CN110632571B - 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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CN110632571B
CN110632571B CN201910892011.8A CN201910892011A CN110632571B CN 110632571 B CN110632571 B CN 110632571B CN 201910892011 A CN201910892011 A CN 201910892011A CN 110632571 B CN110632571 B CN 110632571B
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CN110632571A (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

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 matrix manifold, and converting the clutter covariance matrix estimation of the unit to be detected into the estimation problem of the geometric centroid on the matrix 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 GDA0003001769470000021
Taking K distance units which are adjacent to the unit to be detected and do not contain the target as training samplesEach training sample is used as a training unit, and the echo signal of each training unit is represented 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 GDA0003001769470000022
And (4) calculating.
Computing a positive definite covariance matrix for each training unit
Figure GDA0003001769470000023
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.
Figure GDA0003001769470000024
I denotes an identity matrix.
The second method comprises the following steps: by the Toeplitz method, i.e.
Figure GDA0003001769470000025
Wherein, cjIs the correlation coefficient between training units with interval j, which can be expressed as
Figure GDA0003001769470000031
0≤j≤G-1，xiRepresenting a vector xkThe ith element, x ini+jRepresenting a vector xkThe (i + j) th element in (b).
Figure GDA0003001769470000032
Denotes cjConjugation of (1).
The third method comprises the following steps: solving the problem by the following equation
Figure GDA0003001769470000033
Its optimal solution can be expressed as
Figure GDA0003001769470000034
Λk＝diag([κMλk,λk,…,λk])
Figure GDA0003001769470000035
Wherein | · | purple sweet2Represents a 2 norm, UkIs composed of
Figure GDA0003001769470000036
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.
In the second step of the invention, the clutter covariance matrix to be estimated corresponding to the unit to be detected is determined
Figure GDA0003001769470000037
Functional transformations expressed as covariance matrices of K training units, i.e.
Figure GDA0003001769470000038
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 clutter covariance matrix estimation of the unit to be detected is converted into the estimation problem of the geometric centroid on the matrix manifold.
The invention adopts the geometric mean value to calculate the geometric centroid on the matrix manifold. The clutter covariance matrix estimation of the unit to be detected can be expressed as the following problem:
Figure GDA0003001769470000041
wherein the content of the first and second substances,
Figure GDA0003001769470000042
is shown as
Figure GDA0003001769470000043
And
Figure GDA0003001769470000044
is measured by the geometric distance of (a),
Figure GDA0003001769470000045
is the weighting factor of the kth training unit,
Figure GDA00030017694700000417
and is
Figure GDA0003001769470000046
In the absence of a-priori information,
Figure GDA0003001769470000047
in the third step of the invention, on the matrix manifold, the geometric centroid of all training units corresponding to K points on the matrix manifold is iteratively solved by utilizing the total Skaew Jesen divergence, 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 adopts total Skew Jesen divergence (marked as
Figure GDA0003001769470000048
) As a measure of geometric distance on the matrix manifold, i.e.
Figure GDA0003001769470000049
The calculation formula is as follows:
Figure GDA00030017694700000410
wherein l represents an optimization objective function, alpha represents a skew influence factor,
Figure GDA00030017694700000411
t represents the number of iterations,
Figure GDA00030017694700000412
(p: q) represents the divergence between p and q,
Figure GDA00030017694700000413
ΔFf (q) -F (p), F stands for strictly convex and differentiable function,<·>represents the inner product (·)2Representing the square.
Figure GDA00030017694700000414
Wherein the content of the first and second substances,
Figure GDA00030017694700000415
BF(p: q) denotes the Bregman divergence between p and q.
The result of the t-th iteration can be expressed as
Figure GDA00030017694700000416
F denotes the derivative of the function F. 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 matrix 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 total Jesen Skew 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, 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 GDA0003001769470000061
And (4) calculating. x is the echo signal received by the radar and can be expressed as
Figure GDA0003001769470000062
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 GDA0003001769470000071
In this embodiment, a diagonal loading method is adopted, i.e.
Figure GDA0003001769470000072
Calculating to obtain a positive definite covariance matrix of each training unit
Figure GDA0003001769470000073
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 GDA0003001769470000074
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 GDA0003001769470000075
Is shown as
Figure GDA0003001769470000076
Wherein R is a conjugate positive definite matrix,
Figure GDA0003001769470000077
a set space formed by all positive definite covariance matrixes. Each trainingThe covariance matrix of the cell corresponds to a point on the manifold, and the geometric distance defining the different points on the manifold is dq. On this basis, the covariance matrix estimate can be considered as an estimate of the geometric centroid of the covariance matrix on the matrix 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 GDA0003001769470000078
Wherein the content of the first and second substances,
Figure GDA0003001769470000079
is shown as
Figure GDA00030017694700000710
And
Figure GDA00030017694700000711
is measured by the geometric distance of (a),
Figure GDA00030017694700000712
is the weighting factor of the kth training unit,
Figure GDA00030017694700000713
and is
Figure GDA00030017694700000714
And thirdly, calculating the geometric mass center of corresponding points of K training units on the matrix manifold to obtain 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 adopts total Skew Jesen divergence (marked as
Figure GDA0003001769470000081
) As a measure of geometric distance on the matrix manifold, i.e.
