Small target detection method at sea based on nonlinear dimensionality reduction and feature sample distance

Abstract

The present invention relates to the field of radar target detection technology, and in particular to a method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance, comprising: S1, extracting multidimensional features of historical sea clutter data and historical target data respectively; S2, calculating feature density distance in historical sea clutter data and historical target data respectively based on the same feature; S3, performing nonlinear feature dimensionality reduction on multidimensional feature space based on feature density distance; S4, constructing a concave hull target detector for detecting sea clutter based on historical sea clutter feature samples combined with historical feature sample distance; S5, extracting multidimensional features of a unit to be detected, and performing nonlinear feature dimensionality reduction; S6, obtaining the current feature sample distance between the unit to be detected and a reference unit; S7, judging whether the unit to be detected is a target based on the concave hull target detector combined with the current feature sample distance. The proposed detection method has a higher detection success probability and is less affected by the false alarm probability.

Description

Technical Field

[0001] The present invention relates to the technical field of radar target detection, and in particular to a method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance. Background Art

[0002] Sea clutter generally refers to the backscattered echo of the sea surface under radar illumination. Against the background of sea clutter, radar detection of small targets such as boats, icebergs and frogmen is a difficult task. Due to the wide variety of small targets, their echoes often overlap with sea clutter in the frequency domain. Traditional MTI and MTD methods have limited effects and cannot be accurately distinguished by a single detection statistic. In this case, extracting and combining multiple significant features from radar echoes is considered to be an effective detection method. Unlike adaptive model detection, features usually represent certain statistical information extracted from radar echoes in an intuitive or empirical way, and have a certain ability to classify targets and sea clutter. At present, dozens of explicit, interpretable empirical features extracted from time, frequency and transform domains and many implicit, uninterpretable machine features have been applied to radar target detection.

[0003] Different features are suitable for different situations, and their complementarity is the basis for the robustness and good detection performance of feature-based detectors. The existing commonly used multi-feature target detection methods are usually based on experience, selecting multiple features to construct a multidimensional feature space, and using specific classifiers for training. These classifiers include k-nearest neighbor (KNN) algorithm, support vector machine (SVM), convex hull learning algorithm, concave hull learning algorithm, decision tree algorithm and implicit neural network, etc., to form effective detectors. Given that radar needs to detect targets under various environmental conditions, and it is extremely challenging to comprehensively collect radar echoes of all targets, feature-based target detection often turns into an outlier detection problem. When more than three types of features are used, on the one hand, algorithms such as convex hull or concave hull learning based on feature space will no longer be applicable; on the other hand, as the number of features increases, it will face the dimensionality disaster. To solve this problem, feature dimension reduction techniques such as principal component analysis (PCA), linear discriminant analysis (LDA) and feature compression can be used.

[0004] Although these methods can exploit the correlation between features, this correlation is limited to linear correlation, such as the Pearson correlation coefficient. At the same time, the feature dimensionality reduction process of these methods is linear, which is inconsistent with the nonlinear relationship between different features in actual scenarios, increasing the system error and reducing the detection performance. In addition, during the detection stage, these methods need to compare the positional relationship between the target sample and the judgment area in the three-dimensional feature space, while the target sample has a large dispersion, making it difficult to achieve stable detection. Feature extraction will also be affected by abnormal data such as sea spikes, resulting in the generation of abnormal samples. Summary of the invention

[0005] In order to solve the problems of low detection performance, difficulty in stable detection and easy generation of abnormal samples, the present invention provides a method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance.

[0006] The present invention provides a method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance, comprising the following steps:

[0007] S1, obtaining historical sea clutter data and historical target data of the radar, and extracting multi-dimensional features of the historical sea clutter data and historical target data respectively;

[0008] S2, based on the overlap of the probability density functions of the same feature under the historical sea clutter data and the historical target data, the feature density distance reflecting the classification ability of the feature in the multidimensional feature space is calculated;

[0009] S3, based on feature density distance combined with self-attention mechanism, performs nonlinear feature dimensionality reduction on multi-dimensional feature space;

[0010] S4, constructing a concave hull target detector for detecting sea clutter based on historical sea clutter feature samples combined with historical feature sample distances, wherein the historical feature sample distance is a feature sample distance between adjacent historical sea clutter samples;

[0011] S5, extracting multi-dimensional features of the unit to be detected in the current radar data, and performing non-linear feature dimensionality reduction;

[0012] S6, taking the feature samples adjacent to the unit to be detected as the reference unit, and obtaining the current feature sample distance between the unit to be detected and the reference unit;

[0013] S7, judging whether the unit to be detected is a target based on the concave hull target detector and the current feature sample distance.

