Radar track target classification method based on statistical knowledge and neural network

Abstract

The invention discloses a radar track target classification method based on statistical knowledge and a neural network, and the method comprises the steps: collecting original track data, and carrying out the marking and cleaning processing, and obtaining a standard track data set; extracting kinematics, bistatic radar cross section and track morphological features based on the standard track data set, and constructing an original feature set; performing feature weight learning through a neighborhood component analysis method, and screening according to a preset weight threshold to obtain an effective feature subset; performing statistical distribution analysis on the effective feature subsets according to target categories, determining significant features of each target category, and setting a threshold interval; performing preliminary classification based on a statistical knowledge classifier, and determining whether the to-be-classified track is an easily-classified sample or a difficultly-classified sample through a category discrimination function; and classifying the samples difficult to classify based on a back propagation neural network classifier, outputting the probability value of each target category through a neural network model, and taking the target category with the maximum probability value as a final classification result. According to the invention, the target classification accuracy and real-time performance can be improved.

Description

Technical Field

[0001] This application relates to the field of radar signal processing technology, and relates to, but is not limited to, a radar track target classification method based on statistical knowledge and neural networks. Background Technology

[0002] With the continuous opening and utilization of low-altitude airspace, the demand for target monitoring in low-altitude airspace continues to increase. As a primary detection method, radar systems play an important role in air traffic management, air defense early warning, and bird flock monitoring. Among these, target classification based on radar track data is of paramount importance.

[0003] In existing technologies, target recognition is often accomplished using a single feature or a single classifier. For example, kinematic features such as velocity and acceleration, or radar cross-section features, are used to distinguish different types of targets. However, in complex low-altitude environments, the motion states and echo characteristics of general aviation aircraft, birds, and other small targets are quite similar, and a single feature is often insufficient to guarantee the accuracy and robustness of classification. Existing target classification based on radar track data mainly relies on traditional statistical threshold discrimination methods. Although this method has low computational cost and is simple to implement, it is prone to misclassification or missed classification when the feature intervals between target categories overlap. In addition, classification methods based on machine learning or neural networks can uncover nonlinear relationships between complex features, but they are highly sensitive to the amount of training data and feature selection. Furthermore, in practical applications, they have high computational complexity and poor real-time performance. Moreover, when traditional neural network classifiers lack effective prior screening, they are easily affected by redundant features and noisy data, resulting in slow model convergence and poor generalization performance.

[0004] Therefore, there is an urgent need for a more comprehensive and accurate radar track target classification method to solve the problems of insufficient feature utilization, insufficient accuracy, limited discrimination reliability and insufficient real-time performance of existing classification methods in low-altitude target classification, so as to achieve a significant improvement in the accuracy and real-time performance of radar track target classification. Summary of the Invention

[0005] This application provides a radar track target classification method based on statistical knowledge and neural networks.

[0006] The technical solution of this application embodiment is implemented as follows: In a first aspect, embodiments of this application provide a radar track target classification method based on statistical knowledge and neural networks. The method includes: collecting raw track data of low-altitude airspace targets using a passive radar system; labeling and removing abnormal track data from the raw track data to obtain a standard track dataset; extracting kinematic features, bistatic radar cross section features, and track morphology features from all track points in each track of the standard track dataset to construct an original feature set; learning feature weights for each dimension of the original feature set using neighborhood component analysis to obtain the importance weights of each feature dimension, and filtering them according to a preset weight threshold to obtain an effective feature subset; and performing statistical distribution analysis on the effective feature subset according to target categories to determine... Define the salient features of each target category and set a threshold range for each salient feature; obtain the effective feature vector of the track to be classified, determine the discriminant function value of each salient feature in each target category, and combine the discriminant functions of each salient feature according to a preset logical combination rule to obtain the category discriminant function value of each target category; determine whether the track to be classified can be classified based on the category discriminant function value of each target category, output the classification result of easy-to-classify samples, and pass the difficult-to-classify samples to the backpropagation neural network classifier; construct a neural network model and train the model, input the feature vector of the difficult-to-classify samples into the trained neural network model to perform forward propagation calculation, output the probability value of each target category, and take the target category with the highest probability value as the final classification result.