Figure GDA0003001769470000082
The calculation formula is as follows:
Figure GDA0003001769470000083
wherein l represents an optimization objective function, alpha represents a skew influence factor,
Figure GDA0003001769470000084
t represents the number of iterations,
Figure GDA0003001769470000085
(p: q) represents the divergence between p and q,
Figure GDA0003001769470000086
ΔFf (q) -F (p), F stands for strictly convex and differentiable function,<·>represents the inner product (·)2Representing the square.
Figure GDA0003001769470000087
Wherein the content of the first and second substances,
Figure GDA0003001769470000088
BF(p: q) denotes the Bregman divergence between p and q.
The result of the t-th iteration can be expressed as
Figure GDA0003001769470000089
F denotes the derivative of the function F.
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 GDA00030017694700000810
Namely, it is
Figure GDA0003001769470000091
Wherein, cjIs the correlation coefficient between training units with interval j, which can be expressed as
Figure GDA0003001769470000092
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 GDA0003001769470000093
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 GDA0003001769470000094
Figure GDA0003001769470000095
Its optimal solution can be expressed as
Figure GDA0003001769470000096
Λk＝diag([κMλk,λk,…,λk])
Figure GDA0003001769470000097
Wherein | · | purple sweet2Represents a 2 norm, UkIs composed of
Figure GDA0003001769470000098
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 GDA0003001769470000101
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 (8)

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;
receiving an echo signal by using an airborne radar antenna, and representing the echo signal 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 FDA0003001769460000011
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 FDA0003001769460000012
Calculating to obtain;
secondly, positive definite covariance matrixes of all training units are constructed into a matrix manifold, and clutter covariance matrixes of the units to be detected are estimated and converted into an estimation problem of a geometric centroid on the matrix manifold;
the clutter covariance matrix to be estimated corresponding to the unit to be detected
Figure FDA0003001769460000013
Functional transformations expressed as covariance matrices of K training units, i.e.
Figure FDA0003001769460000014
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 matrix manifold, and the estimation of the clutter covariance matrix of the unit to be detected is represented as the following problem:
Figure FDA0003001769460000015
wherein the content of the first and second substances,
Figure FDA0003001769460000016
is shown as
Figure FDA0003001769460000017
And
Figure FDA0003001769460000018
is measured by the geometric distance of (a),
Figure FDA0003001769460000019
is the weighting factor of the kth training unit,
Figure FDA00030017694600000110
and is
Figure FDA00030017694600000111
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. A robust STAP covariance matrix estimation method based on matrix manifold as claimed in claim 1, wherein in the first step, a diagonal loading method is used, i.e.
Figure FDA0003001769460000021
I represents an identity matrix; calculating to obtain a positive definite covariance matrix of each training unit
Figure FDA0003001769460000022
3. The method of claim 1, wherein in the first step, a positive definite covariance matrix for each training unit is calculated using Toeplitz method
Figure FDA0003001769460000023
Namely, it is
Figure FDA0003001769460000024
Wherein, cjIs the correlation coefficient between training units with interval j, which can be expressed as
Figure FDA0003001769460000025
0≤j≤G-1，xiRepresenting a vector xkThe ith element, x ini+jRepresenting a vector xkThe i + j th element in (a);
Figure FDA0003001769460000026
denotes cjConjugation of (1).
4. The method of claim 1, wherein in the first step, the positive-definite covariance matrix for each training unit is solved by the following optimization problem
Figure FDA0003001769460000027
Figure FDA0003001769460000028
Its optimal solution can be expressed as
Figure FDA0003001769460000031
Λk＝diag([κMλk,λk,…,λk])
Figure FDA0003001769460000032
Wherein I represents a unit matrix, | · |. non-woven phosphor2Represents a 2 norm, UkIs composed of
Figure FDA0003001769460000033
The characteristic value is | | xk||2Corresponding unit feature vector, κMIs a condition number.
5. 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.
6. The method of claim 5, wherein in the third step, a total Skaw Jesen divergence is used
Figure FDA0003001769460000034
As a measure of geometric distance on the matrix manifold, i.e.
Figure FDA0003001769460000035
The calculation formula is as follows:
Figure FDA0003001769460000036
wherein the content of the first and second substances,
Figure FDA00030017694600000312
represents an optimization objective function, alpha represents a skew impact factor,
Figure FDA0003001769460000037
t represents the number of iterations,
Figure FDA0003001769460000038
(p: q) represents the divergence between p and q,
Figure FDA0003001769460000039
ΔFf (q) -F (p), F stands for strictly convex and differentiable function,<·>represents the inner product;
Figure FDA00030017694600000310
wherein the content of the first and second substances,
Figure FDA00030017694600000311
BF(p: q) represents the Bregman divergence between p and q;
the result of the t-th iteration can be expressed as
Figure FDA0003001769460000041
Wherein:
Figure FDA0003001769460000042
represents the derivative of the function F;
and obtaining a clutter covariance matrix estimation value of the unit to be detected by the iterative computation.
7. 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 of any of claims 1 to 6.
8. 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 6.
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