A STAP sample selection method

Abstract

The present invention discloses a STAP sample selection method, which models the multi-channel signals of each reference range cell as forward and backward multi-channel AR models, solves the AR model coefficients using the Burg algorithm, solves the covariance matrix of the multi-channel signals of each reference range cell according to the AR model coefficients, calculates the Kahler median of the multi-channel covariance matrix using the gradient descent method, calculates the Riemannian distance between the covariance matrix of each reference range cell and its Kahler median from the matrix manifold, determines the singularity of the samples according to the Riemannian distance, eliminates the singular samples, and selects the uniform samples. Only the data of each frame needs to be processed separately, and the calculation efficiency is high. In a non-uniform clutter environment, when the number of available reference range cells is small, or the singularity of the non-uniform samples is not strong, the singular samples can also be effectively selected to obtain uniform clutter cells that can be used to estimate the clutter covariance matrix, and the calculation results are accurate.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a sample screening technology. Background Art

[0002] In the space-time adaptive processing of radar array signals, abbreviated as STAP, the selection of training samples is a very important issue. If the clutter in the reference range cell is not independently and identically distributed, then using the traditional covariance matrix estimation method will greatly affect the STAP processing result.

[0003] In the reference range cell, selecting appropriate independently and identically distributed clutter cells can improve the performance of STAP processing. In current research, the selection methods of training samples are mostly based on probability and statistics, and no STAP processing method starting from the essence of information theory has been seen. Summary of the Invention

[0004] In order to solve the problems existing in the prior art, the present invention proposes a STAP sample selection method, providing a new way to select independently and identically distributed uniform clutter cells for space-time adaptive processing, improving the radar space-time adaptive processing performance and the ability to detect moving targets in complex clutter. To achieve the above object, the present invention adopts the following technical solutions.

[0005] Modeling of multi-channel signal AR model: Model the multi-channel signals of each reference range cell as forward and backward multi-channel AR models, and use the Burg algorithm to solve the AR model coefficients.

[0006] Estimating covariance matrix: According to the AR model coefficients, solve the covariance matrix of the multi-channel signals of each reference range cell.

[0007] Calculating the Kahler median: Use the gradient descent method to calculate the Kahler median of the multi-channel covariance matrix.

[0008] Calculating the detection statistic: Calculate the Riemannian distance between the covariance matrix of each reference range cell and its Kahler median from the matrix manifold.

[0009] Screening samples: Judge the singularity of the samples according to the Riemannian distance, eliminate the singular samples, and select the uniform samples.

[0010] Furthermore, for the modeling of the multi-channel signal AR model: Regard the two-dimensional space-time signal of each reference range cell as the sampling of a complex vector time series with p channels, and use to represent, where is the time series, △t is the time interval, and y i(t) is the time - series sampling of the i - th channel, y(t) is a wide - sense stationary process, and the N - th order forward filter of the multi - channel AR model is represented by where e N (t) is a p - order vector representing the output of the forward filter, F kN is a p×p complex matrix representing the coefficients of the forward filter, is the conjugate transpose of F kN The N - th order backward filter is represented by where b N (t) represents the output of the backward filter, and B kN represents the coefficients of the backward filter.

[0011] Furthermore, the Burg algorithm is used to solve the AR model coefficients: Let R i be the covariance matrix of y i (t), R -i is the conjugate transpose of R i , P N =E[e N (t)e N (t) H is the power matrix of the forward filter, P′ N =E[b N (t)b N (t) H is the power matrix of the backward filter. Use to represent the relationship between the power matrix of the forward filter, the covariance matrix, and the filter coefficients. Use to represent the relationship between the power matrix of the backward filter, the covariance matrix, and the filter coefficients. Use to represent the AR model of the forward filter, use to represent the AR model of the backward filter, use to represent the output of the N - th order filter, where e N (m), b N (m) and Y N (m) represent the output of the m - th forward filter, the output of the backward filter, and the signal output respectively. Use to represent the recurrence relation of the filter output, where C N and C′ N represent the reflection coefficient matrices of the forward and backward filters respectively. Use to represent the reflection coefficient matrix when minimizing the mean - square error of the filter output, where represent the output statistics of the (N - 1) - th order filter respectively, M is the total length of the signal. Use to represent the reflection coefficient matrix, then C NSatisfy the Lyapunov equation, denoted by respectively, where e0(m) = y(m) = b0(m) and are the initial conditions, and the filter coefficients of each order are calculated using the multi-channel Burg algorithm.

