Robust moving target detection method for FDA-MIMO radar

Abstract

The invention discloses a robust moving target detection method for an FDA-MIMO radar, and relates to the field of radar target detection. The method comprises the following steps: acquiring receiving data of K pulses to obtain test data; sampling data is obtained based on the obtained multiple training data; the test data and the training data share a noise covariance matrix; constructing a binary hypothesis moving target detection model; constructing a moving target detector based on the sampling covariance, the test data and the combined steering vector; and performing target detection on the currently acquired to-be-detected data of the moving target based on the constructed moving target detector. According to the method, the random variables are introduced, so that the robustness of the detector for target detection is remarkably enhanced; the detectors not only have excellent performance under the condition of no signal mismatch, but also can maintain relatively strong robustness in the face of signal mismatch, so that the moving target detection performance of the FDA-MIMO radar is improved.

Description

Technical Field

[0001] The present application relates to the field of radar target detection technology, and in particular to a robust moving target detection method of a FDA-MIMO radar based on a combination of a frequency diverse array (FDA) and a multiple-input multiple-output (MIMO) technology. Background Art

[0002] FDA-MIMO radar not only solves the distance and angle coupling and time-varying problems of radar beams, but also retains the distance dependence of FDA and the degree of freedom advantage of MIMO. As one of the core functions of radar, target detection has always been a hot topic of research for scholars at home and abroad. Target detection refers to the process of judging whether there is a target in the radar echo in the radar illumination area. This is a binary hypothesis detection problem. However, there are relatively few studies on applying the additional distance dimension information of FDA-MIMO radar to the field of target detection. Specifically, considering the Gaussian clutter environment, the paper "HUANG Bang, JIAN Jiangwei, BASIT A, et al. Adaptive distributed target detection for FDA-MIMO radar in Gaussian clutter without training data [J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 58 (4): 2961-2972" studies the distributed target detection problem of FDA-MIMO radar in the case of unknown covariance matrix, and proposes a two-step GLRT detection method without training data to improve the target detection performance. The paper "GUI R, WANG WQ, ZHENG Z. Low-complexity GLRT for FDA radar without training data-Science Direct [J]. Digital Signal Processing, 2020, 107" proposes a low-complexity unstructured GLRT algorithm for FDA-MIMO radar in the presence of mainlobe deception interference and suppressive interference.

[0003] However, in actual working scenarios, FDA-MIMO radars may face a variety of irrational factors, such as array calibration errors, uncertainty in target arrival angles and Doppler frequencies, and waveform mismatches. These undesirable factors will cause inconsistencies between the transmitted and received signals. Therefore, when the received signal is mismatched, it is particularly important to study how to improve the robustness of the detector. The common solution to signal mismatch is to absorb the mismatched signal into the target detector as much as possible through the signal subspace. However, if the signal subspace is not properly selected, it is very likely to lead to a decrease in target detection performance. Another solution is to regard the error as a random variable and incorporate it into the signal model. This method can significantly enhance the robustness of the detector by supplementing the mismatched signal with a random variable. Although the signal mismatch problem has received extensive research attention, methods for robust target detection of FDA-MIMO radars are still relatively scarce. Summary of the invention

[0004] The present application provides a robust moving target detection method for FDA-MIMO radar to improve the detection performance of FDA-MIMO radar for moving targets.

[0005] The technical solution adopted in this application is:

[0006] A robust moving target detection method for FDA-MIMO radar, the method comprising the following steps:

[0007] Step 1: Get the test data based on the received data of K pulses obtained by the FDA-MIMO radar Where M and N represent the number of transmitting array elements and receiving array elements of FDA-MIMO radar respectively; obtain K pulse training data from the angle unit or distance unit around the cutting unit Where l is the training data number, and the sampling data is obtained based on the training data of the specified training data volume L.

[0008] Among them, the test data and the training data share the same noise covariance matrix R;

[0009] Step 2, construct a moving target detection model based on binary hypothesis;

[0010] exist Assume that

[0011] exist Assume that

[0012] in, is the noise matrix corresponding to the test data Z, corresponds to the lth training data Z lThe noise matrix; ξ is the complex amplitude, the joint steering vector and a t (r,θ),a r (θ) are the sending and receiving steering vectors, θ and r are the azimuth and slant range of the moving target, respectively. is the Kronecker product; ω D (f d ) is the Doppler steering vector, f d is the Doppler shift, Represents the added virtual random signal, which is used to simulate the interference of the signal;

[0013] Step 3, based on the sampling covariance S = YY H , test data Z, joint guidance vector a TR (r,θ) construct a moving target detector;

[0014] Step 4: Based on the moving target detector constructed in step 3, target detection is performed on the data to be detected of the moving target currently collected to obtain the target detection result; wherein the data to be detected and the test data Z maintain the same data format.

