CN110632571A - Steady STAP covariance matrix estimation method based on matrix manifold - Google Patents

Steady STAP covariance matrix estimation method based on matrix manifold Download PDF

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CN110632571A
CN110632571A CN201910892011.8A CN201910892011A CN110632571A CN 110632571 A CN110632571 A CN 110632571A CN 201910892011 A CN201910892011 A CN 201910892011A CN 110632571 A CN110632571 A CN 110632571A
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CN110632571B (en
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程永强
陈茜茜
王宏强
吴昊
杨政
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National University of Defense Technology
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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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/50—Systems of measurement based on relative movement of target
    • 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
    • G01S7/415—Identification of targets based on measurements of movement associated with the target

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Abstract

The invention provides a steady STAP covariance matrix estimation method based on matrix manifold, which comprises the steps of firstly, utilizing the internal structure information among data, and calculating the positive definite covariance matrix of each training unit according to the STAP signal model; secondly, constructing a covariance matrix of the training sample into a matrix manifold, and converting clutter covariance matrix estimation of the unit to be detected into a geometric centroid estimation problem on the manifold; and finally, iteratively solving the geometric centroid by adopting total Jesen Skew divergence to obtain the estimation of the clutter covariance matrix. The method fully utilizes the internal distribution rule of the data, estimates the covariance matrix by constructing the matrix manifold and then based on the geometric measurement on the manifold, has better robustness, and is suitable for the condition of insufficient independent and identically distributed training samples in the heterogeneous environment.

Description

Steady STAP covariance matrix estimation method based on matrix manifold
Technical Field
The invention relates to the field of radar target detection, in particular to a radar moving target detection technology in a strong clutter, and more particularly relates to a robust covariance matrix estimation method for Space-time adaptive processing (STAP) in a complex environment.
Background
The airborne radar is used as a main means for target detection and monitoring, and has wide application in public and national defense safety fields such as air and sea surface target monitoring, early warning detection and the like. Under the complex environment, the clutter intensity of the airborne radar can reach 60-90 dB, the target is easily submerged in the strong clutter, and the detection performance is seriously reduced.
At present, the space-time adaptive processing (STAP) technology has a remarkable effect in solving the problem of strong clutter suppression of airborne radar, and is widely applied to radar signal processing. The core problem of space-time adaptive processing (STAP) techniques is to accurately estimate the covariance matrix of the cell to be detected, which requires enough Independent Identically Distributed (IID) training samples. However, in a practical environment, the complex/sea clutter distribution is usually non-uniform, resulting in insufficient independent co-distributed training samples and deteriorated moving target detection performance.
Aiming at the problems of insufficient independent and identically distributed training samples and stable STAP covariance matrix estimation under the condition of small samples, the traditional method mainly focuses on two aspects: 1. reducing dimension/rank; 2. the sample requirements are reduced using a priori information. The above method relies on statistical properties or prior information of the clutter and performance degrades significantly when the clutter statistical model is mismatched from the actual distribution or the prior information is inaccurate.
Disclosure of Invention
Aiming at the problem of steady estimation of the STAP clutter covariance matrix in the non-uniform environment, the invention aims to provide a method for estimating the steady STAP covariance matrix based on matrix manifold. The method fully utilizes the internal distribution rule of the data, estimates the covariance matrix by constructing the matrix manifold and then based on the geometric measurement on the manifold, has better robustness, and is suitable for the condition of insufficient independent and identically distributed training samples in the heterogeneous environment.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
a robust STAP covariance matrix estimation method based on matrix manifold comprises
First, a positive definite covariance matrix of each training unit is calculated.
And secondly, constructing the positive definite covariance matrixes of all the training units into a rectangular manifold, and converting the clutter covariance matrix estimation of the unit to be detected into the estimation problem of the geometric centroid on the rectangular manifold.
And thirdly, calculating the geometric mass center of K training units corresponding to K points on the matrix manifold, and acquiring clutter covariance matrix estimation of the unit to be detected.
