Two-dimensional concave hull feature target detection method based on bayesian estimation

Abstract

This invention relates to a two-dimensional concave hull feature target detection method based on Bayesian estimation, belonging to the field of radar signal processing and feature detection technology. The steps include: Step 1: Sea clutter echo feature extraction and Gaussianization; Step 2: Training of a two-dimensional concave hull classifier; Step 3: Echo feature extraction and Bayesian estimation; Step 4: Decision on the feature points to be detected. This invention aims to overcome the performance degradation of traditional feature detection methods with short accumulation times and multi-frame accumulation, while achieving feature detection with short accumulation times and multi-frame accumulation.

Description

Technical Field

[0001] This invention relates to a two-dimensional concave hull feature target detection method based on Bayesian estimation, belonging to the field of radar signal processing and feature detection technology. Background Technology

[0002] Detection of small targets at sea has always been an important and complex problem in the field of radar target detection. Because small targets typically have a small radar cross-section, their echo signals are very weak, making them difficult to detect under conditions of rapid pulse accumulation. Furthermore, in complex sea conditions, the echoes from waves and ripples cause long-tailed effects in statistical metrics and features, leading to aliasing between sea clutter and the target's statistical metrics and features. For these reasons, traditional target detection algorithms struggle to accurately detect small targets at sea while maintaining a low false alarm rate.

[0003] Feature detection is a common technique for detecting small targets at sea. Its key advantage lies in its ability to meticulously characterize the differences between sea clutter and small targets through pulse information accumulated over a long period. The traditional three-feature detection method extracts three features from the radar echoes over an accumulated time period, using these features to distinguish targets from sea clutter, and employs a convex hull detector for detection. This method performs well for small target detection when the accumulated time exceeds 0.512 seconds. With further research, time-frequency features, phase features, polarization features, and graph features have also been increasingly applied to small target detection. However, in radar scanning mode, the small number of pulses per frame and the significantly shorter accumulated time compared to the aforementioned algorithms lead to a substantial decrease in the detection probability of traditional methods. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the existing technology and propose a two-dimensional concave hull feature target detection method based on Bayesian estimation, which aims to identify sea surface targets when traditional target features are difficult to use effectively for target detection.

[0005] The two-dimensional concave hull feature target detection method based on Bayesian estimation of the present invention is characterized by including the following steps:

[0006] Step 1: Sea clutter echo feature extraction and Gaussianization

[0007] Collect clutter echo time series from multiple clutter units over a period of time, extract the relative average amplitude and mean phase difference of the clutter echoes, and perform Gaussianization preprocessing using Box-Cox transform as training information.

[0008] Step 2: Training the 2D concave hull classifier

[0009] Using the clutter feature points collected in step 1, a two-dimensional concave hull classifier is trained under false alarm rate conditions.

[0010] Step 3: Feature extraction and Bayesian estimation of the echo to be detected

[0011] In the detection phase, feature points are extracted and Gaussianized from the echo time series of the unit to be detected. Based on the feature input, the prior distribution of the features of the unit to be detected is obtained. Bayesian estimation is performed on the feature points of the unit to be detected in the current frame using the prior distribution. The estimation result is used as the feature points to be detected in the current frame to complete the supplementation of feature information.

[0012] Step 4: Determining the Feature Points to be Detected

[0013] The Bayesian-estimated feature points are input into a two-dimensional concave hull classifier. If a feature point is located within the concave hull classifier, it is classified as clutter; otherwise, it is classified as a target.

[0014] Preferably, the specific steps of step 1 are as follows:

[0015] When the radar collects sea clutter echo data from multiple range cells in a certain azimuth during scanning mode, the data appears as follows:

[0016] x i =[x i,1 ,x i,2 ,x i,3 ,...]; (13)

[0017] Where, x i Let x represent the echo sequence of the i-th clutter range cell. i,1 This represents the first frame echo sequence of the i-th clutter range cell, for x i Feature extraction is performed to obtain a feature sequence in the following form.