[0015] Furthermore, in step 3, the moving target detector is set to:

[0016]

[0017] Among them, λ is the preset detection threshold, I represents the unit matrix of MN*MN, and the auxiliary quantity is the estimated value of the robust factor γ, Indicates the amount of assistance The projection matrix, Indicates about The projection matrix of , det(·) represents the determinant of the matrix, and the symbol “(·) T ”, “(·) H ” represent transposition operation and conjugate transposition operation respectively; symbol (·) * represents the conjugation operation.

[0018] Furthermore, in step 3, the moving target detector is set to:

[0019]

[0020] Among them, the auxiliary

[0021] Furthermore, in step 3, the moving target detector is set to:

[0022]

[0023] Furthermore, in step 3, the moving target detector is set to:

[0024]

[0025] The technical solution provided by this application brings at least the following beneficial effects:

[0026] By introducing random variables, the robustness of detectors for target detection is significantly enhanced in this application; these detectors not only perform well in the absence of signal mismatch, but also maintain strong robustness in the face of signal mismatch, thus providing new ideas and methods for robust target detection of FDA-MIMO radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0028] Figure 1 Schematic diagram of the processing process of the robust moving target detection method for FDA-MIMO radar proposed in this application.

[0029] Figure 2 This is a curve diagram of the change results of the detection threshold of the detector proposed in this application, where (2a) is a curve diagram of the change of the detection threshold with ρ, and (2b) is a curve diagram of the change of the detection threshold with ρ.

[0030] Figure 3 The detection probability result curve diagram (SJNR change curve diagram) of the detector proposed in this application under the condition of no signal mismatch, different training data amounts and transmission snapshot numbers, among which (3a) is the detection probability result curve diagram under the setting of L=4, K=4, and (3b) is the detection probability result curve diagram under the setting of L=6, K=4.

[0031] Figure 4 The detection probability change curve (SJNR change curve) of the detector proposed in this application under different dimensional signal mismatch conditions, where L = 6, K = 4, (4a) is no signal mismatch, and (4b) cos 2 φ=0.80、cos in (4c) 2 Φ=0.80;(4d)cos 2 φ=0.80,cos 2 Φ=0.80.

[0032] Figure 5 The curve diagram of the detection probability of different detectors in this application when the signal is mismatched with the mismatch amount, where L = 6, K = 4, (5a) corresponds to cos2 φ, (5b) corresponds to cos 2 Φ. DETAILED DESCRIPTION

[0033] In order to enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions of the embodiments of the present application will be described in detail and completely in conjunction with the drawings in the embodiments of the present application. Obviously, the embodiments described with reference to the drawings are exemplary and are intended to be used to explain the present application, and cannot be understood as limiting the present application.

[0034] An embodiment of the present application provides a robust moving target detection method for an FDA-MIMO radar, which is used for a target detector of the FDA-MIMO radar to perform signal processing on a received target signal to improve the robustness of the target detector of the FDA-MIMO radar for target detection.

[0035] Consider an FDA-MIMO radar with an M-element uniform linear array transmitting and an N-element uniform linear array receiving. The spacing between the transmitting and receiving array elements is d. The orthogonal waveform it transmits consists of K pulses. Then the carrier frequency at the mth transmitting array element is

[0036] f m =f0+(m-1)Δf,m=1,2,…,M (1)

[0037] Where f0 is the reference carrier frequency, λ=c / f0 is the wavelength corresponding to f0, and c is the speed of light. s ,θ s ) has a far-field point source, where θ s is the azimuth, r s is the slant distance. The target moves at a constant radial velocity v s Move towards the radar. After mixing and matched filtering at the receiving end, K pulses can be collected as a data matrix, which can be described as:

[0038]

[0039] where ξ is the complex amplitude, is the joint steering vector, which has the form

[0040]

[0041] in and are the sending steering vector and the receiving steering vector, Δf is the frequency deviation, and is the Kronecker product, [·] T Indicates transpose.