In a first step of the invention, an echo signal is received by an airborne radar antenna and is denoted x. The range observed by the radar is evenly divided into L range bins based on the radar receiver sampling rate. Setting the first distance unit as the unit to be detected and the echo signal as xlThe clutter covariance matrix to be estimated corresponding to the unit to be detected is
Figure BDA0002209037600000021
Taking K distance units which are adjacent to the unit to be detected and do not contain the target as training samples, taking each training sample as a training unit, and expressing the echo signal of each training unit as xk，k＝1,…,K，xkThe received echo signal of the kth training unit is set to have a data length of G, which can be expressed as xk＝{x1,…xg,…,xG}. The covariance matrix of each training unit may be determined by
Figure BDA0002209037600000022
And (4) calculating.
Computing a positive definite covariance matrix for each training unit
Figure BDA0002209037600000023
The methods of (a) include, but are not limited to, the following three:
the first method comprises the following steps: using diagonal loading methods, i.e.I denotes an identity matrix.
The second method comprises the following steps: by the Toeplitz method, i.e.
Wherein, cjIs the correlation coefficient between training units with interval j, which can be expressed as
Figure BDA0002209037600000031
0≤j≤G-1，xiRepresenting a vector xkThe ith element, x ini+jRepresenting a vector xkThe (i + j) th element in (b).Denotes cjConjugation of (1).
The third method comprises the following steps: solving the problem by the following equation
Figure BDA0002209037600000033
Its optimal solution can be expressed as
Figure BDA0002209037600000034
Λk＝diag([κMλk,λk,…,λk])
Figure BDA0002209037600000035
Wherein | · | purple sweet2Represents a 2 norm, UkIs composed of
Figure BDA0002209037600000036
Characteristic value of xk 2Corresponding unit feature vector, κMThe condition number is empirically obtained. Such as setting kappaMLarger than 1, 1-100 can be selected.
In the second step of the invention, the clutter covariance matrix to be estimated corresponding to the unit to be detected is determined
Figure BDA0002209037600000037
Functional transformations expressed as covariance matrices of K training units, i.e.
Figure BDA0002209037600000038
Where K represents the number of training units.
The matrix manifold is constructed from the positive definite covariance matrices of all training units. The positive definite covariance matrix of each training unit corresponds to a point on the matrix manifold, and the geometric distance between the point on the matrix manifold and the point is defined as dq. Therefore, the estimation of the clutter covariance matrix of the unit to be detected is converted into the estimation problem of the geometric centroid on the rectangular manifold.
The invention adopts the geometric mean value to calculate the geometric centroid on the rectangular manifold. The clutter covariance matrix estimation of the unit to be detected can be expressed as the following problem:
Figure BDA0002209037600000041
wherein the content of the first and second substances,
Figure BDA0002209037600000042
is shown as
Figure BDA0002209037600000043
And
Figure BDA0002209037600000044
is measured by the geometric distance of (a),
Figure BDA0002209037600000045
is the weighting factor of the kth training unit,and isIn the absence of a-priori information,
Figure BDA0002209037600000048
in the third step of the method, on the matrix manifold, the geometric centroid of all training units corresponding to K points on the matrix manifold is solved by utilizing totalskewJesen divergence iteration, so that the clutter covariance matrix estimation value of the unit to be detected is obtained. From the second step, the solution of the covariance matrix can be converted into the solution of the geometric centroid of K training units corresponding to K points on the matrix manifold. The invention uses totalSkewJesen divergence (noted as
Figure BDA0002209037600000049
) As a measure of geometric distance on the matrix manifold, i.e.
Figure BDA00022090376000000410
The calculation formula is as follows:
wherein the content of the first and second substances,represents an optimization objective function, alpha represents a skew impact factor,
Figure BDA00022090376000000412
t represents the number of iterations,
Figure BDA00022090376000000413
(p: q) represents the divergence between p and q,
Figure BDA00022090376000000414
ΔFf (q) -F (p), F stands for strictly convex and differentiable function, inner product, (·)2Representing the square.