[0018]

[0019] Among them, f i,1 x represents i,1 The two-dimensional feature points obtained after feature extraction, RAA i,1 PDM represents the relative average amplitude of the first frame echo of the i-th distance cell. i,1 The feature extraction method for the first frame echo of the i-th distance cell is as follows:

[0020] The relative average amplitude is obtained by dividing the average radar echo of the target element by the average radar echo of the reference element. Since the target echo has strong energy, the relative average amplitude of the target element is generally greater than that of the clutter element. The calculation formulas are shown in Equations (15) and (16):

[0021]

[0022] In equation (15), x(n) and x represent radar echo sequences of length N for the range element to be detected. This represents the average amplitude of the echo sequence of the distance cell to be detected;

[0023]

[0024] In equation (16), x p This represents the radar echo sequence of the reference range element, where P represents the number of reference elements. RAA(x) represents the average amplitude of the echo sequence of the reference cell, and RAA(x) represents the relative average amplitude characteristic of the cell to be detected.

[0025] Phase characteristics refer to the average phase difference characteristics of the echo, which are calculated from the average phase difference of the echo during the coherent processing time. The radar echo of the target unit has a certain Doppler velocity, so the echo phase during the coherent processing time will change slowly with time. However, the echo energy of sea clutter is weak, the bandwidth is large, and the energy is not concentrated, so its phase change is very chaotic. Therefore, the average phase difference of the target echo is usually small and stable, while the phase difference of the clutter echo is usually large and unstable. The calculation method of the average phase difference of the echo is shown in Equations (17) and (18):

[0026] Δφ(n)=arg[x*(n)x(n+1)] (17)

[0027] In equation (17), x*(n) represents the conjugate form of the nth sampling point of the radar echo sequence, and arg[a] represents the calculation of the complex phase a.

[0028]

[0029] In equation (18), x represents the radar echo sequence of the range cell to be detected with a length of N, and PDM(x) represents the average phase difference of the echo of the range cell to be detected.

[0030] The application background of this invention is Gaussian background, which requires prior Gaussianization of the data to ensure that subsequent iterations of the prior distribution can proceed stably.

[0031] The Box-Cox transformation can be performed using the following formula:

[0032]

[0033] In the formula, f is the feature to be Gaussianized, λ is the Gaussianization coefficient, and f g This refers to the Gaussianization characteristic.

[0034] This step makes the data more readily accepted by the iterator without altering the relationship between feature sizes, reduces the impact of extreme data on the iterator, and allows the iteration to proceed more smoothly. The Gaussianized two-dimensional clutter feature point set is denoted as Ω.

[0035] Preferably, the specific steps of step 2 are as follows:

[0036] The formation of the concave hull classifier can be divided into steps (1) to (7).

[0037] (1) Normalize the N two-dimensional feature point set Ω and generate a two-dimensional convex hull to obtain the two-dimensional convex hull vertex set V. Select vertices that meet the requirements to form the vertex set V to be deleted. i Among them, V i Points inside (x) i ,y i )satisfy: It refers to the mean of RAA and PDM among N two-dimensional feature points.

[0038] (2) From V i Select the distance from the feature center point The farthest point v i Remove it from the training set Ω. Also, i = i + 1.

[0039] (3) Based on the sample point set Ω obtained in steps (1) and (2), use the two-dimensional convex hull generation algorithm to obtain the two-dimensional convex hull and vertex set V.

[0040] (4) Filter out those that meet the conditions The set of edges L consisting of vertices f = {L1, L2, ...}, and select the longest edge L. max And the corresponding two vertices v1 and v2.

[0041] (5) Traverse all sample points and find the one that matches L. max The sample point s with the smallest Euclidean distance from the midpoint will be determined by L. max Disassemble into two connected edges L m1 and L m2 L m1 L is obtained by connecting v1 and s. m2 It is obtained by connecting s and v2. Let L be the denoted L. o ={L o1 ,L o2}

[0042] (6) Statistically analyze the sample point set Ω outside the decision region after internal partitioning. out Let s be the j-th external complement point. oi (x j ,y j). Note L o The number of edges contained is L on .

[0043] (7) For the j-th external complement, the point to be complemented is s. oi (x j ,y j ), requires traversing L o For the z-th traversal, extract L o The z-th edge L oz The two vertices v z1 (x z1 ,y z1 ) and v z2 (x z2 ,y z2 ). Calculate the dot product r = (x j -x z1 ,y j -y z1 )·(x z2 -x j ,y z2 -y j If r > 0, then continue iterating through L. o If r < 0, then L z Disassembled into s oi (x j ,y j ) and v z1 (x z1 ,y z1 L composed of ) oz1 and by s oi (x j ,y j ) and v z2 (x z2 ,y z2 L composed of ) oz2 And let L o ={L o1 ,L o2 ,..,L o(z-1) ,L oz1 ,L oz2 ,L o(z+1) ,...},Point s oi (x j ,y j Once the internal complement is complete, repeat step (7) to perform internal complement for the i=i+1th point.