[0042] w d (f d) is the Doppler steering vector, which is expressed as

[0043]

[0044] Among them, T r is the pulse repetition interval (PRI), f d is the Doppler shift.

[0045] is the noise matrix, the noise v of the kth pulse k The covariance matrix of is denoted by R and is actually unknown.

[0046] symbol Represents the added virtual random signal to simulate the interference received by the signal. Divide it into blocks

[0047]

[0048] Assumptions is an independent and identically distributed (IID) Gaussian random variable with mean 0 and variance γΣ, that is,

[0049]

[0050] Among them, γ is a non-negative unknown quantity to evaluate the robustness of the controller, and the covariance Σ is used to enhance the signal energy detection in the case of signal mismatch, which helps to be more inclined to adopt valid hypotheses when making binary hypothesis judgments.

[0051] This application further assumes that the false signal n k With the noise term v k are independent of each other, and the covariance structure Σ of the virtual signal is the same as the covariance R of the noise.

[0052] Considering the operation of FDA-MIMO radar in a noisy environment including receiver thermal noise and suppressive interference or compensated clutter, training data can be obtained from the angle unit or distance unit around the cutting unit (CUT) to estimate the unknown covariance matrix, which can significantly improve the detection performance. Therefore, this application designs a detector based on training data and derives the statistical performance of the detector. Let is the training data matrix, which shares the same noise covariance matrix with the test data, where L represents the number of IID training data. The received data Z k

[0053]

[0054] Similar to Down:

[0055]

[0056] Furthermore, the mathematical problem of testing binary hypotheses can be formulated as:

[0057]

[0058] exist The PDF of the following union is expressed as:

[0059]

[0060] The expression of Z1 in the formula is:

[0061]

[0062] And S is the sampling covariance, S = YY H , where the sample data Y is:

[0063]

[0064] Similar available The following joint PDF:

[0065]

[0066] Where det(·) represents the determinant of the matrix, Tr(·) represents the trace of the matrix, and the symbol “(·) T ”, “(·) H ” represent transposition operation and conjugate transposition operation respectively, where the symbol “(·) H "same

[0067] In the embodiments of the present application, three different detector designs are used to achieve the processing of the target signal, which are described in detail as follows:

[0068] 1. Detector design based on OGLRT criteria

[0069] In view of the above detection problem, this application first designs a detector based on the OGLRT (One-step generalized likelihood ratio test) criterion, and the statistical expression is:

[0070]

[0071] Wherein, λ represents the preset detection threshold.

[0072] First, optimize and solve the molecular part. Solve the MLE (maximum likelihood estimate) of the covariance matrix R. Take the logarithm first, then differentiate R and set the equation to zero, and you get:

[0073]

[0074] Formula (10) can be simplified to get:

[0075]

[0076] make

[0077]

[0078] Available becomes:

[0079]

[0080]

[0081] Then solving the maximum value of equation (18) is equivalent to solving the minimum value of the following equation:

[0082]

[0083] Let w d (f d )=ω D (f d ), express The projection matrix, Represents an orthographic projection matrix.

[0084] Further simplifying (19):

[0085]

[0086] And order

[0087]

[0088] Available

[0089]

[0090] The second equality uses the following inequality det(A+B)≥det(A), where A is a Hermitian positive definite matrix of suitable dimensions and B is a Hermitian positive semidefinite matrix of suitable dimensions, where the equality holds true under the condition is a 0 matrix, that is:

[0091]

[0092] Multiply the left and right sides of equation (24) by Right multiplication The MLE of the unknown amplitude ξ of the obtained signal is:

[0093]

[0094] Inserting equation (25) into equation (20) yields:

[0095]

[0096] in,

[0097] Further get in The covariance matrix estimate is

[0098]

[0099] Combining equation (13) and equation (27), we can get:

[0100]

[0101] Combining equations (14), (16), (26) and (28), we can get the OGLRT detector at a given γ:

[0102]

[0103] Furthermore, the unknown parameter γ can be solved as follows:

[0104]

[0105] and is the only positive solution of (31) at (0,∞)

[0106]

[0107] Among them, x represents the unknown parameter, and δ r , R represent The non-zero eigenvalues ​​and ranks of . Substituting equation (30) into the equation, the final OGLRT detector expression is simplified as follows:

[0108]

[0109] Where I is the identity matrix, for The projection matrix.