[0007] The technical solution provided in this application acquires raw track data of low-altitude targets using a passive radar system, labels and removes abnormal track data from the raw track data to obtain a standard track dataset. This clarifies the correspondence between feature vectors and category labels, providing a reliable foundation for subsequent feature extraction and target classification, and improving overall classification accuracy. Based on all track points in each track of the standard track dataset, kinematic features, bistatic radar cross section features, and track morphology features are extracted to construct an original feature set. This addresses the limited descriptive power of single-type features, significantly enhancing the richness and discriminative power of feature representation. For each dimension of the original feature set, feature weights are learned using neighborhood component analysis to obtain the importance weights of each feature dimension. These weights are then filtered according to a preset weight threshold to obtain an effective feature subset, significantly reducing the feature space dimension and providing refined and highly discriminative feature inputs for subsequent classification processing, thus improving the efficiency of subsequent classification. The effective feature subset is then categorized according to target class. Instead of performing statistical distribution analysis to determine the salient features of each target category, a salient feature threshold range is set for each salient feature, enabling most easily classifiable samples to be efficiently classified through fast logical discrimination, significantly reducing the computational burden on the neural network. Effective feature vectors of the tracks to be classified are obtained, and the discriminant function values ​​of each salient feature in each target category are determined. These discriminant functions are then combined using preset logical combination rules to obtain the category discriminant function value for each target category. Based on the category discriminant function value for each target category, it is determined whether the track to be classified can be classified, outputting the classification results for easily classifiable samples, and passing the difficult-to-classify samples to the backpropagation neural network classifier for refined processing. A neural network model is constructed and trained. The feature vectors of the difficult-to-classify samples are input into the trained neural network model to perform forward propagation calculations, outputting the probability values ​​of each target category. The target category with the highest probability value is taken as the final classification result, thereby significantly improving the overall classification accuracy and robustness. The technical solution provided in this application adopts feature selection and hierarchical classification structure, which can maintain stable performance under conditions of uneven sample distribution or noise interference. It has strong adaptability and practicality, and can bring about a significant improvement in accuracy and efficiency in practical applications, thus having outstanding promotional value.

[0008] Optionally, the original track data includes general aviation aircraft track data, bird track data, and other target track data. The step of labeling and removing abnormal track data from the original track data to obtain a standard track dataset includes: initially labeling the original track data using Automatic Dependent Surveillance Broadcast (ADS) signals; classifying track data not associated with ADS signals through long-term observation and manual assistance to distinguish between general aviation aircraft, birds, and other targets; and removing unreliable and redundant track data from the labeled track data to obtain the standard track dataset, which includes a feature vector and corresponding category label for each track.

[0009] Optionally, based on all track points in each track in the standard track dataset, kinematic features, bistatic radar cross section features, and track morphology features are extracted to construct an original feature set, including: for each track in the standard track dataset, six kinematic features are calculated for the distance, velocity, and acceleration of each track point in each track, including mean, variance, interquartile range, equivalent mode, skewness, and kurtosis, and these are combined with the six statistical features corresponding to the distance, velocity, and acceleration to construct an 18-dimensional kinematic feature sub-vector; and the kinematic feature sub-vector is calculated based on the bistatic radar equation. For each track point, a bistatic radar cross section (BRS) is calculated, and six bistatic RRS features—mean, variance, interquartile range, equivalent mode, skewness, and kurtosis—are calculated for each BRS to construct a 6-dimensional bistatic RRS feature sub-vector. The jitter and clustering of the track are calculated and combined to construct a 2-dimensional morphological feature sub-vector. The 18-dimensional kinematic feature sub-vector, the 6-dimensional bistatic RRS feature sub-vector, and the 2-dimensional morphological feature sub-vector are concatenated to generate the original feature set.

[0010] Optionally, for each feature dimension in the original feature set, feature weight learning is performed based on neighborhood component analysis to obtain the importance weight of each feature dimension, and a subset of effective features is obtained by filtering according to a preset weight threshold. This includes: performing max-min normalization on each feature dimension in the original feature set to obtain normalized features; defining a diagonal weighted matrix; and defining a weighted distance metric based on the diagonal weighted matrix, where each diagonal element of the diagonal weighted matrix represents the weight of the corresponding feature dimension; and transforming the hard discrimination in traditional nearest neighbor classification into a weighted distance classification based on the weighted distance metric. The process involves a soft discrimination of probabilities, determining the probability that each sample is selected as a nearest neighbor by the other samples, and then determining the probability that each sample is correctly classified based on these nearest neighbor probabilities. An objective function is constructed based on these nearest neighbor probabilities, and an L2 regularization term is introduced into the objective function. The objective function is then optimized using a gradient ascent algorithm to obtain the importance weights for each feature dimension. The objective function aims to maximize the expected number of correctly classified samples. Finally, features with importance weights higher than a preset weight threshold are selected from the original feature set to form an effective feature subset.

[0011] Optionally, the step of performing statistical distribution analysis on the effective feature subset according to the target category to determine the salient features of each target category and setting salient feature threshold intervals for each salient feature includes: dividing the training dataset into multiple subsets according to the target category, with each subset corresponding to a target category; for each feature in the effective feature subset, calculating the distribution statistics of each feature on each target category subset, the distribution statistics including the median, upper quartile, and lower quartile, and calculating the box plot beard range of each feature under each target category based on the median, the upper quartile, and the lower quartile; determining the degree of overlap of the box plot beard ranges of each feature under different target categories, and filtering salient features with high discriminative power for specific target categories; setting corresponding salient feature threshold intervals for each salient feature determined for each target category, the salient feature threshold intervals being determined based on the statistical distribution range of the corresponding salient feature under the corresponding target category; constructing a correspondence list between salient features and salient feature threshold intervals for each target category, and constructing a discrimination rule base for a statistical knowledge classifier based on the correspondence list.