Wherein the content of the first and second substances,
Figure BDA00022090376000000416
BF(p: q) denotes the Bregman divergence between p and q.
The result of the t-th iteration can be expressed as
Figure BDA00022090376000000417
Figure BDA0002209037600000051
The derivative of the function F is represented. And obtaining a clutter covariance matrix estimation value of the unit to be detected by the iterative computation.
A computer arrangement comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the robust matrix-manifold-based STAP covariance matrix estimation method.
A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method for robust STAP covariance matrix estimation based on matrix manifolds.
The invention has the beneficial technical effects that:
the method fully excavates the internal distribution rule of data, and solves the problem by constructing a matrix manifold and converting the clutter covariance matrix estimation of the unit to be detected into the estimation of the geometric centroid on the rectangular manifold. The method provided by the invention can reduce the requirement on the training sample, remarkably improve the problem of the reduction of the clutter covariance matrix estimation performance caused by the shortage of the training sample in the non-uniform scene, and effectively improve the moving target detection performance.
Drawings
FIG. 1 is a STAP observation geometry according to the present invention;
FIG. 2 is a schematic diagram comparing geometric centroid and arithmetic centroid according to the present invention;
fig. 3 is a graph of STAP improvement factor versus normalized doppler frequency according to the present invention;
FIG. 4 is a graph of output Signal to noise ratio (SCNR) versus number of samples in accordance with the present invention;
FIG. 5 is a diagram of the output of the adaptive matched filter of the present invention.
Detailed Description
In order to facilitate the practice of the invention, further description is provided below with reference to specific examples.
The invention provides a steady STAP covariance matrix estimation method based on matrix manifold, which comprises the steps of firstly, utilizing the internal structure information among data, and calculating the positive definite covariance matrix of each training unit according to the STAP signal model; secondly, constructing a covariance matrix of the training sample into a matrix manifold, and converting clutter covariance matrix estimation of the unit to be detected into a geometric centroid estimation problem on the manifold; and finally, iteratively solving the geometric centroid by adopting totalJesenSkaw divergence to obtain the estimation of the clutter covariance matrix.
The invention solves the problem of robust estimation of the clutter covariance matrix under the condition of insufficient independent and identically distributed samples in the non-uniform environment, thereby improving the STAP clutter suppression and moving target detection performance. The invention provides the covariance matrix estimation method facing the STAP by constructing the matrix manifold and fully utilizing the distribution rule of data, and the method has better robustness, has less requirements on the number of training samples for estimation performance, and still has better clutter suppression performance and moving target detection performance under the condition of insufficient independent and identically distributed samples in a non-uniform environment.
Example 1:
in the first step, a positive definite covariance matrix of each training unit is calculated according to the STAP signal model.
Considering a side-looking rectangular array airborne radar, wherein the rectangular array is M rows and N columns, each array element transmits P pulses, and a radar observation geometric model is shown in figure 1. The range observed by the radar is evenly divided into L range bins based on the radar receiver sampling rate. Setting the first distance unit as the unit to be detected and the echo signal as xlTaking K distance units which are adjacent to the unit to be detected and do not contain the target as training samples, and taking each training sample as a training unitThe echo signal of each training unit is denoted xk，k＝1,…,K，xkThe received echo signal of the kth training unit is set to have a data length of G, which can be expressed as xk＝{x1,…xg,…,xG}. The covariance matrix of each training unit may be determined by
Figure BDA0002209037600000061
And (4) calculating. x is the echo signal received by the radar and can be expressed as
Figure BDA0002209037600000062
Wherein gamma is the scattering coefficient of the radar target, s is the space-time guiding vector of the signal, NcIs the number of clutter blocks, pi,siRespectively representing the scattering cross section area and the clutter space-time guiding vector of the ith clutter block, and n represents noise. Thus, the STAP weight vector w under the Linear Constrained Minimum Variance (LCMV) ConstraintoptCan be expressed as
wopt＝μR-1s
Wherein, mu is 1/sHR-1s，(·)-1Representation matrix inversion, (.)HRepresenting the matrix conjugate and R the clutter covariance matrix of the cell to be detected. R needs to be estimated by using covariance matrixes of adjacent K training units, and the estimated value of R is expressed as
Figure BDA0002209037600000071
In this embodiment, a diagonal loading method is adopted, i.e.