[0110] 2. Detector design based on TGLRT criterion

[0111] The design principle of TGLRT is to first assume that the covariance matrix is ​​known, derive the detector expression, and then bring the sampling covariance into it to obtain the final expression. Then the statistical expression of the TGLRT detector is

[0112]

[0113] First insert equation (10) and equation (13) into (33), we can get:

[0114]

[0115] After simplifying and taking the logarithm, we get:

[0116]

[0117] Find the MLE for γ in the above formula, that is, set the derivative of γ to zero:

[0118]

[0119] We can get:

[0120]

[0121] Substituting this formula into formula (35) and simplifying it, we get:

[0122]

[0123] Then find the MLE for ξ:

[0124]

[0125] We can get:

[0126]

[0127] Inserting this formula into formula (38) yields:

[0128]

[0129] Among them, cont. represents a constant that does not contain unknown variables.

[0130] Furthermore, by combining equation (35) and equation (41), we can obtain:

[0131]

[0132] Finally, the sampling covariance Substituting in, the final detector expression is:

[0133]

[0134] in,

[0135] 3. Detector design based on Wald criterion

[0136] Let's define the parameter vector as θ:

[0137]

[0138] Among them, θ r Represents useful parameters, and its expression is:

[0139] θ r =[ξ R ,ξ I ,γ] T (45)

[0140] Among them, ξ R , I represent the real and imaginary parts of the unknown parameter ξ respectively.

[0141] θ s =[vec T (R)] T Represents a redundant parameter.

[0142] The statistical expression of the detector designed according to the Wald criterion is:

[0143]

[0144] Further we can get:

[0145]

[0146] In the first step, after taking the logarithm of equation (9), we can r Derivation

[0147]

[0148] in:

[0149]

[0150]

[0151] Then find the first-order derivatives of the above three equations and take the mathematical expectation to get:

[0152]

[0153] as well as

[0154]

[0155] Inserting equation (52)-equation (57) into equation (47) yields:

[0156]

[0157] expression It can be obtained by Schur's complementary decomposition theorem formula (25), that is:

[0158]

[0159] So we still need to ask for Let the three equations be s Find the first-order derivative and take the mathematical expectation:

[0160]

[0161] Then we can get:

[0162]

[0163] Similarly, we can get:

[0164]

[0165] in addition, It can also be expressed as:

[0166]

[0167] So from formula (59) we can get

[0168]

[0169] is θ r exist The MLE under , its expression is:

[0170]

[0171] In the formula They are The real and imaginary parts of can be obtained by equation (40). It can be solved by formula (30). Similarly, we can get:

[0172]

[0173] Substituting into formula (66) we can obtain:

[0174]

[0175] In summary, the final expression is:

[0176]

[0177] 4. Detector design based on Durbin criterion

[0178] First, the expression criteria of Durbin detector are:

[0179]

[0180] in yes exist The MLE under the assumption is obtained.

[0181]

[0182] exist Under the assumption, we can find the MLE for θ. It is expressed as:

[0183] θ r0 =[0,0,0] (73)

[0184]

[0185] Substituting into formula (66), we can obtain:

[0186]

[0187] From equations (58), (73) and (74), we can get

[0188]

[0189] Inserting equation (72), equation (75) and equation (76) into equation (71) yields the final expression:

[0190]

[0191] In actual radar applications, there is often a difference between the actual signal steering vector and the ideal steering vector due to factors such as array calibration errors and waveform mismatch. In order to evaluate this type of error, the generalized square cosine function is used to quantify this difference. The specific expression is:

[0192]

[0193] Among them, cos 2 φ is used to evaluate the degree of signal mismatch in spatial and distance dimensions. and a TR (r0,θ0) are the actual transmit-receive steering vector and the ideal transmit-receive steering vector, respectively. Similarly, let’s define cos 2 Φ is a measure of the signal mismatch in the Doppler dimension, and its expression (35) can be further transformed into:

[0194]

[0195] Among them, ω D (f d,0 ) and ω D (f d ) are the actual and ideal Doppler steering vectors, respectively.

[0196] The embodiment of the present application provides a robust moving target detection method for FDA-MIMO radar, which is used for FDA-MIMO radar to process received target signals, such as Figure 1 As shown, it includes the following steps:

[0197] Step 1: Get the test data based on the received data of K pulses obtained by the FDA-MIMO radar Where M and N represent the number of transmitting array elements and receiving array elements of the FDA-MIMO radar respectively; the training data of K pulses are obtained from the angle unit or distance unit around the cutting unit (CUT) Where l is the training data number, and the sampling data is obtained based on the training data of the specified training data volume L.

