Two-dimensional concave envelope feature target detection method based on Bayesian estimation

Abstract

The invention relates to a two-dimensional concave envelope feature target detection method based on Bayesian estimation, and belongs to the technical field of radar signal processing and feature detection. The method comprises the following steps: step 1, sea clutter echo feature extraction and Gaussian processing; 2, training a two-dimensional concave packet classifier; step 3, feature extraction and Bayesian estimation of echoes to be detected; and 4, judging the to-be-detected feature points. The invention aims to make up for the defect that the detection performance of the traditional short-accumulation-time feature detection method is reduced under the multi-frame accumulation feature detection method in the short accumulation time.

Description

Technical Field

[0001] The invention relates to a two-dimensional concave hull feature target detection method based on Bayesian estimation, and belongs to the technical field of radar signal processing and feature detection. Background Art

[0002] Small target detection at sea has always been an important and complex problem in the field of radar target detection. Since small targets usually have a small radar scattering cross-section, the echo signal is very weak, making it difficult to detect under the condition of accumulating pulses in a short time. In addition, when the sea conditions are complex, the echoes of waves and ripples will cause a long-tail effect in statistics and features, which will cause the statistics and features of sea clutter to alias with those of the target. For these reasons, it is difficult for traditional target detection algorithms to accurately detect small targets at sea while maintaining a low false alarm rate.

[0003] Feature detection is a common technology for detecting small targets at sea. Its key advantage is that it can carefully depict the difference between sea clutter and small targets through pulse information accumulated over a long period of time. The traditional three-feature detection method extracts three features from the time domain and frequency domain by accumulating radar echoes over time, uses these features to distinguish targets from sea clutter, and uses a convex hull detector for detection. This method works better for small target detection when the accumulation time exceeds 0.512 seconds. With the development of research, time-frequency features, phase features, polarization features, and image features are also gradually applied to small target detection. However, in radar scanning mode, due to the small number of pulses per frame of data, the accumulation time is much smaller than the application range of the above algorithms, resulting in a significant decrease in the detection probability of traditional methods. Summary of the invention

[0004] The purpose of the present invention is to solve the shortcomings of the above-mentioned prior art 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 effectively perform target detection.

[0005] The two-dimensional concave hull feature target detection method based on Bayesian estimation of the present invention is special in that it comprises the following steps:

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

[0007] The clutter echo time series of multiple clutter units within a period of time are collected, the relative average amplitude of the clutter echo and the mean of the echo phase difference are extracted, and Gaussian preprocessing is performed using Box-Cox transformation as training information.

[0008] Step 2: Training of 2D Concave Hull Classifier

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

[0010] Step 3: Extraction of echo features to be detected and Bayesian estimation of features

[0011] In the detection stage, 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. The feature points of the unit to be detected in the current frame are Bayesian estimated using the prior distribution. The estimated results are used as the feature points to be detected in the current frame to complete the feature information supplement.

[0012] Step 4: Determination of feature points to be detected

[0013] The feature points after Bayesian estimation are input into the two-dimensional concave hull classifier. If the feature point is located in the concave hull classifier, it is judged as clutter, otherwise it is judged as a target.

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

[0015] The radar collects sea clutter echo data of multiple range units in a certain direction in scanning mode, which is shown in the following form:

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

[0017] Among them, x i represents the echo sequence of the ith clutter range unit, x i,1 represents the first frame echo sequence of the ith clutter range unit, for x i Perform feature extraction and obtain the feature sequence in the following form.

[0018]

[0019] Among them, f i,1 Represents x 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 ith range unit. i,1 It represents the average phase difference of the first frame echo of the i-th range unit. The feature extraction method is as follows:

[0020] 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. The target echo has strong energy, so the relative average amplitude of the target unit is generally greater than that of the clutter unit. The calculation formulas are shown in equations (3) and (4):

[0021]

[0022] In formula (3), x(n), x represents the radar echo sequence of the distance unit to be detected with a length of N. The average amplitude of the echo sequence representing the range unit to be detected;

[0023]

[0024] In formula (4), x p represents the reference range unit radar echo sequence, P represents the number of reference units, RAA(x) represents the average amplitude of the echo sequence of the reference unit, and RAA(x) represents the relative average amplitude characteristic of the unit to be detected.