Figure BDA0002209037600000072
Calculating to obtain a positive definite covariance matrix of each training unit
And secondly, constructing the covariance matrix of the training sample into a matrix manifold, and converting the clutter covariance matrix estimation of the unit to be detected into a geometric centroid estimation problem on the manifold.
First, the unit clutter covariance matrix estimate to be detected can be expressed as a functional transformation of the covariance matrix of the K training units, i.e.
Figure BDA0002209037600000074
Where K represents the number of training samples.
A matrix manifold is then constructed from the positive definite covariance matrices of all the training samples. Defining matrix manifold
Figure BDA0002209037600000075
Is shown as
Figure BDA0002209037600000076
Wherein R is a conjugate positive definite matrix,a set space formed by all positive definite covariance matrixes. The covariance matrix of each training unit corresponds to a point on the manifold, and the geometric distance of different points on the manifold is defined as dq. On this basis, the covariance matrix estimate can be considered as an estimate of the geometric centroid of the covariance matrix on the rectangular manifold.
The traditional method adopts arithmetic mean to calculate the centroid, and the invention adopts geometric mean to calculate the centroid. The geometric centroid versus the arithmetic centroid pair is shown in fig. 2. In summary, the covariance matrix estimation of the cell to be detected can represent the following problems
Figure BDA0002209037600000078
Wherein the content of the first and second substances,
Figure BDA0002209037600000079
is shown asAnd
Figure BDA00022090376000000711
is measured by the geometric distance of (a),
Figure BDA00022090376000000712
is the weighting factor of the kth training unit,
Figure BDA00022090376000000713
and is
Figure BDA00022090376000000714
And thirdly, calculating the geometric mass center of corresponding points of K training units on the rectangular manifold, and acquiring clutter covariance matrix estimation of the unit to be detected.
From the above step, the solution of the covariance matrix can be converted into the solution of the geometric centroid of K points on the matrix manifold corresponding to the K training units. The invention uses totalSkewJesen divergence (noted as
Figure BDA0002209037600000081
) As a measure of geometric distance on the matrix manifold, i.e.The calculation formula is as follows:
wherein the content of the first and second substances,
Figure BDA00022090376000000812
represents an optimization objective function, alpha represents a skew impact factor,
Figure BDA0002209037600000084
t represents the number of iterations,
Figure BDA0002209037600000085
(p: q) represents the divergence between p and q,
Figure BDA0002209037600000086
ΔFf (q) -F (p), F stands for strictly convex and differentiable function, inner product, (·)2Representing the square.
Figure BDA0002209037600000087
Wherein the content of the first and second substances,
Figure BDA0002209037600000088
BF(p: q) denotes the Bregman divergence between p and q.
The result of the t-th iteration can be expressed as
Figure BDA00022090376000000810
The derivative of the function F is represented.
And obtaining a clutter covariance matrix estimation value of the unit to be detected by the iterative computation.
Example 2: the difference from example 1 is that: in the first step of this embodiment, a Toeplitz method is adopted to calculate and obtain a positive definite covariance matrix of each training unit
Figure BDA00022090376000000811
Namely, it is
Figure BDA0002209037600000091
Wherein, cjIs the correlation coefficient between training units with interval j, which can be expressed as
Figure BDA0002209037600000092
0≤j≤G-1，xiRepresenting a vector xkThe ith element, x ini+jDenotes the subscript and xiThe i + j th element that differs by j.
Figure BDA0002209037600000093
Denotes cjConjugation of (1).
The remaining steps in embodiment 2 are the same as those in embodiment 1, and are not described herein again.