[0044] (8) Let the set of edges of the outer surface of the concave hull before external embellishment be L = {L1, L2, ..., L...} o ,...}, which serve as the final decision boundary output for the concave hull.

[0045] Preferably, step 3) involves feature extraction and Bayesian estimation of the echo to be detected, and the specific steps are as follows:

[0046] After feature extraction and Gaussianization of the echo sequence to be detected in step 1), Bayesian estimation is used to supplement the extracted features with information.

[0047] Taking relative average amplitude as an example, let the relative average amplitude feature sequence of the Gaussianized unit to be detected be...

[0048] f ci =[f ci,1 ,f ci,2 ,f ci,3 ,...]; (20)

[0049] In the formula, f ci f represents the relative average amplitude feature sequence of the i-th unit to be detected. ci,1 This represents the first relative average amplitude feature of the i-th unit to be detected.

[0050] The formation and Bayesian estimation of the prior distribution based on a single feature can be subdivided into steps (1) to (4):

[0051] (1) Apply a sliding window to the feature sequence of the unit to be detected. The sliding window step size is 1, the window length is N, the feature sequence length of each unit to be detected is M, and the mean m of the test statistic within the window at the current time is... i Sum of variance v i Perform unbiased estimation.

[0052]

[0053] In the formula, f ci,(n) This represents the nth relative average amplitude feature within the sliding window.

[0054] (2) Secondly, using the mean and variance obtained from the unbiased estimation, combined with the prior distribution, we obtain the Bayesian estimate a of the mean of the test statistic within the current time window. e This is the mean of the posterior probability density function. Similarly, the variance of the posterior probability density function can also be calculated.

[0055]

[0056] In the formula, N represents the length of the sliding window, in meters. i Let v represent the unbiased mean of the features inside the i-th sliding window. i 2 μ represents the variance of the features within the window during the i-th sliding window operation. a σ represents the mean parameter of the prior distribution. a 2This represents the variance parameter of the prior distribution.

[0057] (3) Based on the Bayesian estimates obtained from the current sliding window, perform sequential estimation of the mean and variance of the Bayesian estimates, and update the mean μ of the Bayesian estimates. a and variance σ a 2 .

[0058]

[0059] In the formula, k refers to the number of sliding windows, a e (k+1) represents the Bayesian estimate obtained in the (k+1)th sliding window operation. This represents the sequential mean of the Bayesian estimates. This represents the sequential estimate variance of the Bayesian estimate.

[0060] (4) Based on the Bayesian estimate of the current sliding window, the mean and variance of the Bayesian estimate obtained by sequential estimation, and the variance of the current frame, calculate the mean μ of the prior distribution. a and variance σ a 2 Make corrections. The correction method is as follows.

[0061]

[0062] In the formula, μ a (k) represents the mean of the prior distribution at the k-th sliding window. Let v represent the variance of the prior distribution at the k-th sliding window. i (k+1) represents the variance of the feature samples within the window at the (k+1)th sliding window, and N refers to the window length. The relative average amplitude and mean echo phase difference of the unit to be detected are processed through steps (1) to (4), respectively.

[0063] The prior distribution of the corresponding features can be formed and Bayesian estimation can be completed, and the feature points f = [f1, f2] after two-dimensional Bayesian estimation can be obtained. The next step is to input the feature points f = [f1, f2] into the concave hull classifier trained in step 2 for classification.

[0064] Preferably, in step 4), a two-dimensional concave hull classifier is used to discriminate the Bayesian-optimized feature vectors to obtain the final decision result.

[0065] In the detection phase, let the feature points to be detected be f = [f1, f2], and the vertices forming the concave hull be arranged counterclockwise as Ω. v ={(f v1(1) ,f v1(2) ),(f v2(1) ,f v2(2) ),...,(f vn(1),f vn(2) The following steps can be used to determine whether a feature point f = [f1, f2] is within the concave hull decision region Ω:

[0066] Step (1): Let j = n, t = 0.