[0012] Further, the estimation covariance matrix: Use to represent the relationship between the covariance matrix and the filter coefficients.

[0013] Further, calculate the Kahler median: Use Parameterize each covariance matrix as a Verblunsky coefficient matrix, where Use to represent the Kahler distance between two covariance matrices , where P 0,1 and P 0,2 represent respectively the power matrices in the Verblunsky coefficient matrix of Use j to represent the Kahler median matrix of k covariance matrices {A j , j = 1,..., k}, where X is an arbitrary matrix, and parameterize the matrix A 0,j as P 1,j , Ω n-1,j ,..., Ω 0,j , j = 1,..., k}, {Ω 1,j , j = 1,..., k},..., {Ω n-1,j , j = 1,..., k} are used to calculate the Kahler median of each component respectively, and use to represent the median subgradient 0,j of {P flow algorithm, where A i and A i+1 are the iterative results of the previous step and the next step respectively, ε is the set coefficient, P m is a matrix other than A i , is the set of m, and use to represent the objective function of the gradient descent algorithm for calculating the median of other components, where I is the identity matrix, and use to represent the gradient at 0, where gradf(0; Ω1,..., Ω k ) is the gradient. Let k matrices Ω1,..., Ω k , X0 ∈ SD n be the initial point, ε is the error limit of iteration, when , use to calculate the matrix, and use Calculate the gradient, using the steepest descent algorithm, using Calculate the displacement of the average value point, using Update the Riemann average, where Denote the transformation of matrix Z with respect to matrix Z0, when the algorithm is determined to have converged.

[0014] Furthermore, calculate the detection statistic: use dis(R i , R median ) to calculate the covariance matrix {R i , i = 1, …, k} and the Riemannian distance between the Kahler median R median .

[0015] Furthermore, screen the samples: Determine the distance cells that deviate significantly from most of the distance distributions as singular samples.

[0016] Advantages of the present invention: When selecting samples, only need to process each frame of data separately, perform parallel processing for multi-channel AR model modeling and parameter estimation, with high calculation efficiency; in an environment of non-uniform clutter, when the number of available reference distance cells is small, or the singularity of non-uniform samples is not strong, singular samples can also be effectively selected, so as to obtain uniform clutter cells that can be used to estimate the clutter covariance matrix; using the information essence of radar signals, uniform samples can be effectively selected in complex clutter, and the calculation results are accurate. Specific embodiments

[0017] The technical solutions of the present invention are specifically described below.

[0018] The two-dimensional spatio-temporal signal of each reference unit can be regarded as the sampling of a complex vector time series of p channels:

[0019]

[0020] where is the time series, △t is the time interval, and y i (t) is the time series sampling of the i-th channel. Assume that y(t) is a wide-sense stationary process. N-order forward filter (multi-channel AR model):

[0021] where the p-order vector e N (t) is called the output of the filter, the p×p complex matrix F kN is called the forward filter coefficient, is the conjugate transpose of F kN .

[0022] Similarly, an N-order backward filter can be defined:

[0023] where b N (t) is the output of the filter, and B kN is the backward filter coefficient.

[0024] The filter coefficient matrix is solved using the multi-channel Burg algorithm. The covariance matrix, filter coefficient matrix, and power matrix P N = E[e N (t)e N (t) H , P' N = E[b N (t)b N (t) H satisfy:

[0025]

[0026]

[0027] where R i is the covariance matrix of y i (t), and R -i is the conjugate transpose of R i . Let

[0028] Then the forward AR model can be written as:

[0029]

[0030] Y(t) = [y(t); y(t - △t); …; y(t - N△t)]

[0031]

[0032] The backward AR model can be written as: ...