[0025] Phase characteristics refer to the characteristics of the average phase difference of the echo, which is calculated by the mean value of the echo phase difference within the coherent processing time. The radar echo of the target unit has a certain Doppler speed, so the echo phase within the coherent processing time will change slowly with the time law. 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 mean value of the echo phase difference of the target echo is usually small and stable, while the echo phase difference of the clutter is usually large and unstable. The calculation method of the average phase difference of the echo is shown in formula (5) and formula (6):

[0026] Δφ(n)=arg[x*(n)x(n+1)] (17)

[0027] In formula (5), x*(n) represents the conjugate form of the nth sampling point of the radar echo sequence, and arg[a] represents the phase of the complex number a.

[0028]

[0029] In formula (6), x represents the radar echo sequence of the range unit to be detected with a length of N, and PDM(x) represents the average phase difference of the echo of the unit to be detected;

[0030] The application background of the present invention is a Gaussian background, and the data needs to be Gaussianized first to ensure that subsequent iterations of the prior distribution can be carried out stably.

[0031] The Box-cox transformation can be performed as follows:

[0032]

[0033] In the formula, f is the feature to be Gaussianized, λ is the Gaussianization coefficient, and f g Refers to Gaussian features.

[0034] This step can make the data easier to be accepted by the iterator without changing the feature size relationship, reduce the impact of extreme data on the iterator, and allow 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:

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

[0037] (1) Normalize the N two-dimensional feature point sets Ω and generate a two-dimensional convex hull to obtain a two-dimensional convex hull vertex set V. Filter out the vertices that meet the requirements to form a vertex set V to be deleted. i . Where V i The point inside (x i ,y i )satisfy: Refers to the mean of RAA and PDM in N two-dimensional feature points.

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

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

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

[0041] (5) Traverse all sample points and find max The sample point s with the smallest midpoint Euclidean distance will be represented by L max Split into two connected edges L m1 and L m2 . Where L m1 By connecting v1 and s, L m2 It is obtained by connecting s and v2. o ={L o1 ,L o2}.

[0042] (6) Statistical analysis of the sample point set Ω outside the judgment area out . Let the jth external complement point be s oi (x j ,y j). o The number of edges included is L on .

[0043] (7) For the jth external filling, the external filling point is s oi (x j ,y j ), you need to traverse L o , for the zth traversal, extract L o The zth 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, continue to traverse L o ; If r<0, then L z Disassembled into s oi (x j ,y j ) and v z1 (x z1 ,y z1 ) oz1 and by s oi (x j ,y j ) and v z2 (x z2 ,y z2 ) 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 ) is completed, and (7) is repeated to perform the internal filling of the i=i+1th point.

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

[0045] Preferably, the specific steps of step 3) for performing feature extraction and Bayesian estimation on the echo to be detected are:

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

[0047] Taking the 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 represents the relative average amplitude feature sequence of the i-th unit to be detected, f ci,1 Represents the first relative average amplitude feature of the i-th unit to be detected.

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

[0051] (1) Slide the window of the feature sequence of the unit to be detected, the step size of the sliding window is 1, the window length is N, the length of the feature sequence of each unit to be detected is M, and the mean value m of the test statistic in the window at the current moment is i and variance v i Make an unbiased estimate.

[0052]

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

[0054] (2) Secondly, using the mean and variance obtained by unbiased estimation and combining them with the prior distribution, we can obtain the Bayesian estimate of the mean of the test statistic in the current window: e , which is the mean of the posterior probability density function. Similarly, the variance of the posterior probability density function can also be calculated

[0055]

[0056] Where N is the sliding window length, m i represents the unbiased estimated mean of the features in the i-th sliding window, v i 2 represents the variance of the feature in the i-th sliding window, μ a represents the mean parameter of the prior distribution, σ a 2represents the variance parameter of the prior distribution.

[0057] (3) Based on the Bayesian estimate obtained by the current sliding window, the mean and variance of the Bayesian estimate are sequentially estimated, and the mean μ of the Bayesian estimate is updated. 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 by sliding the window for the k+1th time. represents the sequential estimated mean of the Bayesian estimator, represents the sequential estimated variance of the Bayesian estimator.

[0060] (4) According to 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, the mean μ of the prior distribution is calculated. a and variance σ a 2 The correction method is as follows.

[0061]

[0062] In the formula, μ a (k) represents the mean of the prior distribution at the kth sliding window, represents the variance of the prior distribution at the kth sliding window, v i (k+1) represents the variance of the feature samples in the window during the k+1th sliding window, and N refers to the sliding window length.