[0014] Optionally, the feature density distance is calculated as follows:

[0015] ,

[0016] in, and are the joint probability density functions of the same feature under sea clutter data and target data, The value range is important The characteristic matrix on is the dimension of the feature space, is the number of elements in the multidimensional matrix, is the natural logarithm, Overlapping parameters, is the density parameter, is the degree of overlap, is the feature density distance, Overlap ratio and Each is a characteristic Probability density functions under different data sets, It is a feature The volume of multidimensional feature space under different data sets, The volume at which the peak of the overlapped portion drops to -3dB.

[0017] Optionally, when calculating the probability density function, according to Sklar's theorem, the Copula function is used to combine the marginal distribution functions of the two features into a joint probability density function, and the multi-dimensional joint probability density function is further calculated by constructing a Copula vine. The joint probability density function p(g) is calculated as follows:

[0018] ，

[0019] in, is the inverse function of the standard normal distribution function, I is the d×d dimensional identity matrix, Σ is the covariance matrix,

[0020] ,

[0021] Indicates that feature i and feature j are under the condition that The value of the Copula density function under known conditions,

[0022] ,

[0023] Representation characteristics In the condition of characteristic The marginal distribution function value under known conditions.

[0024] Optionally, the multidimensional features include 11 features, and the nonlinear feature dimensionality reduction in step S3 specifically includes:

[0025] Construct low-order polynomials for each feature;

[0026] Capture the low-order polynomial correlation between each feature based on the self-attention mechanism;

[0027] In the linear dimensionality reduction layer, a projection matrix is ​​used to map the multidimensional feature space into a three-dimensional space and output the re-expressed features;

[0028] Obtain the inverse of the feature density distance of the re-expressed feature as the loss value;

[0029] When the loss value is greater than the preset value, the parameters in the self-attention mechanism and / or the linear dimension reduction layer are updated according to the loss value combined with the gradient optimization algorithm;

[0030] When the loss value is less than the preset value, the optimal nonlinear feature dimensionality reduction is achieved.

[0031] Optionally, step S1 specifically includes extracting 11 feature data on the target unit and the sea clutter unit respectively: relative average amplitude RAA, time domain entropy value mean TEM, relative peak height RPH, relative Doppler peak height RDPH, relative Doppler vector entropy RVE, frequency domain entropy value second order moment SOFE, time-frequency ridge accumulation RI, maximum connected area size MS, number of connected areas NR, time-frequency ridge transform domain peak RRT-MV, and time-frequency ridge transform domain bandwidth RRT-BW.

[0032] Optionally, the specific calculation of the characteristic sample distance in step S4 includes:

[0033] ,

[0034] in, Represents the i-th feature sample point The coordinates of the m-th feature in the feature space.

[0035] Optionally, in step S4, the construction of the concave hull object detector specifically includes:

[0036] S4-1, extracting feature samples from sea clutter data of historical frames of the same scene, and performing nonlinear feature dimensionality reduction;

[0037] S4-2, calculating the characteristic sample distances of adjacent sea clutter samples, and sorting all the characteristic sample distances from large to small;

[0038] S4-3, obtaining the false alarm control point and calculating the false alarm probability, and multiplying the false alarm probability by the number of samples as an index, and selecting the characteristic sample distance of the corresponding sequence number as the distance threshold;

[0039] S4-4, remove the false alarm control points from the historical clutter feature samples, and then construct the concave hull decision area.

[0040] Optionally, in step S6, before the current feature sample distance, the reference unit is subjected to nonlinear feature dimensionality reduction;

[0041] In step S7, the determination of the detection unit specifically includes:

[0042] Analyze and compare the current sample distance with the threshold;

[0043] When the current sample distance is less than the threshold, the unit to be detected is determined to be clutter;

[0044] When the current sample distance is greater than the threshold, the relative positions of the reference unit sample and the concave hull decision area in the three-dimensional feature space are analyzed and compared. When the reference unit sample falls within the concave hull decision area, the unit to be detected is determined to be a target; when the reference unit sample falls outside the concave hull decision area, the unit to be detected is determined to be sea clutter.