[0198] Among them, the test data and the training data share the same noise covariance matrix R;

[0199] Step 2: construct a binary hypothesis moving target detection model, as shown in formula (9);

[0200] Step 3: Based on the sampling covariance, test data Z, and joint guidance vector Construct a moving target detector (as shown in formulas (32), (40), (70) and (77)); where a t (r,θ),a r (θ) are the sending and receiving steering vectors, respectively, and θ and r are the azimuth and slant range of the moving target, respectively;

[0201] Step 4: Based on the moving target detector constructed in step 3, target detection is performed on the currently collected moving target data to be detected (keeping the data format consistent with the test data Z) to obtain the target detection result.

[0202] Consider a FDA-MIMO radar target detection scenario. The number of transmitting array elements and receiving array elements are M = 4 and N = 3 respectively, and the signal carrier frequency is f0 = 2 GHz. The array element spacing is set to That is, the distance between the transmitting array element and the receiving array element is set to The frequency deviation between array elements is equivalent to the signal bandwidth of 1MHz. The target of interest is located at (r,θ) = (15.12Km,30° ) at which the motion Doppler is f d =0.2. This embodiment takes into account the environment including clutter (including noise), suppressive interference and deceptive interference, so the clutter-interference covariance matrix can be established as:

[0203]

[0204] In the formula, and They represent the covariance parts of deceptive interference and suppressive interference respectively, and their expressions are:

[0205]

[0206] and and It represents the power of the dth deceptive interference signal and the uth suppressed interference signal. M×M represents a matrix of all ones. represents the clutter power, represents the clutter covariance part, which satisfies the exponential autoregressive model, that is, The parameter ρ is used to characterize the clutter covariance structure. In addition, we define are the jamming-to-clutter ratio (JCR) for deception jamming and suppression jamming, respectively. Meanwhile, the signal-to-clutter ratio (SCR) is defined as Let’s assume that there are two deceptive targets in the scene, located at (r1,θ1)=(15.165Km,30°) and (r2,θ2)=(30.48Km,28°). jam,1 =δ jam,2 =20dB. In addition, in the scene u = -20° There is a suppressive jammer with a jammer ratio of δ sup =30dB. The definition of signal to jamming-plus-noise ratio (SJNR) is: in, In addition, all simulation results presented in this embodiment are verified by MC (Monte Carlo), where PFA = 10 -3 , the detection threshold and detection probability are respectively and 10 4 The independent MC is obtained.

[0207] The specific simulation parameter settings in this embodiment are shown in Table 1, so as to analyze the target detection performance of each detector under non-mismatch and mismatch conditions to verify the effectiveness of the solution.

[0208] Table 1 Parameter settings

[0209]

[0210] Figure 2 Firstly, the detection threshold of the detector constructed in the embodiment of the present application is given as the R structure changes and the γ changes. Figure 2 p in the figure corresponds to parameter ρ, and y corresponds to parameter γ. It can be seen from the figure that the detection threshold of the detector proposed in the embodiment of the present application remains basically unchanged with the change of ρ or γ, which means that all detectors assume The following has CFAR properties for the covariance matrix R and the robust factor γ.

[0211] Figure 3 It shows the detection probability results of the set detector under different training data amounts and transmission snapshot numbers under the condition of no signal mismatch and with the change of signal-to-interference-noise ratio (SJNR). Among them, '-no' means the detector that does not consider the virtual signal proposed in the embodiment of the present application, namely 'OGLRT-no', 'AMF-no', 'TGLRT-no', so that the comparison between the detector discussed in the present application and the traditional detector can be obtained. Figure (3a) shows that when there are fewer training data and data to be tested, the performance of the robust OGLRT detector and Wald detector constructed in the present application is significantly better than other detectors, among which OGLRT performs the best. At the same time, it can be found that the OGLRT and AMF detectors proposed without considering the virtual signal of the present application have the worst performance at this time. Further analysis of Figure (3b) shows that with the increase of training data, the performance of all detectors tends to be consistent, and the gap with the upper limit of theoretical performance narrows. That is, by Figure 3 It can be seen that: when there are fewer training data and data to be tested, the robust OGLRT detector and Wald detector proposed in the embodiments of the present application perform significantly better than other detectors, among which OGLRT performs the best.