[0067] Step (2): Let i = 1:n, let x i =f vi(1) y i =f vi(1) x j =f vi(1) y j =f vi(1) , calculate (((y) i -f2)! =(y j -f2))&((f1<(x j -x i ))*(f2-y i ) / (y j -y i )+x i If the result is true, then t = ~t. Let j = i. This step is repeated until i = n.

[0068] Step (3): If t = 0, then the feature point to be detected is not in the concave hull decision region, and the sample to be detected is judged as a clutter sample; otherwise, the sample point to be detected is outside the concave hull decision region, and the sample to be detected is judged as a target sample.

[0069] Compared with existing technologies, the two-dimensional concave hull feature target detection method based on Bayesian estimation of the present invention has the following advantages:

[0070] (1) The prior distribution of historical frames is used to support the feature estimation of the current frame, which improves the ability of features to distinguish targets and clutter and solves the problem that traditional target features have poor detection capabilities in a short cumulative time.

[0071] (2) An improved concave hull classifier is used to classify the feature points of the echo to be detected. Compared with the traditional convex hull classifier, it is a better classifier and can obtain a higher target detection probability under the condition that the false alarm rate remains unchanged. Attached Figure Description

[0072] Figure 1 This is a flowchart of the two-dimensional feature target detection method using prior information according to the present invention;

[0073] Figure 2 This is a schematic diagram of the concave bulge detection method of the present invention. Detailed Implementation

[0074] To better understand and implement this invention, specific embodiments are provided below to illustrate the invention in detail. The sea surface target detection method of the invention is as follows:

[0075] 1) Feature extraction and Gaussianization of sea clutter echoes

[0076] When radar collects sea clutter echo data from multiple range cells at a certain azimuth in scanning mode, it can be represented in the following form:

[0077] x i =[x i,1 ,x i,2 ,x i,3 ,...]; (25)

[0078] Where, x i Let x represent the echo sequence of the i-th clutter range cell. i,1 This represents the first frame echo sequence of the i-th clutter range cell. For x... i Feature extraction yields a feature sequence in the following form.

[0079]

[0080] Among them, f i,1 x represents i,1 The two-dimensional feature points obtained after feature extraction, RAA i,1 PDM represents the relative average amplitude of the first frame echo of the i-th distance cell. i,1 This represents the average phase difference of the echo in the first frame of the i-th distance cell. The feature extraction method is as follows:

[0081] The relative average amplitude is obtained by dividing the average radar echo of the target element by the average radar echo of the reference element. Target echo energy is strong, therefore the relative average amplitude of the target element is generally greater than that of the clutter element. The calculation formulas are shown in equations (27) and (28).

[0082]

[0083] In equation (27), x(n) and x represent radar echo sequences of length N for the range element to be detected. This represents the average amplitude of the echo sequence of the distance cell to be detected.

[0084]

[0085] In equation (28), x p This represents the radar echo sequence of the reference range element, where P represents the number of reference elements. RAA(x) represents the average amplitude of the echo sequence of the reference cell, and RAA(x) represents the relative average amplitude characteristic of the cell to be detected.

[0086] Phase characteristics refer to the average phase difference characteristics of the echo, which are calculated from the average phase difference of the echo during the coherent processing time. The radar echo of the target unit has a certain Doppler velocity, so the echo phase will change slowly over time during the coherent processing time. However, the echo energy of sea clutter is weak, the bandwidth is large, and the energy is not concentrated, so its phase change is very chaotic. Therefore, the average phase difference of the target echo is usually small and stable, while the phase difference of the clutter echo is usually large and unstable. The calculation method of the average phase difference of the echo is shown in Equations (29) and (30).

[0087] Δφ(n)=arg[x*(n)x(n+1)] (29)

[0088] In equation (29), x*(n) represents the conjugate form of the nth sampling point of the radar echo sequence, and arg[a] represents the calculation of the complex phase a.

[0089]

[0090] In equation (30), x represents the radar echo sequence of the range cell to be detected with a length of N, and PDM(x) represents the average phase difference of the echo of the range cell to be detected.

[0091] The method proposed in this patent is applied to a Gaussian background, requiring the data to be Gaussianized first to ensure that subsequent iterations of the prior distribution can proceed stably.

[0092] The Box-Cox transformation can be performed using the following formula.

[0093]

[0094] In the formula, f is the feature to be Gaussianized, λ is the Gaussianization coefficient, and f g This refers to the Gaussianization characteristic.