[0045] Optionally, before step S7, a multivariate regression prediction model is constructed, which specifically includes:

[0046] Observations based on multiple historical feature samples are used as training sets;

[0047] The multivariate regression prediction model is trained based on the training set, with the input being the observation value of the historical feature sample at time t, and the output being the observation value of the historical feature sample at time t+1;

[0048] The observed values ​​of historical feature samples are input into the model, and the predicted values ​​of feature samples at the current moment are output;

[0049] The predicted value and observed value of the feature sample at the current moment are weighted and fused as the final fusion coordinate of the current feature sample.

[0050] Optionally, the prediction calculation of the feature samples in the multivariate regression prediction model specifically includes:

[0051] The coordinate prediction value of the feature sample in the feature space at time t is calculated as:

[0052] ,

[0053] in, is the coordinate prediction value of the feature sample in the feature space at time t, Features The predicted value at time t is is the coordinate observation value of the feature sample in the feature space at time tk, is the observed value of the feature at time tk, is the coefficient matrix at time k, C is the constant matrix, and p is the prediction order;

[0054] The constant term and the coefficient matrix constitute the overall coefficient matrix B;

[0055] First, arrange the N feature samples into a lag matrix Z according to the prediction order p, and arrange the Np samples from time p+1 to time N into a sample observation matrix Y, which is calculated as follows:

[0056] ，

[0057] The overall coefficient matrix B is calculated as: ，

[0058] After separating the overall coefficient matrix, we get:

[0059] ,

[0060] in, It represents the tpth row of the lag matrix Z, corresponding to the first p observations required for the feature sample at the prediction time t, is the coordinate observation value of the feature sample at time N in the feature space, C is the constant matrix, and A is the coefficient matrix.

[0061] In summary, the present invention has the following beneficial technical effects:

[0062] The feature density distance is constructed using the Copula function to quantitatively describe the classification ability of multidimensional features for targets and sea clutter. Based on this, a lightweight nonlinear dimensionality reduction network based on the self-attention mechanism is built to achieve the optimal re-expression of multidimensional features into a 3D feature space. A concave hull classifier using feature sample distance is proposed, which uses the sample distance between new features to suppress the negative impact of the dispersion of target samples in the feature space. Furthermore, the features are optimized by using multivariate autoregressive prediction to reduce the erroneous judgments introduced by abnormal feature samples. The proposed detection method has a higher probability of successful detection and is less affected by the false alarm probability. The overall detection performance is better than the existing feature-based detection method. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a flow chart of a method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to an embodiment of the present invention.

[0064] Figure 2 It is a characteristic amplitude distribution diagram on a target or sea clutter unit in an embodiment of the present invention.

[0065] Figure 3 is the B distance of the 11 features in the embodiment of the present invention.

[0066] Figure 4 is a schematic diagram of high-density area calculation in an embodiment of the present invention, where a is The calculation diagram for the smaller time is b. Schematic diagram of calculation when the value is larger.

[0067] Figure 5 is the density parameter of the embodiment of the present invention Schematic diagram of the effect with the false alarm control point.

[0068] Figure 6 It is a schematic diagram of the flow of a nonlinear dimensionality reduction method based on feature density distance measurement in an embodiment of the present invention.

[0069] Figure 7 : is the probability density curve of the characteristic sample distance between adjacent units in the embodiment of the present invention, where a is under level 5 sea conditions and b is under level 2 sea conditions.

[0070] Figure 8 : is a probability density curve of feature sample distances between adjacent units according to an embodiment of the present invention, wherein a is a sea clutter unit and b is a target unit.

[0071] Fig. 9 Schematic diagram of PAC and p-value selection in an embodiment of the present invention.

[0072] Fig.10 It is a schematic diagram of a prediction feature sample curve and a prediction error according to an embodiment of the present invention.

[0073] Fig.11 It is a schematic diagram of generating fused feature samples according to an embodiment of the present invention. DETAILED DESCRIPTION

[0074] The following is combined with Figure 1 -Attached Fig.11 The present invention is described in further detail.