[0012] Optionally, easily classifiable and difficult-to-classify samples are determined through the following process: Based on the list of salient features corresponding to each target category, calculate the discriminant function value of each salient feature, and determine whether the feature measurement value is within the salient feature threshold range based on the discriminant function value; combine the discriminant function values ​​of all salient features of each target category according to a preset logical combination rule to obtain the category discriminant function value of each target category; determine whether the track to be classified can be classified based on the category discriminant function value of each target category, wherein the track to be classified is an easily classifiable sample if and only if the category discriminant function value of one target category is true, and the track to be classified is marked as a difficult-to-classify sample if there is no target category or the category discriminant function values ​​of multiple target categories are true; output the classification result of the easily classifiable sample, the classification result of the easily classifiable sample is the target category corresponding to the easily classifiable sample, and pass the difficult-to-classify sample to the backpropagation neural network classifier.

[0013] Optionally, the step of constructing and training a neural network model, inputting the feature vectors of difficult-to-classify samples into the trained neural network model to perform forward propagation calculation, outputting the probability values ​​of each target category, and taking the target category with the highest probability value as the final classification result, includes: constructing a neural network model, wherein the input vector of the neural network model is a subset of effective features, and the output vector is the probability distribution of each target category; inputting the feature vectors of difficult-to-classify samples into the neural network model to perform forward propagation calculation, outputting the probability distribution through nonlinear transformations of the weight matrix, bias vector, and activation function between layers, calculating the error between the output of the neural network model and the true label through a preset loss function, wherein the preset loss function adopts the cross-entropy loss function; calculating the gradient of the preset loss function with respect to the parameters of each layer through the backpropagation algorithm, and updating the network weights and network bias parameters based on the gradient descent method, and the model training process adopts an early stopping strategy, terminating the training when the preset loss function value on the validation set no longer decreases; and performing a single forward propagation calculation on the feature vectors of difficult-to-classify samples through the trained neural network model, outputting the probability values ​​of each target category, and taking the target category with the highest probability value as the final classification result.

[0014] Secondly, embodiments of this application provide an electronic device, including a memory and a processor. The memory stores a computer program that can run on the processor. When the processor executes the program, it implements the steps in the aforementioned radar track target classification method based on statistical knowledge and neural networks.

[0015] Thirdly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps in the aforementioned radar track target classification method based on statistical knowledge and neural networks.

[0016] The beneficial effects of the technical solutions provided in this application include at least the following: This application provides a radar track target classification method based on statistical knowledge and neural networks. It collects raw track data of low-altitude targets using a passive radar system, labels and removes abnormal track data to obtain a standard track dataset. This clarifies the correspondence between feature vectors and category labels, providing a reliable foundation for subsequent feature extraction and target classification, and improving overall classification accuracy. Based on all track points in each track of the standard track dataset, kinematic features, bistatic radar cross section features, and track morphology features are extracted to construct an original feature set. This addresses the limited descriptive power of single-type features, significantly enhancing the richness and discriminative power of feature representation. For each dimension of the original feature set, feature weights are learned using neighborhood component analysis to obtain the importance weights of each feature dimension. These weights are then filtered according to a preset weight threshold to obtain an effective feature subset, significantly reducing the feature space dimensionality and providing refined and highly discriminative feature inputs for subsequent classification processing, thus improving the efficiency of subsequent classification. The effective feature subset is statistically distributed according to the target category to determine the salient features of each target category. A salient feature threshold range is set for each salient feature, enabling most easily classifiable samples to be efficiently classified through fast logical discrimination, significantly reducing the computational burden on the neural network. Effective feature vectors of the track to be classified are obtained, and the discriminant function values ​​of each salient feature in each target category are determined. These discriminant functions are then combined according to a preset logical combination rule to obtain the category discriminant function value for each target category. Based on the category discriminant function value for each target category, it is determined whether the track to be classified can be classified, outputting the classification results for easily classifiable samples. Difficult samples are passed to the backpropagation neural network classifier for refined processing. A neural network model is constructed and trained. The feature vectors of difficult samples are input into the trained neural network model to perform forward propagation calculations, outputting the probability values ​​of each target category. The target category with the highest probability value is taken as the final classification result, thereby significantly improving the overall classification accuracy and robustness. The technical solution provided in this application adopts feature selection and hierarchical classification structure, which can maintain stable performance under conditions of uneven sample distribution or noise interference. It has strong adaptability and practicality, and can bring about a significant improvement in accuracy and efficiency in practical applications, thus having outstanding promotional value. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1 A flowchart illustrating a radar track target classification method based on statistical knowledge and neural networks, provided for an embodiment of this application; Figure 2 A detailed schematic diagram illustrating feature selection and target classification provided in an embodiment of this application; Figure 3 This is a schematic diagram of the hardware entity of an electronic device provided in an embodiment of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0020] It should be noted that the terms "first, second, and third" used in the embodiments of this application are merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first, second, and third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0021] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of this application pertain. It should also be understood that terms such as those defined in general dictionaries should be understood to have a meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0022] The embodiments of this application will be further described below with reference to the accompanying drawings.