[0033]

[0034] Y'(t) = [y(t + N△t); …; y(t + △t); y(t)]

[0035]

[0036] The output of the Nth-order filter is:

[0037]

[0038]

[0039] Y N (m) = [y(m); y(m - 1); …; y(m - N)]

[0040] e N (m), b N (m) and Y N (m) are the outputs of the m-th forward filter, backward filter, and signal output respectively. Derive the recurrence relation of the filter output error vector:

[0041]

[0042]

[0043] This is the recurrence relation of the filter output, C N and C′ N are the forward and backward reflection coefficient matrices respectively.

[0044] Minimizing the mean square error of the filter output results in the reflection coefficient matrix satisfying the following equation:

[0045] where B, E, G are the statistics of the output calculated according to the (N - 1)-order filter:

[0046]

[0047]

[0048]

[0049] M is the total length of the signal.

[0050] The above is rewritten as:

[0051] G then C N satisfies a Lyapunov equation

[0052] Plus the condition:

[0053] C N =(P′ N-1 ) -1 (C′ N ) H P N-1

[0054]

[0055]

[0056] P′ N =P′ N-1 -(C′ N ) H P N-1 C′ N

[0057] and the initial conditions:

[0058] e0(m) = y(m) = b0(m), where P0 is the signal power matrix, and the filter coefficients of each order are calculated using the multi-channel Burg algorithm.

[0059] Using the obtained filter coefficients, according to the relationship between the covariance matrix and the filter coefficients:

[0060]

[0061] R -N + R 1-N F 1N + … + R0F NN = 0

[0062]

[0063] Calculate the multi-channel signal covariance matrix of each reference distance unit Parameterize each covariance matrix into a Verblunsky coefficient matrix:

[0064]

[0065] where:

[0066] The two covariance matrices The Kahler distance is:

[0067]

[0068] where P 0,1 and P 0,2 are respectively the power matrices in the Verblunsky coefficient matrix of

[0069] The Kahler median of k covariance matrices {A j , j = 1, …, k} is defined as:

[0070]

[0071] X median is the median matrix of {A j , j = 1, …, k}, X is an arbitrary matrix, the matrix A j is parameterized as P 0,j , Ω 1,j [[ID=7,6]]…, Ω n-1,j The Kahler median can be calculated separately for each component:

[0072] {P 0,j, j = 1, …, k}, {Ω 1,j , j = 1, …, k}, …, {Ω n-1,j , j = 1, …, k} where {P 0,j , j = 1, …, k} the median subgradient flow method is

[0073]

[0074] G Ai = {m | P m ≠ A i}

[0075] A i and A i+1 are the iterative results of the previous step and the next step respectively, ε is the set coefficient, P m is all other matrices not equal to A i . is the collection of these m.

[0076] The objective function of the gradient descent method for calculating the median of other components is:

[0077]

[0078] I is the identity matrix, and the expression of the gradient at 0 is:

[0079]

[0080]

[0081] [[ID=5l]]

[0082] gradf(0; Ω1, …, Ω k ) is the gradient.

[0083] The process of the steepest descent method is:

[0084] (1) Given k matrices Ω1, …, Ω k , select X0 ∈ SD n as the initial point;

[0085] (2) ε is the error limit of iteration. When , perform the following operations:

[0086] <1> Calculate the matrix:

[0087]

[0088] <2> Calculate the gradient:

[0089]

[0090] <3>Perform steepest descent, and the displacement of the mean value point is:

[0091]

[0092] <4>Update the Riemann mean:

[0093]

[0094] (3) When , it is considered that the algorithm has converged.

[0095] Calculate the Riemannian distance dis(R i , i = 1, …, k) between the covariance matrix {R median} and the Kahler median R i , R median )

[0096] Judge the singularity of the samples according to the magnitude of the Riemannian distance. The distance units that deviate significantly from the majority of the distance distribution are judged as singular samples, and the remaining ones after removing the singular samples are selected as uniform samples.

[0097] The above are the embodiments of the present invention and do not limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are all included within the protection scope of the present invention.

