A multi-feature nonlinear re-expression and target detection method

Abstract

The application discloses a multi-feature nonlinear re-expression and target detection method, and relates to the technical field of computer vision, which comprises the following steps: step one: selecting three features in time and frequency, and re-expressing the nonlinear relationship among the features through polynomial fitting; step two: using the least square method to realize parameter optimization by minimizing the sum of squares of errors between predicted values and actual observation values; step three: projecting feature sample points onto the curve in the feature space obtained through the above method, that is, the curve of the maximum variance direction, so as to realize re-expression of the features; and step four: using a concave hull classifier to detect targets in a two-dimensional feature space. The application finds the best projection direction by fitting the nonlinear relationship among the features, realizes nonlinear projection with optimal variance, and thus obtains new features with the strongest classification ability for sea clutter and targets, and further improves the detection performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer vision, and in particular to a multi-feature nonlinear re-expression and target detection method. BACKGROUND

[0002] Different features are suitable for different situations, and their complementarity is the basis for feature-based detectors to have robustness and good detection performance, so multi-feature-based target detection is a way to improve detection performance, but the application of a large number of features will bring more information, while also causing problems such as dimension disaster, information redundancy, and rising algorithm design complexity, so it is very important to re-express multi-dimensional features to reduce redundancy while improving sea clutter and target classification ability.

[0003] The existing technology has the following problems:

[0004] Common feature re-expression methods usually use linear relationships between features, such as principal component analysis (PCA), linear discriminant analysis (LDA), and feature compression, although these methods can utilize the correlation and difference between features and achieve dimension reduction, but they do not conform to the fact that features in real-world scenarios of radar sea detection often show nonlinear correlation, so how to effectively implement nonlinear feature re-expression and improve classification ability is an important research direction. SUMMARY

[0005] The present application provides a multi-feature nonlinear re-expression and target detection method to solve the problems raised in the background art.

[0006] To solve the above technical problems, the technical solution adopted by the present application is:

[0007] A multi-feature nonlinear re-expression and target detection method, the multi-feature nonlinear re-expression and target detection method comprising the following steps:

[0008] Step 1: Select three features in time and frequency, time features include relative average amplitude, time domain entropy mean value, and relative peak height, frequency features include relative Doppler peak height, relative Doppler vector entropy, and frequency domain entropy value second moment, and the nonlinear relationship between these features is re-expressed by polynomial fitting, which is in the form of:

[0009] (1);

[0010] wherein, and represent the two features of relative average amplitude and time domain entropy mean value, is a nonlinear parameter thereof, is a constant term parameter;

[0011] Step 2: In order to find the optimal parameters of the quintic polynomial model, the least squares method is used to optimize the parameters by minimizing the sum of squares of the errors between the predicted values ​​and the actual observed values. Specifically, for each observation point , the error is defined as ,in is the value predicted by the model. The loss function is defined as:

[0012] (2);

[0013] The optimization algorithm iteratively adjusts parameters to minimize the loss function, thereby obtaining the optimal fitting parameters of the model and obtaining the curve with the maximum variance in the feature space. Similarly, taking the three features of relative average amplitude, relative peak height, and relative Doppler vector entropy as examples, we can characterize the nonlinear relationship between the three features and obtain the curve with the maximum variance in the three-dimensional feature space:

[0014] (3);

[0015] in, 、 and Represent the three characteristics of relative average amplitude, relative peak height and relative Doppler vector entropy, respectively. is the nonlinear parameter of its relative average amplitude, is a constant parameter, is the nonlinear parameter relative to the peak height;

[0016] Step 3: The total echo signal The total number of echo signals is divided into short echo signals with equal pulse numbers. The corresponding feature samples are extracted from each echo signal. The feature sample points are projected onto the curve with the maximum variance in the feature space using the method described in step 2 to achieve feature re-expression.

[0017] Step 4: Use the concave hull classifier to detect targets in the two-dimensional feature space.

[0018] A further improvement of the technical solution of the present invention is that a linear interpolation projection method is proposed based on the multi-feature nonlinear re-expression method, and then the distance between the sample point and the projection starting point is used to complete the detection. The linear interpolation projection method includes the following steps:

[0019] A1: Calculate the segmented arc lengths of the curve, calculate the Euclidean distances between adjacent points, obtain the length of each segment, accumulate these lengths, and normalize the total length of the entire curve to the interval [0,1].

