A space-time adaptive tracking-before-detection method based on skew-symmetric structure

Abstract

The present invention relates to the field of underwater low-speed weak target detection and tracking, and in particular to a space-time adaptive detection-before-tracking method based on a skew-symmetric structure. The method of the present invention comprises: acquiring data collected by a sonar system, and establishing a binary hypothesis testing problem; constructing a new vector based on the skew-symmetric characteristics of the reverberation covariance matrix, obtaining a sample covariance matrix estimate, and converting the binary hypothesis testing problem into an equivalent binary composite hypothesis test; transforming the data from the complex domain to the real domain, and substituting the detection statistic of the RAO detector under a uniform Gaussian background to obtain the detection statistic of the skew-symmetric RAO under the uniform background, and substituting the discrimination criterion of RAO‑DP‑TBD under the uniform environment to obtain a skew-symmetric RAO‑TBD‑DP value function; using the skew-symmetric RAO‑DP‑TBD value function to perform dynamic iterative optimization to achieve detection and tracking of the target. The present invention can solve the problem of insufficient detection performance under small auxiliary data.

Description

Technical Field

[0001] The present invention relates to the field of underwater low-speed weak target detection and tracking, and in particular to a space-time adaptive pre-detection tracking method based on a skew-symmetrical structure. Background Art

[0002] In complex shallow-water hydrological environments, reverberation severely impacts the detection performance of active sonar. Especially when the sonar carrier moves at a certain speed, reverberation will be incident at different cone angles, causing a significant Doppler expansion, manifesting as a space-time coupling characteristic. Low-speed, weak targets are buried in the reverberation, making them difficult to detect. Due to the low signal-to-noise ratio, effective detection cannot be achieved using a single frame of data. However, accumulating multiple frames of data can improve the signal-to-noise ratio of the echo, thereby enhancing detection performance. Therefore, the underwater single-pulse space-time adaptive detection-before-tracking method can effectively detect low-speed, weak targets.

[0003] The underwater single-pulse space-time adaptive tracking-before-detection method uses the detection statistics of the space-time adaptive detection (STAD) method as the value function of the dynamic programming-based tracking-before-detection (DP-TBD) method, thereby combining the two and improving the output signal-to-noise ratio of low-speed weak targets by effectively suppressing reverberation and multi-frame accumulation, thereby achieving effective detection and tracking of low-speed weak targets.

[0004] However, due to the complexity and variability of the underwater environment, motion sonar often operates in a non-uniform reverberation environment, making it difficult to obtain sufficient independent and identically distributed auxiliary data. According to the RMB criterion, in order to ensure that the algorithm detection loss does not exceed 3dB, the number of auxiliary data must be greater than twice the system space-time dimension. Insufficient auxiliary data will cause inaccurate covariance matrix estimation, thereby affecting the accuracy of the algorithm. The existing implementation method that is most similar to the present invention is the underwater single-pulse space-time adaptive detection and tracking method. This method has good detection performance when there is sufficient auxiliary data, but the detection performance is seriously degraded when there is insufficient auxiliary data.

[0005] In summary, how to improve the robustness of the underwater single pulse space-time adaptive tracking before detection method under small auxiliary data is the core issue of the present invention. Summary of the Invention

[0006] The purpose of the present invention is to solve the problem that due to the complex and changeable underwater environment, active sonar often operates in a non-uniform reverberation environment, making it difficult to obtain sufficient independent and identically distributed auxiliary data, resulting in inaccurate covariance matrix estimation, and thus leading to poor robustness of existing methods.

[0007] To address this issue, we leverage prior knowledge of reverberation's spatial and temporal characteristics to introduce the skew-symmetric structure of the array sample covariance matrix into a binary hypothesis testing model. By constructing a new vector, we effectively double the length of the auxiliary data, effectively improving the estimation accuracy of the reverberation covariance matrix. We use the detection statistic as the value function through dynamic programming iteration and optimization. The final accumulated maximum function is compared with a threshold to obtain the target detection result. The maximum function of the last frame is then used to perform trajectory backtracking.