[0023] In view of the current problems in the research on radar track target classification in the field of radar signal processing technology, this application provides a radar track target classification method based on statistical knowledge and neural networks.

[0024] The technical solution of this application is described below, starting with the method embodiments.

[0025] Please refer to Figure 1 It illustrates a flowchart of a radar track target classification method based on statistical knowledge and neural networks provided in an embodiment of this application, such as... Figure 1 As shown, the method includes at least the following steps S110 to S160.

[0026] Step S110: Collect raw track data of low-altitude airspace targets through a passive radar system, label and remove abnormal track data from the raw track data to obtain a standard track dataset.

[0027] In this embodiment, a passive radar system using digital terrestrial multimedia broadcasting (DTMB) collects track data of targets in low-altitude airspace to obtain raw track data. This raw track data mainly includes three categories: general aviation aircraft track data, bird track data, and other target track data. The other target track data includes vehicle track data, wind turbine track data, pedestrian track data, etc. Further, the raw track data is labeled, and abnormal track data is removed to obtain a standard track dataset. Specifically, each track data in the raw track data is initially labeled using Automatic Dependent Surveillance Broadcast (ADSB) signals. For track data not associated with ADSB signals, i.e., track data not initially labeled using ADSB signals, long-term observation and manual assistance are used to classify the unlabeled track data, thereby distinguishing general aviation aircraft, birds, and other targets in the raw track data. In addition, for the labeled track data, abnormal track data, including unreliable track data and redundant track data, are identified and removed, finally obtaining a standard track dataset. This standard track dataset includes the feature vector and corresponding category label for each track. The expression formula for this standard track dataset is shown in the following formula: ; In the formula, Represents a standard track dataset; Indicates the total number of track data; Indicates the first The feature vector corresponding to each track data; , Indicates the first The category labels corresponding to each track data point are General Aviation Aircraft (GAA), Birds, and Others.

[0028] Step S120: Based on all track points in each track in the standard track dataset, extract kinematic features, bistatic radar cross section features, and track morphology features to construct an original feature set.

[0029] In this embodiment of the application, the standard track dataset contains Data on each flight path, where each flight path contains For each track point in the standard track dataset, kinematic features, bistatic radar cross section features, and track morphology features are extracted to construct the original feature set. Specifically, for each track in the standard track dataset, six kinematic features are calculated for the distance, velocity, and acceleration of each track point in each track: mean, variance, interquartile range, equivalent mode, skewness, and kurtosis. The waypoints, of which the ... The distance between each waypoint is This distance is the absolute distance from the radar to the trackpoint. The speed of each waypoint is , No. The acceleration of each waypoint is For each trackpoint in each track, six kinematic features are extracted based on its distance, velocity, and acceleration. Specifically, for distance, the calculation formulas for the six distance features—mean, variance, interquartile range, equivalent mode, skewness, and kurtosis—are expressed as follows: ; In the formula, The mean of the distance; Represents the variance of the distance; Interquartile range (interquartile range) represents distance; The equivalent mode representing distance; Indicates the skewness of the distance; Kurtosis representing distance; The mean of the distance; This represents the total number of waypoints in each waypoint; Indicates the first Distance between waypoints; Represents the variance of the distance; Interquartile range (interquartile range) represents distance; This represents the 75th percentile of the distance value; This represents the 25th percentile of the distance value; The equivalent mode representing distance; This represents the group of distance values ​​with the largest number of samples after binning, i.e., the group containing the mode of the distance values; This represents the arithmetic mean. Indicates the skewness of the distance; This represents the expectation operation; The standard deviation of distance; Kurtosis representing distance; For defining symbols. Similarly, for velocity, the calculation formulas for its six velocity characteristics—mean, variance, interquartile range, equivalent mode, skewness, and kurtosis—are expressed by the following formulas: ; In the formula, The average value of the velocity; Represents the variance of velocity; The interquartile range representing velocity; The equivalent mode representing speed; Indicates the skewness of velocity; Kurtosis, representing velocity; The mean value of speed, i.e., average speed; Indicates the first The speed of each track point; Represents the variance of velocity; The interquartile range representing velocity; This represents the 75th percentile of the velocity value; This represents the 25th percentile of the velocity value; The equivalent mode representing speed; This represents the group of velocity values ​​with the largest number of samples after binning, i.e., the group containing the mode of the velocity values; Indicates the skewness of velocity; The standard deviation of velocity; Kurtosis represents velocity. Similarly, for acceleration, the six acceleration characteristics—mean, variance, interquartile range, equivalent mode, skewness, and kurtosis—are calculated using the following formulas: ; In the formula, This represents the mean value of acceleration. Represents the variance of acceleration; The interquartile range representing acceleration; The equivalent mode representing acceleration; Indicates the skewness of acceleration; Kuness of acceleration; This represents the mean value of acceleration. Indicates the first The acceleration of each track point; Represents the variance of acceleration; The interquartile range representing acceleration; This represents the 75th percentile of the acceleration value; This represents the 25th percentile of the acceleration value; The equivalent mode representing acceleration; This represents the group of acceleration values ​​with the largest number of samples after binning, i.e., the group containing the mode of the acceleration values; Indicates the skewness of acceleration; The standard deviation of acceleration; This represents the kurtosis of acceleration. Furthermore, the six statistical features corresponding to distance, velocity, and acceleration are combined to construct an 18-dimensional kinematic feature sub-vector. .