[0020] A2: Use linear interpolation to construct a linear model of the curve, treating each small segment of the curve as a straight line;

[0021] A3: For each feature sample, calculate the distance to each line segment in the curve with the maximum variance.

[0022] A4: Obtain the coordinates of the projection point of each feature sample onto the curve and the minimum distance, completing the calculation.

[0023] A5: Obtain new features by the relative position of the projection point on the curve in the direction of maximum variance;

[0024] A6: Use concave hull classifier for object detection in two-dimensional feature space.

[0025] A further improvement of the technical solution of the present invention is that the A3 further includes the following steps:

[0026] B1: For each feature sample, calculate its vertical distance to each line segment;

[0027] B2: Calculate the projection point of the feature sample on each line segment and determine whether the projection point is within the range of the line segment;

[0028] B3: If the projected point is within the range, record its distance; otherwise, calculate the distance from the point to be mapped to the endpoint of the line segment;

[0029] B4: Select the smallest distance as the closest distance from the point to the curve, and record the corresponding coordinates of the closest point as the projection point.

[0030] A further improvement of the technical solution of the present invention is that the relative average amplitude RAA, defined as the ratio of the average amplitude of the unit to be detected to the average amplitude of the reference unit, can be used to measure the amplitude difference between the detection unit and the reference unit. The expression is shown in (4):

[0031] (4);

[0032] (5);

[0033] in, and for and abbreviation of .

[0034] A further improvement of the technical solution of the present invention is that the time domain entropy mean TEM is defined as the average value of the echo information entropy of the unit under test. Since the two echoes fluctuate differently, it reflects the difference in the degree of chaos of the target and sea clutter signal waveforms. The specific calculation is as follows:

[0035] Use a rectangular window with a width of W and a step with a width of S to detect the echo signal of the unit to be detected. Slide to get A short time domain sequence of length W ;

[0036] (6);

[0037] (7);

[0038] (8);

[0039] (9);

[0040] in, Indicates rounding up. Indicates the short sequence The time domain entropy value of N is the length of the echo pulse, Indicates the short sequence No. The entropy value of each element is calculated as follows: Indicates the short sequence No. The value of the element, Indicates the short sequence The value of the last element of Indicates echo signal The mean time domain entropy value of .

[0041] A further improvement of the technical solution of the present invention is that the peak height RPH is defined as the ratio of the pulse echo peak value of the unit to be detected to the average amplitude of the adjacent pulses. It can be used to reflect the difference in the energy proportion of the target and sea clutter echo peaks in the total signal and the degree of peak fluctuation. The expression is shown in (10):

[0042] (10);

[0043] (11);

[0044] in, Representing a collection The number of units in and Together they define the pulse range involved in the ratio operation, where Is to make the echo signal The pulse number when the maximum value is obtained.

[0045] A further improvement of the technical solution of the present invention is that the relative Doppler peak height RDPH, defined as the ratio of the Doppler peak of the detected unit to the mean Doppler peak of the reference unit, can reflect the difference in the energy proportion and mutation degree of the two types of echo frequencies. The specific calculation is as follows:

[0046] (12);

[0047] in It is the echo signal The Doppler peak height of K is the number of reference units. is the echo signal.

[0048] A further improvement of the technical solution of the present invention is that the relative Doppler vector entropy RVE, defined as the ratio of the information entropy of the detected unit to that of the reference unit, can reflect the degree of confusion of the signal waveform. The specific calculation is as follows:

[0049] (13);

[0050] in It is the echo signal The Doppler vector entropy of K is the number of reference units, is the echo signal.

[0051] A further improvement of the technical solution of the present invention is that the second-order moment of frequency domain entropy SOFE is defined as the variance of the information entropy value of the frequency domain unit to be tested, so as to reflect the degree of discreteness of the frequency domain entropy values ​​of the two types of sequences. The specific calculation is as follows:

[0052] (14);

[0053] in Indicates echo signal No. short sequence The frequency domain entropy value of represents averaging, N is the length of the echo pulse, W is the rectangular window and S is the step length.