[0063] By executing steps (1) to (4) for the relative average amplitude and the mean echo phase difference of the unit to be detected, the prior distribution formation and Bayesian estimation of the corresponding features can be completed, and the feature point f = [f1, f2] after two-dimensional Bayesian estimation can be obtained. The next step is to input the feature point f = [f1, f2] into the concave hull classifier trained in step 2 for classification.

[0064] Preferably, the step 4) uses a two-dimensional concave hull classifier to discriminate the feature vector after Bayesian optimization to obtain a final judgment result:

[0065] In the detection stage, let the feature point to be detected be f = [f1, f2], and the vertices that make up the concave hull are 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 the feature point f = [f1, f2] is within the concave hull decision area 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, it is determined that the feature point to be detected is not within the concave hull decision area, and the sample to be detected is determined as a clutter sample. Otherwise, it is determined that the sample point to be detected is outside the concave hull decision area, and the sample to be detected is determined as a target sample.

[0069] Compared with the prior art, the two-dimensional concave hull feature target detection method based on Bayesian estimation of the present invention has the following beneficial effects:

[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 of poor detection ability of traditional target features in a short accumulation time.

[0071] (2) The improved concave hull classifier is used to classify the echo feature points 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 of unchanged false alarm rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a detection flow chart of a two-dimensional feature target detection method using prior information of the present invention;

[0073] Figure 2 It is a schematic diagram of concave hull detection of the present invention. DETAILED DESCRIPTION

[0074] In order to better understand and implement the present invention, a specific embodiment is given below to explain the present invention in detail. The sea surface target detection method of the present invention is as follows:

[0075] 1) Sea clutter echo feature extraction and Gaussianization

[0076] The radar collects sea clutter echo data of multiple range units in a certain direction in scanning mode, which can be expressed as follows:

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

[0078] Among them, x i represents the echo sequence of the ith clutter range unit, x i,1 represents the first frame echo sequence of the ith clutter range unit. i By performing feature extraction, a feature sequence in the following form can be obtained.

[0079]

[0080] Among them, f i,1 Represents x 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 ith range unit. i,1 Represents the average phase difference of the first frame echo of the i-th range unit. The feature extraction method is as follows:

[0081] 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. The target echo has strong energy, so the relative average amplitude of the target unit is generally greater than that of the clutter unit.

[0082] The calculation formulas are shown in formula (3) and formula (4).

[0083]

[0084] In formula (3), x(n), x represents the radar echo sequence of the distance unit to be detected with a length of N. Represents the average amplitude of the echo sequence of the range unit to be detected.

[0085]

[0086] In formula (4), x p represents the reference range unit radar echo sequence, P represents the number of reference units, RAA(x) represents the average amplitude of the echo sequence of the reference unit, and RAA(x) represents the relative average amplitude characteristic of the unit to be detected.

[0087] Phase characteristics refer to the characteristics of the average phase difference of the echo, which is calculated by the mean value of the echo phase difference within the coherent processing time. The radar echo of the target unit has a certain Doppler velocity, so the echo phase within the coherent processing time will change slowly with the time law. 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 mean value of the echo phase difference of the target echo is usually small and stable, while the echo phase difference of the clutter is usually large and unstable. The calculation method of the average phase difference of the echo is shown in Equation (5) and Equation (6).

[0088] Δφ(n)=arg[x*(n)x(n+1)] (29)

[0089] In formula (5), x*(n) represents the conjugate form of the nth sampling point of the radar echo sequence, and arg[a] represents the phase of the complex number a.

[0090]

[0091] In formula (6), x represents the radar echo sequence of the range unit to be detected with a length of N, and PDM(x) represents the average phase difference of the echo of the unit to be detected.

[0092] The application background of the method proposed in this patent is Gaussian background, and the data needs to be Gaussianized first to ensure that the subsequent iteration of the prior distribution can be carried out stably.

[0093] The Box-cox transformation can be performed according to the following formula.

[0094]

[0095] In the formula, f is the feature to be Gaussianized, λ is the Gaussianization coefficient, and f g Refers to Gaussian features.

[0096] This step can make the data easier to be accepted by the iterator without changing the feature size relationship, reduce the impact of extreme data on the iterator, make the iteration go more smoothly and reduce the estimation error. The Gaussianized two-dimensional clutter feature point set is denoted as Ω.

[0097] 2) Training of 2D Concave Hull Classifier

[0098] The formation of the concave hull classifier can be subdivided into steps (1) to (7).