Claims

1. A STAP sample selection method, characterized in that: include: Multi-channel signal AR model modeling: The multi-channel signal of each reference distance unit is modeled as a forward and backward multi-channel AR model, including: the two-dimensional space-time signal of each reference distance unit is regarded as the sampling of the complex vector time series of p channels, and Indicates that is the time series, △t is the time interval, y i (t) is the time series sampling of the i-th channel, y(t) is a wide-sense stationary process, and the N-order forward filter of the multi-channel AR model is Indicates that e N (t) is a p-order vector, representing the output of the forward filter, F kN is a p×p complex matrix, representing the coefficients of the forward filter, F kN The conjugate transpose of the N-th order backward filter is used Indicates that b N (t) represents the output of the backward filter, B kN represents the coefficients of the backward filter; Use Burg algorithm to solve AR model coefficients, including: let R i y i The covariance matrix of (t), R -i R i The conjugate transpose of P N =E[e N (t)e N (t) H ] is the power matrix of the forward filter, P N ′=E[b N (t)b N (t) H ] is the power matrix of the backward filter, and Represents the relationship between the forward filter power matrix, covariance matrix, and filter coefficients, using Represents the relationship between the backward filter power matrix, covariance matrix, and filter coefficients, using Represents the AR model of the forward filter, using Represents the AR model of the backward filter, using represents the output of the N-th order filter, where e N (m), b N (m) and Y N (m) represents the mth forward filter output, backward filter output and signal output, respectively, and Represents the recursive relationship of the filter output, where C N and C′ N Denote the reflection coefficient matrices of the forward and backward filters respectively, and Represents the reflection coefficient matrix when minimizing the mean square error of the filter output, where Represent the output statistics of the N-1 order filter, M is the total length of the signal, and Represents the reflection coefficient matrix, then C N Satisfy the Lyapunov equation, respectively and Represented by, where e0(m)=y(m)=b0(m) and As the initial condition, the multi-channel Burg algorithm is used to calculate the filter coefficients of each order; Estimated covariance matrix: According to the AR model coefficients, solve the multi-channel signal covariance matrix of each reference distance unit, including: Represents the relationship between the covariance matrix and the filter coefficients; Calculate the Kahler median: Use the gradient descent method to calculate the Kahler median of the multi-channel covariance matrix, including: Each covariance matrix is parameterized as a Verblunsky coefficient matrix, where use Represents two covariance matrices Kahler distance, where P 0,1 and P 0,2 Respectively The power matrix of the Verblunsky coefficient matrix is expressed as represents k covariance matrices {A j ,j=1,…,k}, where X is an arbitrary matrix, and the matrix A j Parameterized as P 0,j ,Ω 1,j ,…,Ω n-1,j ,use {P 0,j ,j=1,…,k},{Ω 1,j ,j=1,…,k},…,{Ω n-1,j ,j=1,…,k} calculate the Kahler of each component separately Median, using Indicates {P 0,j ,j=1,…,k}, where A i and A i+1 are the iterative results of the previous step and the next step respectively, ε is the set coefficient, P m For other not equal to A i The matrix, For the collection of m, use Represents the objective function of the gradient descent algorithm for the median calculation of other components, where I is the identity matrix, and Represents the gradient at point 0, where gradf(0;Ω1,…,Ω k ) is the gradient; Compute the test statistic: Calculate the Riemann distance between the covariance matrix of each reference distance unit and its Kahler median from the matrix manifold, using dis(R i ,R median ) Calculate the covariance matrix {R i ,i=1,…,k} and Kahler median R median The Riemann distance of Screening samples: The singularity of the samples is judged based on the Riemann distance, and the distance units that deviate significantly from the majority of the distance distribution are determined as singular samples. The singular samples are eliminated and uniform samples are selected.

2. The STAP sample selection method according to claim 1, characterized in that: Also includes: Set k matrices Ω1,…,Ω k , X0∈SD n is the initial point, ε is the error limit of iteration, when When using Calculate the matrix using Calculate the gradient using the steepest descent algorithm. Calculate the displacement of the mean point using Update the Riemann mean, where Represents the transformation of matrix Z about matrix Z0, when When , the algorithm is judged to have converged.

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