[0054] Due to the adoption of the above technical solution, the present invention has the following technical advancements compared to the prior art:

[0055] 1. The present invention provides a multi-feature nonlinear re-expression and target detection method. By fitting the nonlinear relationship between features, the optimal projection direction is found, and the nonlinear projection with the optimal variance is achieved, thereby obtaining new features with the strongest classification ability for sea clutter and targets, further improving the detection performance. This target detection method can achieve nonlinear re-expression of features, while retaining the effective correlation information between features, while improving the classification ability of features. Through verification by measured data on the SDRDSP public radar data set, this application has better performance than other target detection methods based on linear feature re-expression. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 The relative position relationship of the four-level sea clutter characteristics of the present invention;

[0057] Figure 2 The relative position relationship of the target features of the four-level sea conditions of the present invention;

[0058] Figure 3 The relative position relationship of the five-level sea clutter characteristics of the present invention;

[0059] Figure 4 The relative position relationship of the five-level sea state target features of the present invention;

[0060] Figure 5 This is a comparison diagram of the projection results of the present invention;

[0061] Figure 6 is the re-expression characteristic diagram of the present invention;

[0062] Figure 7 is the Bhattacharyya distance map of the present invention;

[0063] Figure 8 This is the ROC curve diagram of the present invention. DETAILED DESCRIPTION

[0064] The present invention is described in further detail below in conjunction with the embodiments:

[0065] Example 1:

[0066] like Figure 1-4 As shown in the figure, the present invention provides a multi-feature nonlinear re-expression and target detection method. Taking a sea detection radar as an example, assuming that it transmits a series of coherent pulses on each transceiver channel and receives a complex time series for each range unit, the radar target detection problem in sea clutter can be transformed into the following binary hypothesis testing problem:

[0067] (15);

[0068] Where N represents the length of the received complex time sequence, K represents the number of reference units RC, and It is the time series of radar echoes received at the CUT unit to be detected and the reference unit. and is the sea clutter time series of the unit to be detected and the reference unit, It is an unknown radar echo. The null hypothesis H0 and the alternative hypothesis H1 correspond to the presence of only sea clutter or sea clutter and target in the unit to be detected, respectively. The six significant features extracted from the time series of the radar echo response can be divided into two groups according to the extracted feature domain, namely time features and frequency features. The time features include relative average amplitude, mean time domain entropy value, and relative peak height. The frequency features include relative Doppler peak height, relative Doppler vector entropy, and second-order moment of frequency domain entropy value.

[0069] The relative average amplitude RAA is defined as the ratio of the average amplitude of the detected unit to the average amplitude of the reference unit. It can be used to measure the amplitude difference between the detected unit and the reference unit. The expression is shown in (4):

[0070] (4);

[0071] (5);

[0072] in, and for and abbreviation of .

[0073] The time domain entropy mean TEM is defined as the average value of the echo information entropy of the unit under test. Due to the different fluctuations of the two echoes, it reflects the difference in the degree of chaos of the target and sea clutter signal waveforms. The specific calculation is as follows:

[0074] Use a rectangular window with a width of W and a step with a width of S to detect the echo signal of the unit to be detected. Slide to get A short time domain sequence of length W ;

[0075] (6);

[0076] (7);

[0077] (8);

[0078] (9);

[0079] in, Indicates rounding up. denotes the time-domain entropy value of the th short sequence, N is the length of the echo pulse, denotes the time-domain entropy value of the th short sequence, denotes the entropy value calculation proportion of the th element of the th short sequence, denotes the value of the th element of the th short sequence, denotes the value of the last element of the th short sequence, denotes the value of the last element of the th short sequence, denotes the average time-domain entropy value of the echo signal.

[0080] The relative peak height RPH, defined as the ratio of the peak value of the pulse echo of the unit to be detected to the average amplitude of the adjacent pulse, can be used to reflect the difference in the energy proportion of the target and sea clutter echo peak value in the total signal and the fluctuation degree of the peak value, and the expression is shown in equation (10):

[0081] (10);

[0082] (11);

[0083] wherein, denotes the number of units in the set, and together define the pulse range participating in the ratio operation, wherein is the pulse number that makes the echo signal get the maximum value.

[0084] The relative Doppler peak height RDPH, defined as the ratio of the Doppler peak value of the unit to be detected to the average Doppler peak value of the reference unit, can reflect the difference in the energy proportion and mutation degree of the frequency peak values of the two types of echoes, and the specific calculation is as follows:

[0085] (12);

[0086] wherein is the Doppler peak height of the echo signal , K is the number of reference units, is the echo signal.