[0099] (1) Normalize the N two-dimensional feature point sets Ω and generate a two-dimensional convex hull to obtain a two-dimensional convex hull vertex set V. Filter out the vertices that meet the requirements to form a vertex set V to be deleted.i . Where V i The point inside (x i ,y i )satisfy: Refers to the mean of RAA and PDM in N two-dimensional feature points.

[0100] (2) From V i Select the distance feature center point The farthest point v i , remove it from the training set Ω. Meanwhile, i=i+1.

[0101] (3) Based on the sample point set Ω obtained in steps (1) and (2), a two-dimensional convex hull generation algorithm is used to obtain a two-dimensional convex hull and a vertex set V.

[0102] (4) Filter out the items that meet the conditions The edge set L composed of vertices f ={L1,L2,...}, and select the longest side L max And the corresponding two vertices v1 and v2.

[0103] (5) Traverse all sample points and find max The sample point s with the smallest midpoint Euclidean distance will be represented by L max Split into two connected edges L m1 and L m2 . Where L m1 By connecting v1 and s, L m2 It is obtained by connecting s and v2. o ={L o1 ,L o2}.

[0104] (6) Statistical analysis of the sample point set Ω outside the judgment area out . Let the jth external complement point be s oi (x j, y j ). o The number of edges included is L on .

[0105] (7) For the jth external filling, the external filling point is s oi (x j, y j ), you need to traverse L o , for the zth traversal, extract L o The zth edge L oz The two vertices v z1 (x z1 ,y z1 ) and v z2 (xz2 ,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, continue to traverse L o ; If r<0, then L z Disassembled into s oi (x j ,y j ) and v z1 (x z1 ,y z1 ) oz1 and by s oi (x j ,y j ) and v z2 (x z2 ,y z2 ) 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 ) is completed, and (7) is repeated to perform the internal filling of the i=i+1th point.

[0106] (8) Let the set of edges of the outer surface of the concave hull before the outer complement be L = {L1,L2,..,L o ,...}, as the final decision boundary output of the concave hull 3) Feature extraction and Bayesian estimation of the detected echo

[0107] After the echo sequence to be detected is subjected to feature extraction and Gaussianization in step 1), Bayesian estimation is used to supplement the information of the proposed features.

[0108] Taking the relative average amplitude as an example, let the relative average amplitude feature sequence of the Gaussianized unit to be detected be

[0109] f ci =[f ci,1 ,f ci,2 ,f ci,3 ,...]; (32)

[0110] In the formula, f cirepresents the relative average amplitude feature sequence of the i-th unit to be detected, f ci,1 Represents the first relative average amplitude feature of the i-th unit to be detected.

[0111] The formation of a prior distribution based on a single feature and Bayesian estimation can be divided into steps (1) to (4)

[0112] (1) Slide the window of the feature sequence of the unit to be detected, the step size of the sliding window is 1, the window length is N, the length of the feature sequence of each unit to be detected is M, and the mean value m of the test statistic in the window at the current moment is i and variance v i Make an unbiased estimate.

[0113]

[0114] In the formula, f ci,(n) Represents the nth relative average amplitude feature in the sliding window.

[0115] (2) Secondly, using the mean and variance obtained by unbiased estimation and combining them with the prior distribution, we can obtain the Bayesian estimate of the mean of the test statistic in the current window: e , which is the mean of the posterior probability density function. Similarly, the variance of the posterior probability density function can also be calculated

[0116]

[0117] Where N is the sliding window length, m i represents the unbiased estimated mean of the features in the i-th sliding window, v i 2 represents the variance of the feature in the i-th sliding window, μ a represents the mean parameter of the prior distribution, σ a 2 represents the variance parameter of the prior distribution.

[0118] (3) Based on the Bayesian estimate obtained by the current sliding window, the mean and variance of the Bayesian estimate are sequentially estimated, and the mean μ of the Bayesian estimate is updated. a and variance σ a 2 .

[0119]

[0120] In the formula, k refers to the number of sliding windows, a e (k+1) represents the Bayesian estimate obtained by sliding the window for the k+1th time. represents the sequential estimated mean of the Bayesian estimator, represents the sequential estimated variance of the Bayesian estimator.

[0121] (4) According to 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, the mean μ of the prior distribution is calculated. a and variance σ a 2 The correction method is as follows.