[0075] Example 1

[0076] Reference Figure 1 , a method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance in this embodiment includes the following steps:

[0077] S1, obtain historical sea clutter data and historical target data of the radar, and extract multidimensional features of the historical sea clutter data and historical target data respectively; the multidimensional features in this embodiment include 11 features, specifically including: relative average amplitude RAA, time domain entropy value mean (Time domain EnTEM), relative peak height (Relative Peak Height, RPH), relative Doppler peak height (Relative Doppler Peak Height, RDPH), relative Doppler vector entropy (Relative Vector Entropy, RVE), second moment of frequency domain entropy (Second moment of Frequency domain Entropy, SOFE), time-frequency ridge accumulation (Ridge Integration, RI), maximum connected region size (Maximal Size of connected regions, MS), number of connected regions (Number of connected Regions, NR), time-frequency ridge transform domain peak value (Ridges Radon Transform Maxiumin Value, RRT-MV), time-frequency ridge transform domain bandwidth (Ridges Radon Transform Band Width, RRT-BW). Using the data of level 5 sea conditions in the SDRDSP measured data set, the 11 features introduced in Section 2.2 are extracted from the target unit and the clutter unit respectively. After normalization, the amplitude distribution characteristics are analyzed and the results are as follows: Figure 2 shown.

[0078] First, we need to quantitatively measure the classification ability of a single feature for sea clutter and targets. Here we introduce the Bhattacharyya distance (BD), which is defined as follows:

[0079] ,

[0080] Among them, p and q are the probability density functions (PDF) of the same feature under different categories of data, and g is a feature with a range of [0,1], which represents the range of a single feature. Its physical meaning is to take the logarithm and the opposite number of the proportion of the overlap of the two types of PDFs to the total, that is, the larger the overlap area of ​​the PDFs of the two types of data, the smaller the B distance, and the more difficult it is to distinguish the two categories, and vice versa.

[0081] Reference Figure 3, the B distances of 11 features to sea clutter and targets are calculated. It can be judged from the B distance that the PDF overlap degree of samples on the two types of units corresponding to various features under the same conditions is quite different. RI, RDPH, and RAA have strong resolution effects when used alone, while SOFE, MS, and NR have weaker discrimination capabilities. This is mainly because the target under this data condition is a low-speed floating target. This shows that the performance of detection is limited when relying on only one feature.

[0082] S2, based on the overlap of the probability density functions of the same feature under the historical sea clutter data and the historical target data, the feature density distance reflecting the classification ability of the feature in the multidimensional feature space is calculated;

[0083] The feature density distance is calculated as follows:

[0084] ,

[0085] in, and are the joint probability density functions of the same feature under sea clutter data and target data, The value range is important The characteristic matrix on is the dimension of the feature space, is the number of elements in the multidimensional matrix, is the natural logarithm, Overlapping parameters, is the density parameter, is the degree of overlap, is the feature density distance, Overlap ratio and Each is a characteristic Probability density functions under different data sets, It is a feature The volume of multidimensional feature space under different data sets, is the volume where the peak value of the overlapping part drops to -3dB. The calculation of the volume in this embodiment specifically involves obtaining the joint integration of p(g) and q(g).

[0086] The feature density distance is similar to the Bhattacharyya distance. Part of it is the overlap parameter, which is used to indicate the degree of overlap of the joint probability density function. Compared with the Bhattacharyya distance, which uses the logarithmic function to make meaningless and infinite-scale fine divisions of low overlap areas, The definition of can focus more on the high overlap area, give more feedback on the reduction of the overlap ratio, and better describe the classification ability brought by the overlap degree. Figure 4 is a schematic diagram of high-density area calculation in an embodiment of the present invention, where a is The calculation diagram for the smaller time is b. Schematic diagram of calculation when the characteristic density distance is large. The part is a density parameter, which is used to represent the density of the overlapping part of the two types of joint probability density functions. The multidimensional feature space volume occupied by the peak of the overlapping part drops to -3dB to quantify the degree of aggregation of samples in the overlapping area. The stronger the degree of aggregation, The smaller it is, The larger it is, the larger the feature density distance will be.

[0087] Reference Figure 5 , The significance of this parameter is that when using a classifier in the feature space, such as a concave hull-based target detector, the false alarm control points in the overlapping area will be eliminated during the concave hull construction process. The more concentrated the sample density is, the easier it is for the target sample to escape from the concave hull and be correctly detected.

