z, and h by h(i)A matrix of components, h(i)Represents the intermediate variable, and i ═ 1,2 … N, N represents the corresponding dimension of the uniform linear array, GNNRepresentation matrix
Figure FDA00024654911900000211
The matrix of block elements of (a) is,
Figure FDA0002465491190000029
the estimated value of R (G) is shown,
Figure FDA00024654911900000210
representing the estimated value of R, G representing an intermediate matrix, Rc(u, v) represents a clutter covariance matrix.
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CN114527444A (en) * 2022-04-24 2022-05-24 中国人民解放军空军预警学院 Airborne MIMO radar self-adaptive clutter suppression method based on space-time sampling matrix
CN114527444B (en) * 2022-04-24 2022-07-15 中国人民解放军空军预警学院 Airborne MIMO radar self-adaptive clutter suppression method based on space-time sampling matrix

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