[0122]

[0123] In the formula, μ a (k) represents the mean of the prior distribution at the kth sliding window, represents the variance of the prior distribution at the kth sliding window, v i (k+1) represents the variance of the feature samples in the window during the k+1th sliding window, and N refers to the sliding window length.

[0124] By executing steps (1) to (4) for the relative average amplitude and the mean echo phase difference of the unit to be detected, the prior distribution formation and Bayesian estimation of the corresponding features can be completed, and the feature point f = [f1, f2] after two-dimensional Bayesian estimation can be obtained. The next step is to input the feature point f = [f1, f2] into the concave hull classifier trained in step 2 for classification.

[0125] 4) Judgment of feature points to be detected

[0126] In the detection stage, let the feature point to be detected be f = [f1, f2], and the vertices that make up the concave hull are 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 the feature point f = [f1, f2] is within the concave hull decision area Ω:

[0127] Step (1): Let j=n, t=0.

[0128] 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-yi ) / (y j -y i )+x i )), if the result is true, then t = ~t. Let j = i. This step is repeated until i = n.

[0129] Step (3): If t==0, it is determined that the feature point to be detected is not within the concave hull decision area, and the sample to be detected is determined as a clutter sample. Otherwise, it is determined that the sample point to be detected is outside the concave hull decision area, and the sample to be detected is determined as a target sample.