[0212] Figure 4It shows the change of the detection probability of the detector with the change of the signal-to-interference-to-noise ratio (SJNR) under the signal mismatch conditions of different dimensions. It can be seen from the figure that when there is an error in the transmit-receive dimension signal, Figure (4b) shows that when there is an error in the transmit-receive dimension signal, the OGLRT and Wald detectors proposed in the embodiment of the present application show strong robustness, while the performance of the Durbin detector is at a medium level, and the OGLRT and AMF detectors without virtual signals added have the strongest selectivity. And Figure (4c) points out that under the signal mismatch of the Doppler dimension, the performance of all detectors has declined, but the performance of the detector with the virtual signal added is slightly better than that without the virtual signal. In addition, by comparing Figures (4b) and (4c), it can be found that under the same degree of signal mismatch, the signal mismatch in the transmit-receive dimension has a more significant impact on the detector performance. It can be seen from Figure (4d) that when there are errors in the three dimensions of space and time, the TGLRT and Durbin detectors have the best robustness.

[0213] Figure 5 It shows how the detection probability of different detectors changes with the amount of mismatch when the signal is mismatched. It further shows that the TGLRT and Durbin detectors mentioned in this application have the best robustness, and the worst is the detector without adding virtual signals. Overall, the performance of the detectors designed in this application is better than that of the detectors without adding virtual signals.

[0214] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A robust moving target detection method for FDA-MIMO radar, characterized in that: The following steps are involved: Step 1: Get the test data based on the received data of K pulses obtained by the FDA-MIMO radar Where M and N represent the number of transmitting array elements and receiving array elements of FDA-MIMO radar respectively; obtain K pulse training data from the angle unit or distance unit around the cutting unit Where l is the training data number, and the sampling data is obtained based on the training data of the specified training data volume L. Among them, the test data and the training data share the same noise covariance matrix R; Step 2, construct a moving target detection model based on binary hypothesis; exist Assume that exist Assume that in, is the noise matrix corresponding to the test data Z, is the number corresponding to the lth training data Z l The noise matrix; ξ is the complex amplitude, the joint steering vector and a t (r,θ),a r (θ) are the sending and receiving steering vectors, θ and r are the azimuth and slant range of the moving target, respectively. is the Kronecker product; ω D (f d ) is the Doppler steering vector, f d is the Doppler shift, Represents the added virtual random signal, which is used to simulate the interference of the signal; Step 3, based on the sampling covariance S = YY H , test data Z, joint guidance vector a TR (r,θ) constructs a moving target detector, where (·) H represents the conjugate transpose operation; Step 4: Based on the moving target detector constructed in step 3, target detection is performed on the data to be detected of the moving target currently collected to obtain the target detection result; wherein the data to be detected and the test data Z maintain the same data format.

2. The method according to claim 1, characterized in that In step 3, the moving object detector is set as: Among them, λ is the preset detection threshold, I represents the unit matrix of MN*MN, and the auxiliary quantity is the estimated value of the robust factor γ, Indicates the auxiliary amount The projection matrix, Indicates about The projection matrix of , det(·) represents the determinant of the matrix, and the symbol (·) * represents the conjugation operation.

3. The method according to claim 1, characterized in that In step 3, the moving object detector is set as: Among them, λ is the preset detection threshold, and the auxiliary Auxiliary amount symbol(·) * represents the conjugation operation.

4. The method according to claim 1, characterized in that In step 3, the moving object detector is set as: Among them, λ is the preset detection threshold, is the estimated value of the robust factor γ, the auxiliary Auxiliary amount Indicates the auxiliary amount The projection matrix, Indicates about The projection matrix, auxiliary quantity I represents the identity matrix, symbol (·) H 、(·) * denote the conjugate transpose operation and the conjugate operation respectively.

5. The method according to claim 1, characterized in that In step 3, the moving object detector is set as: Among them, λ is the preset detection threshold, and the auxiliary Auxiliary amount Auxiliary amount Indicates the auxiliary amount The projection matrix, Indicates about The projection matrix, I represents the identity matrix, symbol (·) H 、(·) * denote the conjugate transpose operation and the conjugate operation respectively.

6. The method according to claim 2 or 4, characterized in that Estimation of the robust factor γ for: Among them, δ r , R' are The nonzero eigenvalues ​​and rank of .

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