[0030] In this embodiment, for each track in the standard track dataset, the bistatic radar cross section (BRS) of each track point in each track is calculated according to the bistatic radar equation. For each BRS, six bistatic radar cross section features—mean, variance, interquartile range, equivalent mode, skewness, and kurtosis—are calculated to construct a 6-dimensional bistatic radar cross section feature sub-vector. Specifically, for each track... The waypoints, of which the ... The formula for calculating the bistatic radar cross section of a single track point is expressed by the following formula: ; In the formula, Indicates the first Bistatic radar cross section of each track point; Indicates system parameters, , Represents the Boltzmann constant. Indicates the noise temperature. Indicates signal bandwidth. This represents the noise figure of the radar receiver. Indicates system loss. Indicates the transmission power. Indicates the transmit antenna gain. Indicates the receiving antenna gain. Indicates the emission pattern factor; Indicates the receive pattern factor. Indicates the wavelength of the transmitted signal; Indicates the first The distance from each track point to the receiving antenna; Indicates the first The distance from each track point to the transmitting antenna; Indicates the first The signal-to-noise ratio of the received signal at each track point. Furthermore, for each bistatic radar cross section... Calculate the six statistical characteristics and bistatic radar cross section respectively. The formulas for calculating the six bistatic radar cross-section characteristics—mean, variance, interquartile range, equivalent mode, skewness, and kurtosis—are similar to those for calculating the kinematic characteristics, and are expressed as follows: ; In the formula, , This represents the mean value of the bistatic radar cross section; , The variance of the bistatic radar cross section is represented. , The interquartile range represents the cross-sectional area of ​​a bistatic radar cross section; , The equivalent mode of a bistatic radar cross section; , Indicates the skewness of the bistatic radar cross section; , The kurtosis of the bistatic radar cross section is represented by the six bistatic radar cross section features mentioned above. Based on these six features, a 6-dimensional bistatic radar cross section feature sub-vector can be constructed. .

[0031] In this embodiment of the application, for each track in the standard track dataset, two track morphological features are selected for extraction, which are used to characterize the track jitter level and the track clustering level, respectively. The track jitter level and clustering level are calculated and combined to construct a 2D morphological feature sub-vector. Specifically, the calculation formula for the track jitter level is expressed by the following formula: ; In the formula, , Indicates the degree of vibration in the flight path; Represents the coefficient of x. , Indicates the first trackpoints coordinate, Indicates the first trackpoints coordinate; Represents the coefficient of y. , Indicates the first trackpoints coordinate, Indicates the first trackpoints coordinate; Represents a constant term. ; Indicates the first trackpoints coordinate; Indicates the first trackpoints coordinate; Indicates the first The first waypoint to the second The and the first The distance between the straight lines connecting each waypoint. The formula for calculating the clustering of waypoints is expressed as follows: ; In the formula, , Indicates the degree of clustering of flight paths; Indicates the first The offset vector of each waypoint , Indicates the first trackpoints Directional offset , Indicates the center of the track coordinate, Indicates the first trackpoints Directional offset , Indicates the center of the track coordinate, The minimum point operation combines the jitter and clustering of the trajectory to obtain a 2D morphological feature vector. Finally, the 18-dimensional kinematic feature vectors are... 6-dimensional bistatic radar cross section characteristic sub-vectors and 2D morphological feature vectors[ The features are concatenated to generate the original feature set. .