Claims

1. A two-dimensional concave hull feature target detection method based on Bayesian estimation, characterized in that The following steps are involved: Step 1: Sea clutter echo feature extraction and Gaussianization Collect the clutter echo time series of multiple clutter units within a period of time, extract the relative average amplitude of the clutter echo and the mean value of the echo phase difference, and use the Box-Cox transformation to perform Gaussian preprocessing as training information; Step 2: Training of 2D Concave Hull Classifier Use the clutter feature points collected in step 1 to train a two-dimensional concave hull classifier under the false alarm rate condition; Step 3: Extraction of echo features to be detected and Bayesian estimation of features In the detection stage, feature points are extracted and Gaussianized from the echo time series of the unit to be detected. Based on the input of the features, the feature prior distribution of the unit to be detected is obtained. The feature points of the unit to be detected in the current frame are estimated by Bayesian method using the prior distribution. The estimated results are used as the feature points to be detected in the current frame to complete the feature information supplement. Step 4: Determination of feature points to be detected The feature points after Bayesian estimation are input into the two-dimensional concave hull classifier. If the feature point is located in the concave hull classifier, it is judged as clutter, otherwise it is judged 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: The radar collects sea clutter echo data of multiple range units in a certain direction in scanning mode, which is shown in the following form: x i =[x i,1 ,x i,2 ,x i,3 ,...];(1) Among them, x i represents the echo sequence of the ith clutter range unit, x i,1 represents the first frame echo sequence of the ith clutter range unit, for x i Perform feature extraction and obtain a feature sequence in the following form; Among them, f i,1 Represents x 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 ith range unit. i,1 It represents the average phase difference of the first frame echo of the i-th range unit. The feature extraction method is as follows: 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. The target echo has strong energy, so the relative average amplitude of the target unit is generally greater than that of the clutter unit. The calculation formulas are shown in equations (3) and (4): In formula (3), x(n), x represents the radar echo sequence of the distance unit to be detected with a length of N. The average amplitude of the echo sequence representing the range unit to be detected; In formula (4), x p represents the reference range unit radar echo sequence, P represents the number of reference units, represents the average amplitude of the echo sequence of the reference unit, and RAA(x) represents the relative average amplitude characteristic of the unit to be detected; The phase feature refers to the echo average phase difference feature. The calculation method of the echo average phase difference is shown in formula (5) and formula (6): Δφ(n)=arg[x*(n)x(n+1)] (5) In formula (5), x*(n) represents the conjugate form of the nth sampling point of the radar echo sequence, and arg[a] represents the phase of the complex number a. In formula (6), x represents the radar echo sequence of the range unit to be detected with a length of N, and PDM(x) represents the average phase difference of the echo of the unit 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 Refers to Gaussian features; 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: The formation of the concave hull classifier is subdivided into steps (1) to (7); (1) Normalize the N two-dimensional feature point sets Ω and generate a two-dimensional convex hull to obtain a two-dimensional convex hull vertex set V. Filter out the vertices that meet the requirements to form a vertex set V to be deleted. i , where V i The point inside (x i ,y i )satisfy: Refers to the mean of RAA and PDM among N two-dimensional feature points; (2) From V i Select the distance feature center point The farthest point v i , remove it from the training set Ω, and i=i+1; (3) Based on the sample point set Ω obtained in steps (1) and (2), a two-dimensional convex hull generation algorithm is used to obtain a two-dimensional convex hull and a vertex set V; (4) Filter out the items that meet the conditions The edge set L composed of vertices f ={L1,L2,...}, and select the longest side L max And the corresponding two vertices v1 and v2; (5) Traverse all sample points and find max The sample point s with the smallest midpoint Euclidean distance will be represented by L max Split into two connected edges L m1 and L m2 , where L m1 By connecting v1 and s, L m2 It is obtained by connecting s and v2, denoted by L o ={L o1 ,L o2 }; (6) Statistical analysis of the sample point set Ω outside the judgment area out , let the jth external complement point be s oi (x j ,y j ), record L o The number of edges included is L on ; (7) For the jth external filling, the external filling point is s oi (x j, y j ), you need to traverse L o , for the zth traversal, extract L o The zth 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, continue to traverse L o ; If r<0, then L z Disassembled into s oi (x j ,y j ) and v z1 (x z1 ,y z1 ) oz1 and by s oi (x j ,y j ) and v z2 (x z2 ,y z2 ) 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 ) The internal filling is completed, and (7) is repeated to perform the internal filling of the i=i+1th point; (8) Let the set of edges of the outer surface of the concave hull before the outer complement be L = {L1,L2,..,L o ,...}, which is output as the final decision boundary of 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: After the echo sequence to be detected is subjected to feature extraction and Gaussianization in step 1), the proposed features are supplemented with information using Bayesian estimation; Taking the relative average amplitude as an example, let the relative average amplitude feature sequence of the Gaussianized unit to be detected be f ci =[f ci,1 ,f ci,2 ,f ci ,3,...];(8) In the formula, f ci represents the relative average amplitude feature sequence of the i-th unit to be detected, f ci,1 represents the first relative average amplitude feature of the i-th unit to be detected; The formation of a prior distribution based on a single feature and the Bayesian estimation can be divided into steps (1) to (4): (1) Slide the window of the feature sequence of the unit to be detected, the step size of the sliding window is 1, the window length is N, the length of the feature sequence of each unit to be detected is M, and the mean value m of the test statistic in the window at the current moment is i and variance v i Make unbiased estimates; In the formula, f ci,(n) Represents the nth relative average amplitude feature in the sliding window; (2) Secondly, using the mean and variance obtained by unbiased estimation and combining them with the prior distribution, we can obtain the Bayesian estimate of the mean of the test statistic in the current window: e , which is the mean of the posterior probability density function. Similarly, the variance of the posterior probability density function can also be calculated. Where N is the sliding window length, m i represents the unbiased estimated mean of the features in the i-th sliding window, v i 2 represents the variance of the feature in the i-th sliding window, μ a represents the mean parameter of the prior distribution, σ a 2 represents the variance parameter of the prior distribution; (3) Based on the Bayesian estimate obtained by the current sliding window, the mean and variance of the Bayesian estimate are sequentially estimated, and the mean μ of the Bayesian estimate is updated. 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 by sliding the window for the k+1th time. represents the sequential estimated mean of the Bayesian estimator, represents the sequential estimated variance of the Bayesian estimate; (4) According to 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, the mean μ of the prior distribution is calculated. a and variance σ a 2 Make corrections, the correction method is as follows: In the formula, μ a (k) represents the mean of the prior distribution at the kth sliding window, represents the variance of the prior distribution at the kth sliding window, v i (k+1) represents the variance of the feature samples in the window during the k+1th sliding window, and N refers to the sliding window length; By executing steps (1) to (4) respectively for the relative average amplitude and the mean echo phase difference of the unit to be detected, the prior distribution formation and Bayesian estimation of the corresponding features can be completed, and the feature point f = [f1, f2] after two-dimensional Bayesian estimation can be obtained. The next step is to input the feature point 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: In step 4), a two-dimensional concave hull classifier is used to discriminate the feature vector after Bayesian optimization to obtain the final judgment result: In the detection stage, let the feature point to be detected be f = [f1, f2], and the vertices that make up the concave hull are 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 the feature point f = [f1, f2] is within the concave hull decision area 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, it is determined that the feature point to be detected is not within the concave hull decision area, and the sample to be detected is determined as a clutter sample. Otherwise, it is determined that the sample point to be detected is outside the concave hull decision area, and the sample to be detected is determined as a target sample.

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