[0008] The present invention provides a robust space-time adaptive detection-before-tracking method based on a skew-symmetric structure, which can provide accurate and reliable prior knowledge for target detection, solve the problem of target detection performance degradation in the case of small sample data, and effectively improve the target detection and tracking performance of the sonar system.

[0009] To achieve the above objectives, the present invention is implemented through the following technical solutions.

[0010] The present invention proposes a space-time adaptive tracking-before-detection method based on a skew-symmetric structure, the method comprising:

[0011] Step S1. Processing the echo data collected by the sonar system and establishing a binary composite hypothesis testing model of the target to be detected based on the skew symmetry of the reverberation covariance matrix;

[0012] Step S2. For the binary composite hypothesis test model of the target to be detected, based on the RAO detection criterion, obtain the skew-symmetric RAO-DP-TBD value function;

[0013] Step S3: Use the skew-symmetric RAO-DP-TBD value function to perform dynamic iterative optimization to achieve target detection and tracking.

[0014] As an improvement to the above technical solution, step S1 specifically includes:

[0015] Step S1-1. Acquire echo data collected by the sonar system;

[0016] Step S1-2. Obtaining the corresponding observation vector based on each frame of echo data, and establishing a binary hypothesis testing model for the observation vector;

[0017] Step S1-3. Construct a new vector based on the skew symmetry of the reverberation covariance matrix;

[0018] Step S1-4. Based on the constructed new vector, obtain the covariance matrix estimate and convert the binary hypothesis test model into an equivalent binary composite hypothesis test model.

[0019] As an improvement to the above technical solution, in step S1-2, obtaining a corresponding observation vector based on each frame of echo data specifically includes: in the k-th frame of echo data obtained in the k-th scan, there are L range units, and the data of each range unit includes MN sampling data, where M is the number of sampling points in each range unit, and N is the number of array elements; the MN sampling data constitute the observation vector corresponding to each range unit in the k-th frame of echo data;

[0020] For each frame of data, the established binary hypothesis test model expression is:

[0021]

[0022] Among them, z is the unit data to be detected; z l is the data of the lth auxiliary unit; α is the unknown signal amplitude, which is a definite parameter; v is the signal space-time steering vector; L represents the number of distance units; n and n l is an independent and identically distributed complex Gaussian reverberation vector with mean 0 and covariance matrix R; H0 and H1 represent the no-target hypothesis and the targeted hypothesis, respectively.

[0023] As an improvement to the above technical solution, in step S1-3, the new vector constructed includes:

[0024]

[0025]

[0026]

[0027]

[0028] Among them, z a and z b is a complex Gaussian vector that satisfies independent and identical distribution based on z, z al and z bl It is based on z l The constructed complex Gaussian vectors satisfy independent and identical distribution; the superscript * indicates the conjugate operation; J is an M×N dimensional permutation matrix that satisfies the following formula:

[0029]

[0030] As an improvement to the above technical solution, in step S1-4, the sample covariance matrix estimate The expression is:

[0031]

[0032] Wherein, the superscript H represents the conjugate transpose operation;

[0033] The expression of the binary composite hypothesis test model is:

[0034]

[0035] Among them, the vector n a 、n b 、n al and n bl The expressions are:

[0036] n a =(n+Jn * ) / 2,n b =(n-Jn * ) / 2,n al =(n l +Jn l * ) / 2,n bl =(n l -Jn l * ) / 2;

[0037] α r represents the real part of α, α i Represents the imaginary part of α, expressed as: α r =Re{α},α i =Im{α}, where Re{·} represents the real part, Im{·} represents the imaginary part; v represents the space-time steering vector.