[0032] Step S130: For each feature in the original feature set, feature weights are learned based on the neighborhood component analysis method to obtain the importance weights of each feature dimension, and then filtered according to a preset weight threshold to obtain an effective feature subset.

[0033] In this embodiment, feature weights are learned for each dimension of the original feature set based on neighborhood component analysis to obtain the importance weights of each feature dimension, thereby alleviating feature irrelevance and redundancy. A subset of effective features is then obtained by filtering based on a preset weight threshold. Specifically, a standard track dataset is used. Perform min-max normalization on each feature dimension in the original feature set, normalizing each feature dimension to... This yields the normalized features. A diagonal weighted matrix is ​​defined. Each diagonal element of this diagonal weighted matrix represents the weight of the corresponding feature dimension, for example... Indicates the first The weights of the dimensional features are used to define a weighted distance metric based on the diagonal weighted matrix. ,in, Indicates sample and samples The weighted squared distance between them Indicates the first The normalized feature vector of each sample Indicates the first The normalized feature vector of each sample This represents the transpose operation, which directly embeds feature weights into the metric. The larger the weight of a feature dimension, the greater the impact of that dimension's difference on the distance.

[0034] Furthermore, traditional nearest neighbor classification uses... Make predictions. Indicates sample The nearest neighbor sample index, the hard-discriminate correct classification indicator function is However, it is not differentiable, among which Indicates the first The true class label of each sample The predicted class label of the nearest neighbor sample is represented by a weighted distance metric. This transforms the hard discrimination in traditional nearest neighbor classification into a probability-based soft discrimination, determining the probability that each sample is selected as a nearest neighbor by the remaining samples. This nearest neighbor probability is calculated using the following formula: ; In the formula, Indicates sample Select Sample The probability of being a neighbor is called the nearest neighbor probability. Indicates sample and samples The weighted squared distance between the nearest neighbors is used to determine the probability of each sample being correctly classified. The probability of a sample being correctly classified is calculated using the following formula: ; In the formula, sample The probability of being correctly classified, i.e., the expected value of the indices; Represents a similar sample indicator function. , Indicates the first The true class label of each sample.

[0035] Furthermore, an objective function is constructed based on the nearest neighbor probability, and the formula for this objective function is expressed as follows: ; In the formula, Let represent the objective function, which is the expected number of correctly classified samples obtained by summing all samples. An L2 regularization term is introduced into the objective function to suppress unbounded weight increase and overfitting, resulting in the final objective function, expressed as follows: ; In the formula, Describe the final objective function; The regularization coefficient is determined by using cross-validation on the training data to find the value that minimizes the classification loss. Represents the first element in the diagonal weighted matrix. Each component. Further, the objective function (i.e., the final objective function) is optimized using the gradient ascent algorithm by incorporating an L2 regularization term, yielding the importance weights for each feature dimension. Maximizing the final objective function is equivalent to maximizing the expected accuracy of nearest neighbor classification while constraining the weight size. and samples In the The squared difference over the dimensional features is ,in Indicates sample In the The eigenvectors normalized on the 1 / 2-dimensional feature set, Indicates sample In the For the eigenvectors normalized over 3D features, the gradient of the objective function with respect to the weights in the diagonal case is expressed by the following formula: ; If the first Dimensional features bring similar features closer together and dissimilar features further apart; parentheses indicate positive values, and gradients promote... Emphasis is placed on the gradient, which in turn promotes... Suppressed or close to 0, thus achieving automatic feature selection, the process of optimizing the final objective function is essentially learning an optimized metric space, ultimately maximizing the final objective function. Furthermore, based on preset weight thresholds... Features with importance weights higher than a preset weight threshold are selected from the original feature set to form an effective feature subset. Please refer to this. Figure 2 It illustrates a detailed schematic diagram of feature selection and target classification provided in an embodiment of this application, wherein, Figure 2 The “feature selection” section corresponds to the content described in steps S120 and S130.

[0036] Step S140: Perform statistical distribution analysis on the effective feature subset according to the target category, determine the significant features of each target category, and set a significant feature threshold range for each significant feature.

[0037] In this embodiment, the effective feature subset is statistically distributed according to the target category to determine the salient features of each target category, and a salient feature threshold range is set for each salient feature. Specifically, the training dataset is divided into multiple subsets according to the target category, with each subset corresponding to one target category, and a threshold range is set for each salient feature subset. For each feature in the dataset, distribution statistics are performed according to the target category. Specifically, the distribution statistics for each feature are calculated over a subset of each target category, including the median, upper quartile, and lower quartile. Based on the median, upper quartile, and lower quartile, the box plot range for each feature under each target category is then calculated. ,in This represents the median. The quartiles are used to determine the degree of overlap of the box plot lines for each feature across different target categories. Significant features with high discriminative power for specific target categories are selected. For each significant feature identified in each target category, a corresponding significant feature threshold interval is set. This threshold interval is determined based on the statistical distribution range of the corresponding significant feature within the corresponding target category. For each target category, a correspondence list between significant features and significant feature threshold intervals is constructed. Based on this correspondence list, the discrimination rule base for the Statistical Knowledge (SK) classifier can be built.