[0087] The relative Doppler vector entropy RVE, defined as the ratio of the information entropy of the unit to be detected to the reference unit, can reflect the chaos degree of the signal waveform, and the specific calculation is as follows:

[0088] (13);

[0089] in It is the echo signal The Doppler vector entropy of K is the number of reference units, is the echo signal.

[0090] The second-order moment of frequency domain entropy value SOFE is defined as the variance of the information entropy value of the frequency domain unit to be tested, which reflects the discrete degree of the frequency domain entropy value of the two types of sequences. The specific calculation is as follows:

[0091] (14);

[0092] in Indicates echo signal No. short sequence The frequency domain entropy value of represents averaging, N is the length of the echo pulse, W is the rectangular window and S is the step length.

[0093] In this embodiment, the present invention uses the measured data under different sea conditions in the dataset SDRDSP to calculate the two features of RAA and RVE, and displays the relative position relationship of the feature samples;

[0094] like Figure 1-4 It can be seen that neither the characteristic samples of the target unit nor the characteristic samples of the sea clutter unit obey a linear relationship. Their distribution is closer to a nonlinear relationship close to a polynomial. Moreover, as the sea conditions improve, this nonlinear relationship does not disappear, but the divergence of the target samples increases.

[0095] If linear dimensionality reduction techniques such as PCA are forcibly used in the feature re-expression process, the direction of maximum variance that can be found is the direction of maximum variance under linear conditions, rather than the direction of maximum variance of the true distribution between samples. Therefore, a nonlinear feature re-expression method that maximizes variance is required.

[0096] Example 2:

[0097] like Figure 5-8 As shown, based on Example 1, the present invention provides a technical solution: Preferably, the multi-feature nonlinear re-expression and target detection method includes the following steps:

[0098] Step 1: Select three features from time and frequency. The time features include relative average amplitude, mean time domain entropy value, and relative peak height. The frequency features include relative Doppler peak height, relative Doppler vector entropy, and second-order moment of frequency domain entropy value. Use polynomial fitting to express the nonlinear relationship between these features. The form is:

[0099] (1);

[0100] in, and Represent the two characteristics of relative average amplitude and time domain entropy mean, is its nonlinear parameter, is a constant parameter;

[0101] Step 2: In order to find the best parameters of the quintic polynomial model, the least squares method is used to optimize the parameters by minimizing the sum of squares of the errors between the predicted values ​​and the actual observed values. Specifically, for each observation point , the error is defined as ,in is the value predicted by the model. The loss function is defined as:

[0102] (2);

[0103] The optimization algorithm iteratively adjusts parameters to minimize the loss function, thereby obtaining the optimal fitting parameters of the model and obtaining the curve with the maximum variance in the feature space. Similarly, taking the three features of relative average amplitude, relative peak height, and relative Doppler vector entropy as examples, we can characterize the nonlinear relationship between the three features and obtain the curve with the maximum variance in the three-dimensional feature space:

[0104] (3);

[0105] in, 、 and Represent the three characteristics of relative average amplitude, relative peak height and relative Doppler vector entropy, respectively. is the nonlinear parameter of its relative average amplitude, is a constant parameter, is the nonlinear parameter relative to the peak height;

[0106] Step 3: The total echo signal The total number of echo signals is divided into short echo signals with equal pulse numbers. The corresponding feature samples are extracted from each echo signal. The feature sample points are projected onto the curve with the maximum variance in the feature space using the method described in step 2 to achieve feature re-expression.

[0107] Step 4: Use the concave hull classifier to detect targets in the two-dimensional feature space.

[0108] A linear interpolation projection method is proposed based on the multi-feature nonlinear re-expression method, and then the distance between the sample point and the projection starting point is used to complete the detection. The linear interpolation projection method includes the following steps:

[0109] A1: Calculate the segment lengths of the curve, calculate the Euclidean distances between adjacent points, obtain the length of each segment, accumulate these lengths, and normalize the total length of the entire curve to the interval [0,1].

[0110] A2: Use linear interpolation to construct a linear model of the curve, treating each small segment of the curve as a straight line;

[0111] A3: For each feature sample, calculate the distance to each line segment in the curve with the maximum variance.

[0112] A4: Obtain the coordinates of the projection point of each feature sample onto the curve and the minimum distance, completing the calculation.

[0113] A5: Obtain new features by the relative position of the projection point on the curve in the direction of maximum variance;

[0114] A6: Use concave hull classifier for object detection in two-dimensional feature space.