[0038] As an improvement to the above technical solution, step S2 specifically includes:

[0039] Step S2-1. Transform the detection unit data from the complex domain to the real domain;

[0040] Step S2-2. Transform the space-time steering vector from the complex domain to the real domain;

[0041] Step S2-3. transforming the reverberation covariance matrix estimate from the complex domain to the real domain;

[0042] Step S2-4. List the calculation formula of the detection statistic of the RAO detector under a uniform Gaussian background;

[0043] Step S2-5. Substitute the data obtained in steps S2-1 to S2-3 into step S2-4 to obtain the detection statistic of the skew-symmetric RAO detector;

[0044] Step S2-6. Substitute the detection statistic of the skew-symmetric RAO detector into the discrimination criterion of RAO-DP-TBD to obtain the skew-symmetric RAO-DP-TBD value function.

[0045] As an improvement to the above technical solution, the expression of step S2-1 is:

[0046]

[0047]

[0048] Among them, z erj 、z orj They represent the detection unit data in the echo data transformed from the complex domain to the real domain, and I represents the unit matrix;

[0049] In step S2-2, the space-time steering vector v is transformed into the real number domain r The expression is:

[0050] v r =Re{v}-Im{v}

[0051] In step S2-3, the reverberation covariance matrix estimate is transformed into the real domain The expression is:

[0052]

[0053] The detection statistic λ of the RAO detector under the uniform Gaussian background in step S2-4 RAO The calculation formula is:

[0054]

[0055] in, represents the sample covariance matrix, η RAO Indicates the RAO decision threshold;

[0056] The detection statistic λ of the skew-symmetric RAO detector in step S2-5 is P-RAO The expression is:

[0057]

[0058] Among them, η P-RAO Represents the P-RAO decision threshold, real domain vector Z r =[z erj z orj ].

[0059] As an improvement to the above technical solution, in step S2-6, the discrimination criterion expression of RAO-DP-TBD is:

[0060]

[0061] Where D represents the range-Doppler position of the target in the range-Doppler plane, v(v k ) represents the space-time steering vector of the kth scan, z lk,k Indicates the distance unit l where there is a target in the kth scan k The observation vector, represents the k-th scan sample covariance matrix, z l,k represents the observation vector of the k-th scan of the l-th auxiliary range unit, η RAO-DP-TBD Indicates the decision threshold of RAO-DP-TBD.

[0062] As an improvement to the above technical solution, the skew-symmetric RAO-DP-TBD value function expression obtained in step S2-6 is:

[0063]

[0064] in, Represents the estimated value of the sample covariance matrix of the k-th scan transformed into the real domain, Z rk represents the real domain observation vector of the k-th scan with the target distance unit, v r (v k ) represents the space-time steering vector of the k-th scan transformation to the real domain, η P-RAO-DP-TBD Indicates the decision threshold of P-RAO-DP-TBD.

[0065] As an improvement to the above technical solution, step S3 specifically includes:

[0066] The value function of the skew-symmetric RAO-DP-TBD is dynamically programmed and optimized, and the final accumulated maximum function is compared with the threshold to obtain the target detection result. The maximum function of the last frame is then used to perform trajectory backtracking, estimate the target trajectory, and achieve target detection and tracking. Compared with the existing technology, the advantages of this invention are:

[0067] 1. The present invention proposes a robust space-time adaptive tracking-before-detection method based on a skew-symmetric structure, which can effectively solve the problem of insufficient detection performance of existing methods under small auxiliary data, and improve the detection and tracking capabilities of active sonar;

[0068] 2. The process of deriving the P-RAO-DP-TBD value function (i.e., the skew-symmetric RAO-DP-TBD function) of the present invention has a small amount of calculation and is convenient;

[0069] 3. The present invention utilizes the skew symmetry of reverberation and constructs a new vector, which is equivalent to doubling the length of the auxiliary data, effectively improving the estimation accuracy of the reverberation covariance matrix and improving the detection and tracking performance of the algorithm under small auxiliary sample data. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a flow chart of the steps of the space-time adaptive tracking before detection method based on the skew-symmetric structure of the present invention;

[0071] Figure 2 Detection probability diagram when L=MN+1 in an embodiment of the present invention;