[0038] Step S150: Obtain the effective feature vector of the track to be classified, determine the discriminant function value of each significant feature in each target category, and combine the discriminant functions of each significant feature according to the preset logical combination rules to obtain the category discriminant function value of each target category. Based on the category discriminant function value of each target category, determine whether the track to be classified can be classified, output the classification result of easy-to-classify samples, and pass the difficult-to-classify samples to the backpropagation neural network classifier.

[0039] In this embodiment, classification is performed based on the SK classifier to distinguish between easily classified and difficult-to-classify samples. Specifically, the target category is determined based on a list of salient features corresponding to each target category. Selected One significant feature and its corresponding salient feature threshold range ,in , Let represent the lower and upper bounds of the threshold interval, respectively. Calculate the discriminant function value for each significant feature, and count the th value in a track. The measurement value of each significant feature The discriminant function is expressed by the following formula: ; In the formula, This represents the discriminant function value, which determines whether the feature measurement value falls within the significant feature threshold range. The discriminant function values ​​of all significant features for each target category are combined using a preset logical combination rule to obtain the category discriminant function, and thus the category discriminant function value for each target category. This category discriminant function value can be determined using two rules. In the case of the full AND rule, the expression formula for the category discriminant function is as follows: ; In the case of a full OR rule, the class discriminant function is expressed by the following formula: ;; Based on the class discriminant function value for each target category, it can be determined whether the track to be classified can be classified if and only if When, that is, if and only if the class discriminant function of a target category is true, the track to be classified is marked as an easy sample and the classification result of the easy sample is output. The track to be classified is directly labeled as the target category. When there is no target category or the category discrimination function values ​​for multiple target categories are true, meaning that no unique value has been obtained. If the SK classifier cannot distinguish the track, it is considered a difficult sample to classify and is then handed over to the subsequent Backpropagation Neural Network (BPNN) classifier for classification. The content described in step S150 above corresponds to... Figure 2 The "SK Classifier" section.

[0040] In one specific embodiment, at average speed For example, if statistics show the average speed of birds Most of them fall into Average speed of general aviation aircraft Always there The above settings can then be configured. Based on this, fall into hour ,fall into hour The intermediate transition zone (20-50) is determined by other significant features or BPNN classifiers. Since the above methods cover their respective high probability density regions and have little overlap between classes, easy-to-classify samples can be obtained at low cost.

[0041] Step S160: Construct a neural network model and train the model. Input the feature vectors of the hard-to-distinguish samples into the trained neural network model to perform forward propagation calculation, output the probability values ​​of each target category, and take the target category with the highest probability value as the final classification result.

[0042] In this embodiment, a BPNN classifier is used to classify difficult-to-classify samples to obtain the final classification result. Specifically, a neural network model is constructed, where the input vector of the neural network model is the effective feature subset, and the output vector is the probability distribution of each target category. The effective feature subset of the difficult-to-classify samples that were not successfully classified by the SK classifier is... As network input vector The input neural network model performs forward propagation layer by layer, and this process can be expressed by the following formula; ; In the formula, Indicates the first Weighted input of the layer; Indicates the first During the nth iteration Layer weights; Indicates the first The layer's output value; Indicates the first During the nth iteration Layer bias; This represents the total number of layers in the neural network; Indicates the first The layer's output value; Indicates the first Layer activation function; the last layer (i.e., the first layer) The output value of the layer is This is the output layer vector. Through nonlinear transformations of the weight matrix, bias vector, and activation function between layers, the output probability distribution is obtained. The error between the neural network model output and the true label is calculated using a preset loss function, which is the cross-entropy loss function. The gradient of the preset loss function with respect to the parameters of each layer is calculated using the backpropagation algorithm, and the network weights and bias parameters are updated based on the gradient descent method. The formula for this update process is expressed as follows: ; In the formula, Indicates the first During the nth iteration Layer weights; Indicates the learning rate; Indicates the pre-set loss; Indicates the first During the nth iteration Layer bias; Indicates the preset loss Regarding the first During the nth iteration Layer weights The gradient; Indicates the preset loss Regarding the first During the nth iteration Layer bias The gradient. The model training process employs an early stopping strategy; training terminates when the preset loss function value on the validation set no longer decreases. During inference, the trained neural network model performs a single forward propagation calculation on the feature vectors of hard-to-classify samples, outputting the probability values ​​of each target category, and taking the target category with the highest probability value as the final classification result. The content described in step S160 above corresponds to... Figure 2 The "BPNN classifier" part.