Example 3: the difference from example 1 is that: in the first step of this embodiment, the positive definite covariance matrix of each training unit is solved by the following optimization problem
Figure BDA0002209037600000095
Its optimal solution can be expressed as
Figure BDA0002209037600000096
Λk＝diag([κMλk,λk,…,λk])
Figure BDA0002209037600000097
Wherein | · | purple sweet2Represents a 2 norm, UkIs composed of
Figure BDA0002209037600000098
The characteristic value is | | xk||2Corresponding unit feature vector, κMThe condition number is empirically obtained. Such as setting kappaMLarger than 1, 1-100 can be selected.
The remaining steps in embodiment 3 are the same as those in embodiment 1, and are not described herein again.
In an embodiment of the present invention, the experimental parameters are set as shown in table 1, and the clutter covariance matrix estimation value of the unit to be detected is obtained by using the method provided by the present invention.
Under the condition that the number of training samples is 32, the STAP influence factor changes along with the normalized Doppler frequency as shown in FIG. 3, and it can be seen that compared with the conventional method, the method provided by the invention has high gain and narrow notch under the condition of small samples, which indicates that the clutter suppression performance is better.
The variation of the output SCNR with the number of samples is shown in fig. 4, and compared with the conventional method, the method provided by the invention has the advantages that the output SCNR is not substantially varied with the variation of the samples, and the robustness is better.
Under the condition that the number of training samples is 32, the output result after adaptive matching filtering is shown in fig. 5, and compared with the traditional method, the method provided by the invention has lower side lobes under the condition of small samples, so that the moving target detection performance is better.
In conclusion, the method provided by the invention has better robustness, the estimation performance has less requirements on the number of training samples, and the method still has better clutter suppression performance and moving target detection performance under the condition that independent and identically distributed samples are insufficient in a non-uniform environment.
TABLE 1 Radar parameter settings
Figure BDA0002209037600000101
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (11)

1. A robust STAP covariance matrix estimation method based on matrix manifold is characterized by comprising the following steps:
firstly, calculating a positive definite covariance matrix of each training unit;
secondly, positive definite covariance matrixes of all training units are constructed into a rectangular manifold, and clutter covariance matrixes of the units to be detected are estimated and converted into an estimation problem of geometric centroids on the rectangular manifold;
and thirdly, calculating the geometric mass center of K training units corresponding to K points on the matrix manifold, and acquiring clutter covariance matrix estimation of the unit to be detected.
2. The method of claim 1, wherein in a first step, an echo signal is received using an airborne radar antenna and represented as x; according to the sampling rate of the radar receiver, the distance observed by the radar is uniformly divided into L distance units; setting the first distance unit as the unit to be detected and the echo signal as xlThe clutter covariance matrix to be estimated corresponding to the unit to be detected is
Figure RE-FDA0002271133800000011
Taking K distance units which are adjacent to the unit to be detected and do not contain the target as training samples, taking each training sample as a training unit, and expressing the echo signal of each training unit as xk，k＝1,…,K，xkThe received echo signal of the kth training unit is set to have a data length of G, which can be expressed as xk＝{x1,…xg,…,xG}; the covariance matrix of each training unit may be determined by
Figure RE-FDA0002271133800000012
And (4) calculating.
3. A robust STAP covariance matrix estimation method based on matrix manifold as claimed in claim 2, wherein in the first step, a diagonal loading method is used, i.e.
Figure RE-FDA0002271133800000013
Calculating to obtain a positive definite covariance matrix of each training unit
Figure RE-FDA0002271133800000014
4. The method of claim 2, wherein in the first step, a positive definite covariance matrix for each training unit is calculated using Toeplitz method
Figure RE-FDA0002271133800000015
Namely, it is
Figure RE-FDA0002271133800000021
Wherein, cjIs the correlation coefficient between training units with interval j, which can be expressed as
Figure RE-FDA0002271133800000022
0≤j≤G-1，xiRepresenting a vector xkThe ith element, x ini+jRepresenting a vector xkThe i + j th element in (a);
Figure RE-FDA0002271133800000023
denotes cjConjugation of (1).