[0072] Figure 3 This is an accurate tracking probability diagram when L=MN+1 in an embodiment of the present invention;

[0073] Figure 4 Detection probability diagram when L=2MN+1 in an embodiment of the present invention;

[0074] Figure 5 This is an accurate tracking probability diagram when L=2MN+1 in an embodiment of the present invention. DETAILED DESCRIPTION

[0075] like Figure 1 FIG. 1 is a flowchart of a robust space-time adaptive tracking-before-detection method based on a skew-symmetric structure according to the present invention, comprising the following steps:

[0076] 1) Obtain data collected by the uniform linear array of the sonar system;

[0077] Among them, the number of sonar array elements is N, the number of sampling points in each distance unit is M, and for L distance units, the sonar system transmits a single pulse signal once to obtain MN×L-dimensional space-time data as a frame of data, and transmits K single pulse signals to obtain K frames of echo data.

[0078] 2) Taking the k-th frame of data, the binary hypothesis test problem can be written as follows:

[0079]

[0080] 3) Based on the skew symmetry of the reverberation covariance matrix, a new vector is constructed using formulas (3) to (6), and the estimated value of the sample covariance matrix is:

[0081]

[0082] 4) Convert the binary hypothesis test problem of formula (2) into an equivalent binary composite hypothesis test:

[0083]

[0084] 5) Convert data from complex domain to real domain:

[0085]

[0086]

[0087] v r =Re{v}-Im{v}(13)

[0088]

[0089] 6) Substituting formulas (11) to (14) into the detection statistics of the RAO detector under a uniform Gaussian background, we obtain the detection statistics of the skew-symmetric RAO under a uniform background:

[0090]

[0091] 7) Substituting formula (16) into the discrimination criterion of RAO-DP-TBD in a uniform environment, the skew-symmetric RAO-TBD-DP value function is obtained as follows:

[0092]

[0093] 8) Compare the final accumulated maximum function with the threshold to obtain the target detection result, and then use the maximum function of the last frame to realize trajectory backtracking and estimate the trajectory of the target.

[0094] Preferably, in step 3), the skew symmetry characteristic of the reverberation covariance is utilized to construct a new vector according to (3) to (6) to estimate the reverberation covariance matrix.

[0095] Preferably, in step 4), a new vector is constructed according to (3) to (6) and converted into an equivalent binary composite hypothesis test.

[0096] Preferably, in step 5), the received data, the space-time steering vector and the reverberation covariance matrix are transformed from the complex domain to the real domain.

[0097] Preferably, in step 6), the detection statistic of the RAO detector under a uniform Gaussian background is substituted to obtain the detection statistic of the skew-symmetric RAO under a uniform background.

[0098] Preferably, in step 7), the obtained detection statistic of the skew-symmetric RAO-DP-TBD under the uniform background is used as the value function to perform dynamic programming iteration and optimization.

[0099] Preferably, in step 8), the target detection result is obtained by comparing the final accumulated maximum function with the threshold, and then the maximum function of the last frame is used to realize trajectory backtracking to estimate the trajectory of the target.

[0100] The technical solution provided by the present invention is further illustrated below with reference to embodiments.

[0101] Example

[0102] The present invention proposes a robust space-time adaptive tracking-before-detection method based on a skew-symmetric structure.

[0103] 1. Problem Modeling

[0104] Assume that the receiving array in the sonar system is a uniform linear array with N elements and d element spacing. The transmitted pulse width is T p , L distance units, signal carrier frequency is f c , echo wavelength λ=c / f c Sampling frequency f s , then the number of sampling points in each distance unit is M = T p f s The sonar system emits a single pulse signal to obtain MN×L-dimensional space-time data, which is called a frame of data. Emitting K single pulse signals means scanning the detection area K times to obtain K frames of echo data. When scanning the l-th distance unit for the kth time, MN sampling data can be obtained. These MN data constitute an observation vector z lk , now perform a binary hypothesis test on the observation vector:

[0105]

[0106] Among them, H0 and H1 represent the hypothesis of no target and target respectively; n lk ~CN(0,R k ) obeys zero mean and the covariance matrix is ​​R k Complex Gaussian distribution, α k is the amplitude of the target signal at the kth scan, l k is the distance unit with target for the kth scan, is the space-time steering vector, s tk (v dk ) is the spatial steering vector, s sk (v sk ) is the time domain steering vector.