[0088] In the process of calculating the feature density distance, there is a problem similar to the Bhattacharyya distance, that is, the calculation of the joint probability density function. Therefore, when calculating the probability density function, according to Sklar's theorem, the Copula function is used to combine the marginal distribution functions of the two features into a joint probability density function, and the multi-dimensional joint probability density function is further calculated by constructing the Copula vine. The joint probability density function p(g) is calculated as follows:

[0089] ，

[0090] in, is the inverse function of the standard normal distribution function, I is the d×d dimensional identity matrix, Σ is the covariance matrix,

[0091] ,

[0092] Indicates that feature i and feature j are under the condition that The value of the Copula density function under known conditions,

[0093] ,

[0094] Representation characteristics In the condition of characteristic The marginal distribution function value under known conditions.

[0095] In summary, the feature density distance A higher value can be obtained when the overlap ratio of the two types of joint probability density functions is small and the overlap density is high. Through the nonlinear weighting of the two parameters, their mutual influence is realized. For example, when the overlap ratio is very low, the influence of the overlap density is reduced, and when the overlap ratio is very high, the influence of the overlap density is automatically amplified. At this point, the problem of nonlinear dimensionality reduction of features becomes how to reduce the feature dimension and achieve the feature density distance of the new feature. of maximization.

[0096] S3, based on feature density distance combined with self-attention mechanism, performs nonlinear feature dimensionality reduction on multi-dimensional feature space; refer to Figure 6 , specifically including:

[0097] Construct low-order polynomials for each feature;

[0098] Capture the low-order polynomial correlation between each feature based on the self-attention mechanism;

[0099] In the linear dimensionality reduction layer, a projection matrix is ​​used to map the multidimensional feature space into a three-dimensional space and output the re-expressed features;

[0100] Obtain the inverse of the feature density distance of the re-expressed feature as the loss value;

[0101] When the loss value is greater than the preset value, the parameters in the self-attention mechanism and / or the linear dimension reduction layer are updated according to the loss value combined with the gradient optimization algorithm;

[0102] When the loss value is less than the preset value, the optimal nonlinear feature dimensionality reduction is achieved.

[0103] S4, based on the historical sea clutter feature samples combined with the historical feature sample distance, a concave hull target detector for detecting sea clutter is constructed. The historical feature sample distance is the feature sample distance between adjacent historical sea clutter samples; the multidimensional feature vector can essentially be regarded as the coordinate value of the sample point in the multidimensional feature space, and the feature sequence of adjacent distance units can essentially be regarded as two time series that change with time at the same time, so the feature sample distance can be calculated between two adjacent feature samples at the same time. In this paper, the Euclidean distance between sample points is defined as the feature sample distance.

[0104] The specific calculation of feature sample distance includes:

[0105] ,

[0106] in, Represents the i-th feature sample point The coordinates of the m-th feature in the feature space.

[0107] like Figure 7It is the probability density curve of the feature sample distance between adjacent units in the embodiment of the present invention, where a is under level 5 sea conditions and b is under level 2 sea conditions. The feature sample distance between two fixed feature sample points in the multidimensional space shows completely different distribution modes with the different dimensions of the feature space. Using the data of level 5 sea conditions in the SDRDSP measured data set, 11 features are extracted and normalized on the target unit and the clutter unit respectively, and two fixed samples are selected on the target unit and the clutter unit respectively. Different numbers of multiple features are combined into a multidimensional feature space, and their feature sample distances are calculated.

[0108] It can be concluded that with the increase of dimension, the characteristic sample distance of both clutter samples and target samples becomes more dispersed, and the discrimination gradually weakens. This is our most intuitive explanation of the "dimensionality curse", that is, high-dimensional features blur the separability between samples while bringing information. Through calculation, it can be concluded that the characteristic sample distance of target samples is significantly more affected by the increase of dimension. The degree of aggregation of clutter samples in low-dimensional feature space is higher than that of target samples. By observing the probability density function of feature distance in feature space of different dimensions, it can be found that the sample distance in 3D feature space is in a stable period from too aggregated to too dispersed, and at the same time, it maintains a good degree of aggregation, so the characteristic sample distance can be considered as one of the bases for classification of targets and sea clutter.