[0095] This step makes the data more readily accepted by the iterator without altering the relationship between feature sizes, reduces the impact of extreme data on the iterator, allows the iteration to proceed more smoothly, and reduces estimation errors. The Gaussianized two-dimensional clutter feature point set is denoted as Ω.

[0096] 2) Training of the two-dimensional concave hull classifier

[0097] The formation of the concave hull classifier can be divided into steps (1) to (7).

[0098] (1) Normalize the N two-dimensional feature point set Ω and generate a two-dimensional convex hull to obtain the two-dimensional convex hull vertex set V. Select vertices that meet the requirements to form the vertex set V to be deleted. i Among them, V i Points inside (x) i ,yi )satisfy: It refers to the mean of RAA and PDM among N two-dimensional feature points.

[0099] (2) From V i Select the distance from the feature center point The farthest point v i Remove it from the training set Ω. Also, i = i + 1.

[0100] (3) Based on the sample point set Ω obtained in steps (1) and (2), use the two-dimensional convex hull generation algorithm to obtain the two-dimensional convex hull and vertex set V.

[0101] (4) Filter out those that meet the conditions The set of edges L consisting of vertices f = {L1, L2, ...}, and select the longest edge L. max And the corresponding two vertices v1 and v2.

[0102] (5) Traverse all sample points and find the one that matches L. max The sample point s with the smallest Euclidean distance from the midpoint will be determined by L. max Disassemble into two connected edges L m1 and L m2 L m1 L is obtained by connecting v1 and s. m2 It is obtained by connecting s and v2. Let L be the denoted L. o ={L o1 ,L o2}

[0103] (6) Statistically analyze the sample point set Ω outside the decision region after internal partitioning. out Let s be the j-th external complement point. oi (x j ,y j ). Note L o The number of edges contained is L on .

[0104] (7) For the j-th external complement, the point to be complemented is s. oi (x j ,y j ), requires traversing L o For the z-th traversal, extract L o The z-th edge L oz The two vertices v z1 (x z1 ,y z1 ) and v z2 (x z2 ,y z2 ). Calculate the dot product r = (x j-x z1 ,y j -y z1 )·(x z2 -x j ,y z2 -y j If r > 0, then continue iterating through L. o If r < 0, then L z Disassembled into s oi (x j ,y j ) and v z1 (x z1 ,y z1 L composed of ) oz1 and by s oi (x j ,y j ) and v z2 (x z2 ,y z2 L composed of ) oz2 And let L o ={L o1 ,L o2 ,..,L o(z-1) ,L oz1 ,L oz2 ,L o(z+1) ,...},Point s oi (x j ,y j Once the internal complement is complete, repeat step (7) to perform internal complement for the i=i+1th point.

[0105] (8) Let the set of edges of the outer surface of the concave hull before external embellishment be L = {L1, L2, ..., L...} o ,...}, as the final decision boundary output of the concave hull 3) Perform feature extraction and Bayesian estimation on the echo to be detected.

[0106] After feature extraction and Gaussianization of the echo sequence to be detected in step 1), Bayesian estimation is used to supplement the extracted features with information.

[0107] Taking relative average amplitude as an example, let the relative average amplitude feature sequence of the Gaussianized unit to be detected be...

[0108] f ci =[f ci,1 ,f ci,2 ,f ci,3 ,...]; (32)

[0109] In the formula, f ci f represents the relative average amplitude feature sequence of the i-th unit to be detected. ci,1 This represents the first relative average amplitude feature of the i-th unit to be detected.

[0110] The formation and Bayesian estimation of the prior distribution based on a single feature can be subdivided into steps (1) to (4).

[0111] (1) Apply a sliding window to the feature sequence of the unit to be detected. The sliding window step size is 1, the window length is N, the feature sequence length of each unit to be detected is M, and the mean m of the test statistic within the window at the current time is... i Sum of variance v i Perform unbiased estimation.

[0112]

[0113] In the formula, f ci,(n) This represents the nth relative average amplitude feature within the sliding window.

[0114] (2) Secondly, using the mean and variance obtained from the unbiased estimation, combined with the prior distribution, we obtain the Bayesian estimate a of the mean of the test statistic within the current time window. e This is the mean of the posterior probability density function. Similarly, the variance of the posterior probability density function can also be calculated.