[0107] To simplify the analysis, we take one frame of data from equation (1) for analysis. For the kth frame of data, the binary hypothesis test problem can be written as follows:

[0108]

[0109] Among them, z is the unit data to be detected; z l is the auxiliary unit data; α is the unknown signal amplitude, which is a definite parameter; v is the signal space-time steering vector; L represents the number of distance units; n and n l is an independent and identically distributed complex Gaussian reverberation vector with mean 0 and covariance matrix R.

[0110] Assuming that the number of elements N of the uniform linear array is an odd number and the phase center of the array is the middle element, the reverberation covariance matrix satisfies the skew symmetry property: it is conjugate symmetric about the main diagonal and symmetric about the secondary diagonal. l is a conjugate symmetric vector, construct a new vector:

[0111]

[0112]

[0113]

[0114]

[0115] Among them, z a 、z b 、z al and z bl is a complex Gaussian vector that satisfies independent and identical distribution, and L represents the number of distance units.

[0116] is an MN-dimensional permutation matrix, written as follows:

[0117]

[0118] but:

[0119] E[z a z a H ]=E[z b z b H ]=E[z al z al H ]=E[z bl z bl H ]=R / 2 (8)

[0120] The estimated sample covariance matrix based on skew symmetry is:

[0121]

[0122] Where L represents the number of distance units, (·) H Represents the conjugate transpose operation.

[0123] Based on the skew-symmetric structure of the reverberation matrix, a new vector is constructed according to (3) to (6), and the binary hypothesis test problem in formula (2) is transformed into an equivalent binary composite hypothesis test:

[0124]

[0125] Among them, na =(n+Jn * ) / 2,n b =(n-Jn * ) / 2,n al =(n l +Jn l * ) / 2,n bl =(n l -Jn l * ) / 2,α r =Re{α},α i =Im{α}, (·)* represents a conjugate operation, Re{·} represents taking the real part, and Im{·} represents taking the imaginary part.

[0126] 2. Detector Design

[0127] For the transformed hypothesis problem, based on the RAO detection criterion, a skew-symmetric RAO-DP-TBD method is proposed under uniform reverberation background, denoted as P-RAO-DP-TBD.

[0128] First, transform the detection unit data from the complex domain to the real domain:

[0129]

[0130]

[0131] The space-time steering vector is transformed from the complex domain to the real domain:

[0132] v r =Re{v}-Im{v} (13)

[0133] The reverberation covariance matrix is ​​transformed from the complex domain to the real domain:

[0134]

[0135] The detection statistic of the RAO detector under a uniform Gaussian background is:

[0136]

[0137] Substituting equations (11) to (14) into equation (15), we can obtain the detection statistic of skew-symmetric RAO under uniform background:

[0138]

[0139] Among them, Z r =[z erj z orj ].

[0140] The criteria for judging RAO-DP-TBD in a uniform environment are:

[0141]

[0142] Substituting equation (16) into (17), we obtain the skew-symmetric RAO-DP-TBD value function:

[0143]

[0144] (18) is iterated and optimized by dynamic programming. The final accumulated maximum function is compared with the threshold to obtain the target detection result. The maximum function of the last frame is then used to realize trajectory backtracking and estimate the trajectory of the target.

[0145] 3. Performance Analysis

[0146] The simulation parameters are: number of array elements N = 3, number of single pulse sampling points M = 20, space-time dimension MN = 60, and number of scans K = 6. The performance of the skew-symmetric RAO-DP-TBD algorithm is analyzed for both insufficient auxiliary data (the number of auxiliary data equals MN, i.e., the number of range cells L = MN + 1) and sufficient auxiliary data (L = 2MN + 1), and compared with the performance of the conventional RAO-DP-TBD algorithm.