[0115] Said A3 further comprises the following steps:

[0116] B1: For each feature sample, calculate its vertical distance to each line segment;

[0117] B2: Calculate the projection point of the feature sample on each line segment and determine whether the projection point is within the range of the line segment;

[0118] B3: If the projected point is within the range, record its distance; otherwise, calculate the distance from the point to be mapped to the endpoint of the line segment;

[0119] B4: Select the smallest distance as the closest distance from the point to the curve, and record the corresponding coordinates of the closest point as the projection point.

[0120] In this embodiment, under the condition of level 5 sea state data, the proposed method is used to perform nonlinear re-expression on the six extracted features, and the projection results are as follows: Figure 5 As shown, it can be seen that using the polynomial model to describe the nonlinear relationship between features can conform to the spatial coordinate correlation in the actual scene.

[0121] Furthermore, we performed probability density function fitting and Bhattacharyya distance calculation on the time domain features and the new features obtained by re-expression to verify the improvement of their classification ability. The results are as follows: Figure 6 and Figure 7As shown in the figure, it can be seen that even under the harsh observation of level 5 sea conditions, the new features still have a high ability to distinguish targets in sea clutter. Compared with the three time domain features that have not been re-expressed, the Bhattacharyya distance of the new features is larger, indicating that its feature samples have a lower degree of overlap. When using the concave hull classifier for target detection, it can distinguish targets more stably. This shows that the proposed nonlinear feature re-expression method is effective under the measured sea clutter data.

[0122] Finally, PCA and LDA feature dimensionality reduction methods are used as comparative methods to compress the six-dimensional features into a two-dimensional feature space. The same concave hull classifier is used together with the proposed method to perform target detection experiments. The ROC curves under different false alarm probabilities are shown in the figure below. Figure 8 As shown, it can be seen that the false alarm probability Under the condition of , the detection probability of the new feature is the highest, about 5% higher than the second-place LDA. As the false alarm probability increases, although the detection performance of other algorithms becomes close, their stability is still insufficient. In summary, the target detection stability of the proposed algorithm under harsh sea conditions and low false alarm conditions can be verified.

[0123] The above generally describes the present invention in detail, but it is obvious to a person skilled in the art that some modifications or improvements can be made to the present invention. Therefore, modifications or improvements that do not depart from the spirit of the present invention are within the scope of protection of the present invention.

Claims

1. A multi-feature nonlinear re-expression and target detection method, characterized by: The multi-feature nonlinear re-expression and target detection method comprises the following steps: Step 1: Select three features from time and frequency. The time features include relative average amplitude, mean time domain entropy value, and relative peak height. The frequency features include relative Doppler peak height, relative Doppler vector entropy, and second-order moment of frequency domain entropy value. Taking relative average amplitude and mean time domain entropy value as examples, the nonlinear relationship between the two can be obtained by polynomial fitting, which is in the form of: （1）； in, and Represent the two characteristics of relative average amplitude and time domain entropy mean, is its nonlinear parameter, is a constant parameter; Step 2: In order to find the best parameters of the quintic polynomial model, the least squares method is used to optimize the parameters by minimizing the sum of squares of the errors between the predicted values ​​and the actual observed values. Specifically, for each observation point , the error is defined as ,in is the value predicted by the model, and the loss function is defined as: （2）； The optimization algorithm iteratively adjusts parameters to minimize the loss function, thereby obtaining the optimal fitting parameters of the model and obtaining the curve with the maximum variance in the feature space. Similarly, taking the three features of relative average amplitude, relative peak height, and relative Doppler vector entropy as examples, we can characterize the nonlinear relationship between the three features and obtain the curve with the maximum variance in the three-dimensional feature space: （3）； in, 、 and Represent the three characteristics of relative average amplitude, relative peak height and relative Doppler vector entropy, respectively. is the nonlinear parameter of its relative average amplitude, is a constant parameter, is the nonlinear parameter relative to the peak height; Step 3: The total echo signal The total number of echo signals is divided into short echo signals with equal pulse numbers. The corresponding feature samples are extracted from each echo signal. The feature sample points are projected onto the curve with the maximum variance in the feature space using the method described in step 2 to achieve feature re-expression. Step 4: Use the concave hull classifier to detect targets in the two-dimensional feature space.