[0115]

[0116] In the formula, N represents the length of the sliding window, in meters. i Let v represent the unbiased mean of the features inside the i-th sliding window. i 2 μ represents the variance of the features within the window during the i-th sliding window operation. a σ represents the mean parameter of the prior distribution. a 2 This represents the variance parameter of the prior distribution.

[0117] (3) Based on the Bayesian estimates obtained from the current sliding window, perform sequential estimation of the mean and variance of the Bayesian estimates, and update the mean μ of the Bayesian estimates. a and variance σ a 2 .

[0118]

[0119] In the formula, k refers to the number of sliding windows, a e (k+1) represents the Bayesian estimate obtained in the (k+1)th sliding window operation. This represents the sequential mean of the Bayesian estimates. This represents the sequential estimate variance of the Bayesian estimate.

[0120] (4) Based on the Bayesian estimate of the current sliding window, the mean and variance of the Bayesian estimate obtained by sequential estimation, and the variance of the current frame, calculate the mean μ of the prior distribution. a and variance σ a 2 Make corrections. The correction method is as follows.

[0121]

[0122] In the formula, μ a (k) represents the mean of the prior distribution at the k-th sliding window. Let v represent the variance of the prior distribution at the k-th sliding window. i (k+1) represents the variance of the feature samples within the window during the (k+1)th sliding window operation, and N refers to the window length.

[0123] By performing steps (1) to (4) on the relative average amplitude and mean echo phase difference of the unit to be detected, the prior distribution of the corresponding features can be formed and Bayesian estimation can be completed, and the feature points f = [f1, f2] after two-dimensional Bayesian estimation can be obtained. The next step is to input the feature points f = [f1, f2] into the concave hull classifier trained in step 2 for classification.

[0124] 4) Decision on the feature points to be detected

[0125] In the detection phase, let the feature points to be detected be f = [f1, f2], and the vertices forming the concave hull be arranged counterclockwise as Ω. v ={(f v1(1) ,f v1(2) ),(f v2(1) ,f v2(2) ),...,(f vn(1) ,f vn(2) The following steps can be used to determine whether a feature point f = [f1, f2] is within the concave hull decision region Ω:

[0126] Step (1): Let j = n, t = 0.

[0127] Step (2): Let i = 1:n, let x i =f vi(1) y i =f vi(1) x j =f vi(1) y j =f vi(1) , calculate (((y) i -f2)! =(y j -f2))&((f1<(x j -x i ))*(f2-y i ) / (yj -y i )+x i If the result is true, then t = ~t. Let j = i. This step is repeated until i = n.

[0128] Step (3): If t = 0, then the feature point to be detected is not in the concave hull decision region, and the sample to be detected is judged as a clutter sample; otherwise, the sample point to be detected is outside the concave hull decision region, and the sample to be detected is judged as a target sample.

Claims

1. A two-dimensional concave hull feature target detection method based on Bayesian estimation, characterized in that... Includes the following steps: Step 1: Sea clutter echo feature extraction and Gaussianization Collect clutter echo time series of multiple clutter units over a period of time, extract the relative average amplitude and the average phase difference of the clutter echoes, and perform Gaussianization preprocessing using Box-Cox transform as training information. The relative average amplitude is obtained by dividing the average radar echo of the unit to be detected by the average radar echo of the reference unit. Step 2: Training the 2D concave hull classifier Using the clutter feature points collected in step 1, a two-dimensional concave hull classifier is trained under the false alarm rate condition; Step 3: Feature extraction and Bayesian estimation of the echo to be detected In the detection phase, feature points are extracted and Gaussianized from the echo time series of the unit to be detected. Based on the feature input, the feature prior distribution of the unit to be detected is obtained. Bayesian estimation is performed on the feature points of the unit to be detected in the current frame using the prior distribution. The estimation result is used as the feature points to be detected in the current frame to complete the supplementation of feature information. Step 4: Determination of the feature points to be detected The Bayesian-estimated feature points are input into a two-dimensional concave hull classifier. If a feature point is located within the concave hull classifier, it is classified as clutter; otherwise, it is classified as a target.