[0147] Figure 2 and Figure 3 The comparison of detection probability and accurate tracking probability between the RAO-DP-TBD method based on skew-symmetric structure and the conventional RAO-DP-TBD method when auxiliary data is insufficient. Figure 4 and Figure 5 The comparison of detection probability and accurate tracking probability of P-RAO-DP-TBD method and conventional RAO-DP-TBD method when auxiliary data is sufficient is shown. Figure 2 and Figure 3 It can be seen that when the auxiliary data is insufficient, the conventional RAO-DP-TBD algorithm has become ineffective and cannot detect and track, while the P-RAO-DP-TBD algorithm still has good detection and tracking capabilities. Figure 4 and Figure 5 It can be seen that when the auxiliary data is sufficient, both the conventional RAO-DP-TBD algorithm and the P-RAO-DP-TBD algorithm can work normally, but the detection performance and tracking accuracy of the P-RAO-DP-TBD algorithm are better than those of the conventional RAO-DP-TBD algorithm.

[0148] From the above specific description of the present invention, it can be seen that the method of the present invention solves the problem of detection and tracking of low-speed weak targets in a uniform reverberation background, and the problem of poor detection and tracking performance of the conventional space-time adaptive detection-before-tracking algorithm caused by insufficient auxiliary sample data.

[0149] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention and are intended to be encompassed by the claims of the present invention.

Claims

1. A space-time adaptive tracking-before-detection method based on a skew-symmetric structure, the method comprising: Step S1. Processing the echo data collected by the sonar system and establishing a binary composite hypothesis testing model of the target to be detected based on the skew symmetry of the reverberation covariance matrix; Step S2. For the binary composite hypothesis testing model of the target to be detected, based on the RAO detection criterion, obtain the skew-symmetric RAO-DP-TBD value function; Step S3. Using the skew-symmetric RAO-DP-TBD value function to perform dynamic iterative optimization to achieve target detection and tracking; The step S2 specifically includes: Step S2-1. Transform the detection unit data from the complex domain to the real domain; Step S2-2. Transform the signal space-time steering vector from the complex domain to the real domain; Step S2-3. transforming the reverberation covariance matrix estimate from the complex domain to the real domain; Step S2-4. List the calculation formula of the detection statistic of the RAO detector under a uniform Gaussian background; Step S2-5. Substitute the data obtained in steps S2-1 to S2-3 into step S2-4 to obtain the detection statistic of the skew-symmetric RAO detector; Step S2-6. Substitute the detection statistic of the skew-symmetric RAO detector into the discrimination criterion of RAO-DP-TBD to obtain the skew-symmetric RAO-DP-TBD value function; In step S2-6, the discrimination criterion expression of RAO-DP-TBD is: Where D represents the range-Doppler position of the target in the range-Doppler plane, v(v k ) represents the space-time steering vector of the signal of the kth scan, z lk,k Indicates the distance unit l where there is a target in the kth scan k The observation vector, represents the k-th scan sample covariance matrix, z l,k represents the observation vector of the k-th scan of the l-th auxiliary range unit, η RAO-DP-TBD Indicates the decision threshold of RAO-DP-TBD.

2. The space-time adaptive tracking-before-detection method based on skew-symmetric structure according to claim 1, characterized in that: The step S1 specifically includes: Step S1-1. Acquire echo data collected by the sonar system; Step S1-2. Obtaining the corresponding observation vector based on each frame of echo data, and establishing a binary hypothesis testing model for the observation vector; Step S1-3. Construct a new vector based on the skew-symmetric characteristics of the reverberation covariance matrix; Step S1-4. Based on the constructed new vector, obtain the covariance matrix estimate and convert the binary hypothesis test model into an equivalent binary composite hypothesis test model.