5. The method of claim 2, wherein in the first step, the positive-definite covariance matrix for each training unit is solved by the following optimization problem
Figure RE-FDA0002271133800000024
Figure RE-FDA0002271133800000025
Its optimal solution can be expressed as
Figure RE-FDA0002271133800000026
Λk＝diag([κMλk,λk,…,λk])
Figure RE-FDA0002271133800000027
Wherein I represents a unit matrix, | · |. non-woven phosphor2Represents a 2 norm, UkIs composed of
Figure RE-FDA0002271133800000028
The characteristic value is | | xk||2Corresponding unit feature vector, κMIs a condition number.
6. The method of claim 3, 4 or 5, wherein in the second step, the clutter covariance matrix to be estimated corresponding to the cell to be detected is estimated
Figure RE-FDA0002271133800000029
Functional transformations expressed as covariance matrices of K training units, i.e.
Figure RE-FDA0002271133800000031
Wherein K represents the number of training units;
forming a matrix manifold by positive definite covariance matrixes of all training units; the positive definite covariance matrix of each training unit corresponds to a point on the matrix manifold, and the geometric distance between the point on the matrix manifold and the point is defined as dq(ii) a Therefore, the estimation of the clutter covariance matrix of the unit to be detected is converted into the estimation problem of the geometric centroid on the rectangular manifold.
7. The method of claim 6, wherein in the second step, the unit to be detected clutter covariance matrix estimation is represented by the following problem:
Figure RE-FDA0002271133800000032
wherein the content of the first and second substances,is shown as
Figure RE-FDA0002271133800000034
Andis measured by the geometric distance of (a),
Figure RE-FDA0002271133800000036
is the weighting factor of the kth training unit,and is
Figure RE-FDA0002271133800000038
8. The method according to claim 1, wherein in the third step, the geometric centroids of K points on the matrix manifold corresponding to all training units are iteratively solved by using total Skew Jesen divergence on the matrix manifold, thereby obtaining the clutter covariance matrix estimate of the unit to be detected.
9. The method of claim 8, wherein in the third step, a total Skew Jesen divergence is used
Figure RE-FDA0002271133800000039
As a measure of geometric distance on the matrix manifold, i.e.
Figure RE-FDA00022711338000000310
The calculation formula is as follows:
wherein l represents an optimization objective function, alpha represents a skew influence factor,
Figure RE-FDA00022711338000000312
t represents the number of iterations,
Figure RE-FDA00022711338000000313
(p: q) represents the divergence between p and q,
Figure RE-FDA0002271133800000041
ΔFf (q) -F (p), F stands for strictly convex and differentiable function,<·>represents the inner product;
wherein the content of the first and second substances,
Figure RE-FDA0002271133800000043
BF(p: q) represents the Bregman divergence between p and q;
the result of the t-th iteration can be expressed as
Figure RE-FDA0002271133800000044
And obtaining a clutter covariance matrix estimation value of the unit to be detected by the iterative computation.
10. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the matrix manifold-based robust STAP covariance matrix estimation method according to any of claims 1 to 8.
11. A computer readable storage medium having stored thereon a computer program, wherein the computer program, when being executed by a processor, is adapted to carry out the steps of the matrix manifold based robust STAP covariance matrix estimation method according to any of the claims 1 to 8.
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CN111474526A (en) * 2020-04-24 2020-07-31 成都航空职业技术学院 Rapid reconstruction method of airborne STAP clutter covariance matrix
CN113311417A (en) * 2021-05-24 2021-08-27 中国人民解放军国防科技大学 Signal detection method and system based on manifold filtering and JBLD divergence
CN115687931A (en) * 2022-11-22 2023-02-03 中国人民解放军空军预警学院 Space-time adaptive processing method and system for extremely low training sample number
CN116559819A (en) * 2023-07-07 2023-08-08 中国人民解放军空军预警学院 Airborne radar knowledge auxiliary color loading clutter suppression method and device

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