2. The two-dimensional concave hull feature target detection method based on Bayesian estimation according to claim 1, characterized in that... The specific steps of step 1 are as follows: When the radar collects sea clutter echo data from multiple range cells in a certain azimuth during scanning mode, the data appears as follows: x i =[x i,1 ,x i,2 ,x i,3 ,...]; (1) Where, x i Let x represent the echo sequence of the i-th clutter range cell. i,1 This represents the first frame echo sequence of the i-th clutter range cell, for x i Feature extraction is performed to obtain a feature sequence in the following form; Among them, f i,1 x represents i,1 The two-dimensional feature points obtained after feature extraction, RAA i,1 PDM represents the relative average amplitude of the first frame echo of the i-th distance cell. i,1 The feature extraction method for the first frame echo of the i-th distance cell is as follows: The relative average amplitude is obtained by dividing the average radar echo of the target element by the average radar echo of the reference element. Since the target echo has strong energy, the relative average amplitude of the target element is generally greater than that of the clutter element. The calculation formulas are shown in equations (3) and (4): In equation (3), x(n) and x represent radar echo sequences of length N for the range element to be detected. This represents the average amplitude of the echo sequence of the distance cell to be detected; In equation (4), x p This represents the radar echo sequence of the reference range element, where P represents the number of reference elements. RAA(x) represents the average amplitude of the echo sequence of the reference cell, and RAA(x) represents the relative average amplitude characteristic of the cell to be detected. Phase characteristics refer to the characteristics of the average phase difference of the echo. The calculation method of the average phase difference of the echo is shown in Equations (5) and (6): Δφ(n)=arg[x*(n)x(n+1)] (5) In equation (5), x*(n) represents the conjugate form of the nth sampling point of the radar echo sequence, and arg[a] represents the calculation of the complex phase a; In equation (6), x represents the radar echo sequence of the range cell to be detected with a length of N, and PDM(x) represents the average phase difference of the echo of the range cell to be detected. The Box-Cox transformation is performed according to the following formula: In the formula, f is the feature to be Gaussianized, λ is the Gaussianization coefficient, and f g The Gaussianization feature; the set of two-dimensional clutter feature points after Gaussianization is denoted as Ω.

3. The two-dimensional concave hull feature target detection method based on Bayesian estimation according to claim 1, characterized in that... The specific steps of step 2 are as follows: The formation of the concave hull classifier is divided into steps (1) to (7); (1) Normalize the N two-dimensional feature point set Ω and generate a two-dimensional convex hull to obtain the two-dimensional convex hull vertex set V. Select vertices that meet the requirements to form the vertex set V to be deleted. i V i Points inside (x) i ,y i )satisfy: The mean of RAA and PDM among N two-dimensional feature points; (2) From V i Select the distance from the feature center point The farthest point v i Remove it from the training set Ω, and set i = i + 1; (3) Based on the sample point set Ω obtained in steps (1) and (2), use the two-dimensional convex hull generation algorithm to obtain the two-dimensional convex hull and vertex set V; (4) Filter out those that meet the conditions The set of edges L consisting of vertices f = {L1, L2, ...}, and select the longest edge L. max and the corresponding two vertices v1 and v2; (5) Traverse all sample points and find the one that matches L. max The sample point s with the smallest Euclidean distance from the midpoint will be determined by L. max Disassemble into two connected edges L m1 and L m2 L m1 L is obtained by connecting v1 and s. m2 It is obtained by connecting s and v2, denoted as L. o ={L o1 ,L o2 }; (6) Statistically analyze the sample point set Ω outside the decision region after internal partitioning. out Let s be the j-th external complement point. oi (x j ,y j ), let L o The number of edges contained is L on ; (7) For the j-th external complement, the point to be complemented is s. oi (x j ,y j ), requires traversing L o For the z-th traversal, extract L o The z-th edge L oz The two vertices v z1 (x z1 ,y z1 ) and v z2 (x z2 ,y z2 ), calculate the dot product r = (x j -x z1 ,y j -y z1 )·(x z2 -x j ,y z2 -y j If r > 0, then continue iterating through L. o If r < 0, then L z Disassembled into s oi (x j ,y j ) and v z1 (x z1 ,y z1 L composed of ) oz1 and by s oi (x j ,y j ) and v z2 (x z2 ,y z2 L composed of ) oz2 And let L o ={L o1 ,L o2 ,..,L o(z-1) ,L oz1 ,L oz2 ,L o(z+1) ,...},Point s oi (x j ,y j After the internal complement is completed, repeat (7) to perform internal complement for the i=i+1th point; (8) Let the set of edges of the outer surface of the concave hull before external embellishment be L = {L1, L2, ..., L...} o ,...}, which serve as the final decision boundary output for the concave hull.