3. The space-time adaptive tracking-before-detection method based on skew-symmetric structure according to claim 2, characterized in that: In step S1-2, obtaining a corresponding observation vector based on each frame of echo data specifically includes: in the k-th frame of echo data obtained in the k-th scan, there are L range units, and the data of each range unit includes MN sampling data, where M is the number of sampling points in each range unit, and N is the number of array elements; the MN sampling data constitute the observation vector corresponding to each range unit in the k-th frame of echo data; For each frame of data, the established binary hypothesis test model expression is: Among them, z is the unit data to be detected; z l is the data of the lth auxiliary unit; α is the unknown signal amplitude, which is a definite parameter; v is the signal space-time steering vector; L represents the number of distance units; n and n l is an independent and identically distributed complex Gaussian reverberation vector with mean 0 and covariance matrix R; H0 and H1 represent the no-target hypothesis and the targeted hypothesis, respectively.

4. The space-time adaptive tracking-before-detection method based on skew-symmetric structure according to claim 3, characterized in that: In step S1-3, the constructed new vector includes: Among them, z a and z b is a complex Gaussian vector that satisfies independent and identical distribution based on z, z al and z bl It is based on z l The constructed complex Gaussian vectors satisfy independent and identical distribution; the superscript * indicates the conjugate operation; J is an M×N dimensional permutation matrix that satisfies the following formula:

5. The space-time adaptive tracking-before-detection method based on skew-symmetric structure according to claim 4, characterized in that: In step S1-4, the covariance matrix estimate The expression is: Wherein, the superscript H represents the conjugate transpose operation; The expression of the binary composite hypothesis test model is: Among them, the vector n a 、n b 、n al and n bl The expressions are: n a =(n+Jn * ) / 2,n b =(n-Jn * ) / 2,n al =(n l +Jn l * ) / 2,n bl =(n l -Jn l * ) / 2; α r represents the real part of α, α i Represents the imaginary part of α, expressed as: α r =Re{α},α i =Im{α}, where Re{·} represents the real part, Im{·} represents the imaginary part; v represents the signal space-time steering vector.

6. The space-time adaptive tracking-before-detection method based on skew-symmetric structure according to claim 1, characterized in that: The expression of step S2-1 is: Among them, z erj 、z orj They represent the detection unit data in the echo data transformed from the complex domain to the real domain, and I represents the unit matrix; In step S2-2, the signal space-time steering vector v is transformed into the real domain r The expression is: v r =Re{v}-Im{v} In step S2-3, the reverberation covariance matrix estimate is transformed into the real domain The expression is: The detection statistic λ of the RAO detector under the uniform Gaussian background in step S2-4 RAO The calculation formula is: in, represents the sample covariance matrix, η RAO Indicates the RAO decision threshold; The detection statistic λ of the skew-symmetric RAO detector in step S2-5 is P-RAO The expression is: Among them, η P-RAO Represents the P-RAO decision threshold, real domain vector Z r =[z erj z orj ].

7. The space-time adaptive tracking-before-detection method based on skew-symmetric structure according to claim 1, characterized in that: The skew-symmetric RAO-DP-TBD value function expression obtained in step S2-6 is: in, Represents the estimated value of the sample covariance matrix of the k-th scan transformed into the real domain, Z rk represents the real domain observation vector of the k-th scan with the target distance unit, v r (v k ) represents the space-time steering vector of the signal transformed from the kth scan to the real domain, η P-RAO-DP-TBD Indicates the decision threshold of P-RAO-DP-TBD.

8. The space-time adaptive tracking-before-detection method based on skew-symmetric structure according to claim 1, characterized in that: The step S3 specifically includes: The value function of the skew-symmetric RAO-DP-TBD is dynamically programmed and optimized. The final accumulated maximum function is compared with the threshold to obtain the target detection result. The maximum function of the last frame is then used to realize trajectory backtracking, estimate the trajectory of the target, and realize target detection and tracking.

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