[0109] like Figure 8 It is the probability density curve of the characteristic sample distance between adjacent units of the embodiment of the present invention, where a is the sea clutter unit and b is the target unit. By statistically analyzing the characteristic sample distances in the three cases, it can be seen that when the adjacent units are samples of the same type, because they can be regarded as stable and continuous data, their sample characteristic distance is small, and the probability density function is more clustered; when the adjacent units are target samples and clutter samples, respectively, the sample distance will rise sharply, and the overlap with the probability density function of the first case is very small. And the better the sea conditions, the more obvious this situation is. Therefore, in the three-dimensional feature space, the use of the characteristic sample distances of adjacent units can effectively judge the similarities and differences of feature categories.

[0110] The construction of the concave hull object detector specifically includes:

[0111] S4-1, extracting feature samples from sea clutter data of historical frames of the same scene, and performing nonlinear feature dimensionality reduction;

[0112] S4-2, calculating the characteristic sample distances of adjacent sea clutter samples, and sorting all the characteristic sample distances from large to small;

[0113] S4-3, obtaining the false alarm control point and calculating the false alarm probability, and multiplying the false alarm probability by the number of samples as an index, and selecting the characteristic sample distance of the corresponding sequence number as the distance threshold;

[0114] S4-4, remove the false alarm control points from the historical clutter feature samples, and then construct the concave hull decision area.

[0115] S5, extracting multi-dimensional features of the unit to be detected in the current radar data, and performing non-linear feature dimensionality reduction;

[0116] S6, taking the feature samples adjacent to the unit to be detected as the reference unit, performing nonlinear feature dimensionality reduction on the reference unit, and obtaining the current feature sample distance between the unit to be detected and the reference unit;

[0117] S7, judging whether the unit to be detected is a target based on the concave hull target detector and the current feature sample distance. The judgment of the detection unit specifically includes:

[0118] Analyze and compare the current sample distance with the threshold;

[0119] When the current sample distance is less than the threshold, the unit to be detected is determined to be clutter;

[0120] When the current sample distance is greater than the threshold, the relative positions of the reference unit sample and the concave hull judgment area in the three-dimensional feature space are analyzed and compared. When the reference unit sample falls within the concave hull judgment area, the unit to be detected is determined to be a target; when the reference unit sample falls outside the concave hull judgment area, the unit to be detected is determined to be sea clutter. The feature samples of small targets at sea at the same time generally do not span distance units, so the reference unit of the distance unit where the small target is located is generally a sea clutter unit.

[0121] There is a possibility of false alarm here, that is, although the reference unit sample is judged as clutter, its true category is a relatively scattered target sample. At this time, due to the large distance of the feature sample, the clutter of the unit to be detected is judged as a target, resulting in a false alarm. However, the selection of the reference unit and the unit to be detected is mutual. When the original reference unit is used as the unit to be detected for detection, it will also be judged as a target, and the adjacent targets will be combined into a larger target across the distance unit, thus offsetting the negative effects of such false alarms.

[0122] The detection decision of the target in the feature space is converted into the detection decision of the clutter. Although the sea clutter samples are less dispersed than the target samples in the feature space, they are more likely to produce a small number of singular points due to actual scene problems such as sea peaks, and they are out of the clutter concave area, forming false alarms. This situation is particularly obvious when extracting feature samples from short pulse time series, which will cause the feature variance to increase. Therefore, before step S7, it also includes constructing a multivariate regression prediction model, which specifically includes:

[0123] Observations based on multiple historical feature samples are used as training sets;

[0124] The multivariate regression prediction model is trained based on the training set, with the input being the observation value of the historical feature sample at time t, and the output being the observation value of the historical feature sample at time t+1;

[0125] The observed values ​​of historical feature samples are input into the model, and the predicted values ​​of feature samples at the current moment are output;

[0126] The predicted value and observed value of the feature sample at the current moment are weighted and fused as the final fusion coordinate of the current feature sample, such as Fig.11 shown.