2. The multi-feature nonlinear re-expression and target detection method according to claim 1, characterized in that: A linear interpolation projection method is proposed based on the multi-feature nonlinear re-expression method, and then the distance between the sample point and the projection starting point is used to complete the detection. The linear interpolation projection method includes the following steps: A1: Calculate the segmented arc lengths of the curve, calculate the Euclidean distances between adjacent points, obtain the length of each segment, accumulate these lengths, and normalize the total length of the entire curve to the interval [0,1]. A2: Use linear interpolation to construct a linear model of the curve, treating each small segment of the curve as a straight line whose coefficients are determined by the coordinates of adjacent points; A3: For each feature sample, calculate the distance to each line segment in the curve with the maximum variance. A4: Obtain the coordinates of the projection point of each feature sample onto the curve and the minimum distance, completing the calculation. A5: Obtain new features by the relative position of the projection point on the curve in the direction of maximum variance; A6: Use concave hull classifier for object detection in two-dimensional feature space.

3. The multi-feature nonlinear re-expression and target detection method according to claim 2, characterized in that: Said A3 further comprises the following steps: B1: For each feature sample, calculate its vertical distance to each line segment; B2: Calculate the projection point of the feature sample on each line segment and determine whether the projection point is within the range of the line segment; B3: If the projected point is within the range, record its distance; otherwise, calculate the distance from the point to be mapped to the endpoint of the line segment; B4: Select the smallest distance as the closest distance from the point to the curve, and record the corresponding coordinates of the closest point as the projection point.

4. The multi-feature nonlinear re-expression and target detection method according to claim 1, characterized in that: The relative average amplitude RAA is defined as the ratio of the average amplitude of the detected unit to the average amplitude of the reference unit. It can be used to measure the amplitude difference between the detected unit and the reference unit. The expression is shown in (4): (4)； (5)； in, and for and abbreviation of .

5. The multi-feature nonlinear re-expression and target detection method according to claim 1, characterized in that: The time domain entropy mean TEM is defined as the average value of the echo information entropy of the unit under test. Due to the different fluctuations of the two echoes, it reflects the difference in the degree of chaos of the target and sea clutter signal waveforms. The specific calculation is as follows: Use a rectangular window with a width of W and a step with a width of S to detect the echo signal of the unit to be detected. Slide to get A short time domain sequence of length W ; (6)； (7)； (8)； (9)； in, Indicates rounding up. Indicates the short sequence The time domain entropy value of N is the length of the echo pulse, Indicates the short sequence No. The entropy value of each element is calculated as follows: surface Shidi short sequence No. The value of the element, Indicates the short sequence The value of the last element of Indicates echo signal The mean time domain entropy value of .

6. The multi-feature nonlinear re-expression and target detection method according to claim 1, characterized in that: The relative peak height RPH is defined as the ratio of the peak value of the pulse echo of the unit to be detected to the average amplitude of the adjacent pulses. It can be used to reflect the difference in the energy proportion of the target and sea clutter echo peaks in the total signal and the degree of peak fluctuation. The expression is shown in (10): (10)； (11)； in, Representing a collection The number of units in and Together they define the pulse range involved in the ratio operation, where Is to make the echo signal The pulse number when the maximum value is obtained.

7. The multi-feature nonlinear re-expression and target detection method according to claim 1, characterized in that: The relative Doppler peak height (RDPH) is defined as the ratio of the Doppler peak of the detected unit to the mean Doppler peak of the reference unit. It can reflect the difference in the peak energy ratio and mutation degree of the two types of echo frequencies. The specific calculation is as follows: (12)； in It is the echo signal The Doppler peak height is K, the number of reference units, is the echo signal.

8. The multi-feature nonlinear re-expression and target detection method according to claim 1, characterized in that: The relative Doppler vector entropy RVE is defined as the ratio of the information entropy of the unit to be detected to that of the reference unit. It can reflect the degree of confusion of the signal waveform. The specific calculation is as follows: (13); in It is the echo signal The Doppler vector entropy of K is the number of reference units, is the echo signal.

9. The multi-feature nonlinear re-expression and target detection method according to claim 1, characterized in that: The second-order moment of frequency domain entropy value SOFE is defined as the variance of the information entropy value of the frequency domain unit to be tested, which reflects the discrete degree of the frequency domain entropy value of the two types of sequences. The specific calculation is as follows: （14）； in Indicates echo signal No. short sequence The frequency domain entropy value of represents averaging, N is the length of the echo pulse, W is the rectangular window and S is the step length.

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