4. The two-dimensional concave hull feature target detection method based on Bayesian estimation according to claim 1, characterized in that, The specific steps of step 3 are as follows: After feature extraction and Gaussianization of the echo sequence to be detected in step 1, Bayesian estimation is used to supplement the extracted features with information. For the relative average amplitude, let the Gaussianized relative average amplitude feature sequence of the target unit be... f ci =[f ci,1 ,f ci,2 ,f ci,3 ,...]; (8) In the formula, f ci f represents the relative average amplitude feature sequence of the i-th unit to be detected. ci,1 This represents the first relative average amplitude feature of the i-th unit to be detected; The formation and Bayesian estimation of the prior distribution based on a single feature can be subdivided into steps (1) to (4): (1) Apply a sliding window to the feature sequence of the unit to be detected. The sliding window step size is 1, the window length is N, the feature sequence length of each unit to be detected is M, and the mean m of the test statistic within the window at the current time is... i and variance v i Perform unbiased estimation; In the formula, f ci,(n) This represents the nth relative average amplitude feature within the sliding window; (2) Secondly, using the mean and variance obtained from the unbiased estimation, combined with the prior distribution, we obtain the Bayesian estimate a of the mean of the test statistic within the current time window. e This is the mean of the posterior probability density function. Similarly, the variance of the posterior probability density function can also be calculated. In the formula, N represents the length of the sliding window, in meters. i Let v represent the unbiased mean of the features inside the i-th sliding window. i 2 μ represents the variance of the features within the window during the i-th sliding window operation. a σ represents the mean parameter of the prior distribution. a 2 The variance parameter represents the prior distribution; (3) Based on the Bayesian estimates obtained from the current sliding window, perform sequential estimation of the mean and variance of the Bayesian estimates, and update the mean μ of the Bayesian estimates. a and variance σ a 2 : In the formula, k refers to the number of sliding windows, a e (k+1) represents the Bayesian estimate obtained in the (k+1)th sliding window operation. This represents the sequential mean of the Bayesian estimates. This represents the sequential variance of the Bayesian estimates; (4) Based on the Bayesian estimate of the current sliding window, the mean and variance of the Bayesian estimate obtained by sequential estimation, and the variance of the current frame, calculate the mean μ of the prior distribution. a and variance σ a 2 The correction method is as follows: In the formula, μ a (k) represents the mean of the prior distribution at the k-th sliding window. Let v represent the variance of the prior distribution at the k-th sliding window. i (k+1) represents the variance of the feature samples within the window at the (k+1)th sliding window, and N refers to the window length. By performing steps (1) to (4) on the relative average amplitude and the mean echo phase difference of the unit to be detected, the prior distribution of the corresponding features can be formed and Bayesian estimation can be completed, and the feature points f = [f1, f2] after two-dimensional Bayesian estimation can be obtained. The next step is to input the feature points f = [f1, f2] into the concave hull classifier trained in step 2 for classification.

5. The two-dimensional concave hull feature target detection method based on Bayesian estimation according to claim 1, characterized in that, Step 4 uses a two-dimensional concave hull classifier to discriminate the Bayesian-optimized feature vectors, obtaining the final decision result: During the detection phase, let the feature points to be detected be f = [f1, f2], and the vertices forming the concave hull be arranged counterclockwise as Ω. v ={(f v1(1) ,f v1(2) ),(f v2(1) ,f v2(2) ),...,(f vn(1) ,f vn(2) The following steps can be used to determine whether a feature point f = [f1, f2] is within the concave hull decision region Ω: Step (1): Let j = n, t = 0; Step (2): Let i = 1:n, let x i =f vi(1) y i =f vi(1) x j =f vi(1) y j =f vi(1) , calculate (((y) i -f2)! =(y j -f2))&((f1<(x j -x i ))*(f2-y i ) / (y j -y i )+x i If the result is true, then t = ~t, let j = i, and repeat this step until i = n; Step (3): If t = 0, then the feature point to be detected is not in the concave hull decision region, and the sample to be detected is judged as a clutter sample; otherwise, the sample point to be detected is outside the concave hull decision region, and the sample to be detected is judged as a target sample.

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