[0127] The prediction calculation of feature samples in the multivariate regression prediction model specifically includes:

[0128] The coordinate prediction value of the feature sample in the feature space at time t is calculated as:

[0129] ,

[0130] in, is the coordinate prediction value of the feature sample in the feature space at time t, Features The predicted value at time t is is the coordinate observation value of the feature sample in the feature space at time tk, Features The observed value at time tk, is the coefficient matrix at time k, C is the constant matrix, and p is the prediction order;

[0131] Before fitting the coefficient matrix to the autoregressive model, it is necessary to determine the prediction order p of the fitting model. The applicable AR model order can be determined by the partial autocorrelation coefficient (PAC) of the feature sequence. PAC (expressed as ) is defined as:

[0132] ,

[0133] Where E() represents expectation, PAC is the ratio of conditional autocovariance function to conditional variance, which is actually the conditional autocorrelation coefficient. Calculate the PAC value of the characteristic sequence, and find the lag order at which the PAC value first becomes insignificant as the prediction order p. Here, a PAC value below 0 is defined as insignificant.

[0134] Reference Fig. 9 , which is the PAC curve corresponding to the three new features obtained after nonlinear dimensionality reduction. It can be seen that their respective prediction orders p are similar, so the maximum insignificant point is taken as the prediction order.

[0135] The constant term and the coefficient matrix constitute the overall coefficient matrix B;

[0136] First, arrange the N feature samples into a lag matrix Z according to the prediction order p, and arrange the Np samples from time p+1 to time N into a sample observation matrix Y, which is calculated as follows:

[0137] ,

[0138] The overall coefficient matrix B is calculated as: ,

[0139] After separating the overall coefficient matrix, we get:

[0140] ,

[0141] in, represents the tpth row of the lag matrix Z, corresponding to the first p observations required for the feature sample at the prediction time t, is the coordinate observation value of the feature sample in the feature space at time N, C is the constant matrix, and A is the coefficient matrix.

[0142] Reference Fig.10 , the prediction effect of the algorithm is predicted using the measured data, and the results are shown in the figure. It can be seen that the error between the predicted value curve of each feature sample and the observed sequence is small, proving that its prediction effect is good.

[0143] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. As for the method disclosed in the embodiment, since it corresponds to the system disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0144] Professionals may further appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

Claims

1. A method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance, characterized in that: The following steps are involved: S1, obtaining historical sea clutter data and historical target data of the radar, and extracting multi-dimensional features of the historical sea clutter data and historical target data respectively; S2, based on the overlap of the probability density functions of the same feature under the historical sea clutter data and the historical target data, the feature density distance reflecting the classification ability of the feature in the multidimensional feature space is calculated; S3, based on feature density distance combined with self-attention mechanism, performs nonlinear feature dimensionality reduction on multi-dimensional feature space; S4, constructing a concave hull target detector for detecting sea clutter based on historical sea clutter feature samples combined with historical feature sample distances, wherein the historical feature sample distance is a feature sample distance between adjacent historical sea clutter samples; S5, extracting multi-dimensional features of the unit to be detected in the current radar data, and performing non-linear feature dimensionality reduction; S6, taking the feature samples adjacent to the unit to be detected as the reference unit, and obtaining the current feature sample distance between the unit to be detected and the reference unit; S7, judging whether the unit to be detected is a target based on the concave hull target detector and the current feature sample distance.

2. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 1, characterized in that: The feature density distance is calculated as follows: ， in, and are the joint probability density functions of the same feature under sea clutter data and target data, The value range is important The characteristic matrix on is the dimension of the feature space, is the number of elements in the multidimensional matrix, is the natural logarithm, Overlapping parameters, is the density parameter, is the degree of overlap, is the feature density distance, Overlap ratio and Each is a characteristic Probability density functions under different data sets, It is a feature The volume of multidimensional feature space under different data sets, The volume at which the peak of the overlapped portion drops to -3dB.

3. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 2, characterized in that: When calculating the probability density function, according to Sklar's theorem, the Copula function is used to combine the marginal distribution functions of the two features into a joint probability density function, and the multi-dimensional joint probability density function is further calculated by constructing the Copula vine. The joint probability density function p(g) is calculated as follows: ， in, is the inverse function of the standard normal distribution function, I is the d×d dimensional identity matrix, Σ is the covariance matrix, ， Indicates that feature i and feature j are under the condition that The value of the Copula density function under known conditions, ， Representation characteristics In the condition of characteristic The marginal distribution function value under known conditions.

4. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 1, characterized in that: The multidimensional features include 11 features, and the nonlinear feature dimensionality reduction in step S3 specifically includes: Construct low-order polynomials for each feature; Capture the low-order polynomial correlation between each feature based on the self-attention mechanism; In the linear dimensionality reduction layer, a projection matrix is ​​used to map the multidimensional feature space into a three-dimensional space and output the re-expressed features; Obtain the inverse of the feature density distance of the re-expressed feature as the loss value; When the loss value is greater than the preset value, the parameters in the self-attention mechanism and / or the linear dimension reduction layer are updated according to the loss value combined with the gradient optimization algorithm; When the loss value is less than the preset value, the optimal nonlinear feature dimensionality reduction is achieved.

5. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 4, characterized in that: In step S1, specifically, 11 characteristic data are extracted on the target unit and the sea clutter unit respectively: relative average amplitude RAA, time domain entropy value mean TEM, relative peak height RPH, relative Doppler peak height RDPH, relative Doppler vector entropy RVE, frequency domain entropy value second order moment SOFE, time-frequency ridge accumulation RI, maximum connected area size MS, number of connected areas NR, time-frequency ridge transform domain peak RRT-MV, time-frequency ridge transform domain bandwidth RRT-BW.

6. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 1, characterized in that: The specific calculation of the characteristic sample distance in step S4 includes: ， in, Represents the i-th feature sample point The coordinates of the mth feature in the feature space.

7. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 1, characterized in that: In step S4, the construction of the concave hull target detector specifically includes: S4-1, extracting feature samples from sea clutter data of historical frames of the same scene, and performing nonlinear feature dimensionality reduction; S4-2, calculating the characteristic sample distances of adjacent sea clutter samples, and sorting all the characteristic sample distances from large to small; S4-3, obtaining the false alarm control point and calculating the false alarm probability, and multiplying the false alarm probability by the number of samples as an index, and selecting the characteristic sample distance of the corresponding sequence number as the distance threshold; S4-4, remove the false alarm control points from the historical clutter feature samples, and then construct the concave hull decision area.

8. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 7, characterized in that: In step S6, before the current feature sample distance, the reference unit is subjected to nonlinear feature dimensionality reduction; In step S7, the determination of the detection unit specifically includes: Analyze and compare the current sample distance with the threshold; When the current sample distance is less than the threshold, the unit to be detected is determined to be clutter; When the current sample distance is greater than the threshold, the relative positions of the reference unit sample and the concave hull decision area in the three-dimensional feature space are analyzed and compared. When the reference unit sample falls within the concave hull decision area, the unit to be detected is determined to be a target; when the reference unit sample falls outside the concave hull decision area, the unit to be detected is determined to be sea clutter.

9. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 1, characterized in that: Before step S7, the method further includes constructing a multivariate regression prediction model, which specifically includes: Observations based on multiple historical feature samples are used as training sets; The multivariate regression prediction model is trained based on the training set, with the input being the observation value of the historical feature sample at time t, and the output being the observation value of the historical feature sample at time t+1; The observed values ​​of historical feature samples are input into the model, and the predicted values ​​of feature samples at the current moment are output; The predicted value and observed value of the feature sample at the current moment are weighted and fused as the final fusion coordinate of the current feature sample.

10. The method for detecting small targets at sea based on nonlinear dimensionality reduction and feature sample distance according to claim 8, characterized in that: The prediction calculation of feature samples in the multivariate regression prediction model specifically includes: The coordinate prediction value of the feature sample in the feature space at time t is calculated as: ， in, is the coordinate prediction value of the feature sample in the feature space at time t, Features The predicted value at time t is is the coordinate observation value of the feature sample in the feature space at time tk, Features The observed value at time tk, is the coefficient matrix at time k, C is the constant matrix, and p is the prediction order; The constant term and the coefficient matrix constitute the overall coefficient matrix B; First, arrange the N feature samples into a lag matrix Z according to the prediction order p, and arrange the Np samples from time p+1 to time N into a sample observation matrix Y, which is calculated as follows: ， The overall coefficient matrix B is calculated as: , After separating the overall coefficient matrix, we get: ， in, represents the tpth row of the lag matrix Z, corresponding to the first p observations required for the feature sample at the prediction time t, is the coordinate observation value of the feature sample in the feature space at time N, C is the constant matrix, and A is the coefficient matrix.

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