[0043] In summary, the radar track target classification method based on statistical knowledge and neural networks provided in this application collects raw track data of low-altitude targets using a passive radar system. Abnormal track data is labeled and removed from the raw track data to obtain a standard track dataset. This clarifies the correspondence between feature vectors and category labels, providing a reliable foundation for subsequent feature extraction and target classification, and improving overall classification accuracy. Based on all track points in each track of the standard track dataset, kinematic features, bistatic radar cross section features, and track morphology features are extracted to construct an original feature set. This addresses the limited descriptive power of single-type features, significantly enhancing the richness and discriminative power of feature representation. For each dimension of the original feature set, feature weights are learned using neighborhood component analysis to obtain the importance weights of each feature dimension. These weights are then filtered according to a preset weight threshold to obtain an effective feature subset, significantly reducing the feature space dimensionality. This provides refined and highly discriminative feature inputs for subsequent classification processing, improving the efficiency of subsequent classification. The system performs statistical distribution analysis on the effective feature subset according to the target category to determine the salient features of each target category. A salient feature threshold range is set for each salient feature, enabling most easily classifiable samples to be efficiently classified through fast logical discrimination, significantly reducing the computational burden on the neural network. Effective feature vectors of the track to be classified are obtained, and the discriminant function values ​​of each salient feature in each target category are determined. These discriminant functions are then combined using preset logical combination rules to obtain the category discriminant function value for each target category. Based on the category discriminant function value for each target category, it is determined whether the track to be classified can be classified, outputting the classification results for easily classifiable samples. Difficult samples are passed to the backpropagation neural network classifier for refined processing. A neural network model is constructed and trained. The feature vectors of difficult samples are input into the trained neural network model to perform forward propagation calculations, outputting the probability values ​​of each target category. The target category with the highest probability value is taken as the final classification result, thus significantly improving the overall classification accuracy and robustness. The technical solution provided in this application adopts feature selection and hierarchical classification structure, which can maintain stable performance under conditions of uneven sample distribution or noise interference. It has strong adaptability and practicality, and can bring about a significant improvement in accuracy and efficiency in practical applications, thus having outstanding promotional value.

[0044] It should be noted that, in the embodiments of this application, if the aforementioned radar track target classification method based on statistical knowledge and neural networks is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of this application, or the part that contributes to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a magnetic disk, or an optical disk. Thus, the embodiments of this application are not limited to any specific hardware and software combination.

[0045] Correspondingly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon. When executed by a processor, this computer program implements the steps in any of the radar track target classification methods based on statistical knowledge and neural networks described in the above embodiments. Correspondingly, embodiments of this application also provide a computer program product. When executed by a processor of an electronic device, this computer program product is used to implement the steps in any of the radar track target classification methods based on statistical knowledge and neural networks described in the above embodiments.

[0046] Based on the same technical concept, this application provides an electronic device for implementing a radar track target classification method based on statistical knowledge and neural networks as described in the above method embodiments. Figure 3 This is a schematic diagram of the hardware entity of an electronic device provided in an embodiment of this application, such as... Figure 3 As shown, the electronic device 300 includes a memory 310 and a processor 320. The memory 310 stores a computer program that can run on the processor 320. When the processor 320 executes the program, it implements the steps in any of the radar track target classification methods based on statistical knowledge and neural networks described in the embodiments of this application.

[0047] The memory 310 is configured to store instructions and applications executable by the processor 320, and can also cache data to be processed or already processed by the processor 320 and various modules in the electronic device (e.g., image data, audio data, voice communication data and video communication data), which can be implemented by flash memory or random access memory (RAM).

[0048] When the processor 320 executes a program, it implements the steps of a radar track target classification method based on statistical knowledge and neural networks, as described above. The processor 320 typically controls the overall operation of the electronic equipment 300.

[0049] The aforementioned processor can be at least one of the following: Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Digital Signal Processing Device (DSPD), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), Central Processing Unit (CPU), Controller, Microcontroller, and Microprocessor. It is understood that other electronic devices can also implement the functions of the aforementioned processor, and this application does not specifically limit the specific implementation.

[0050] The aforementioned computer storage media / memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc, or compact disc read-only memory (CD-ROM), etc.; or it can be various electronic devices that include one or any combination of the above-mentioned memories, such as mobile phones, computers, tablet devices, personal digital assistants, etc.

[0051] It should be noted that the descriptions of the storage medium and device embodiments above are similar to the descriptions of the method embodiments above, and have similar beneficial effects. For technical details not disclosed in the storage medium and device embodiments of this application, please refer to the descriptions of the method embodiments of this application for understanding.

[0052] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of this application, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. The sequence numbers of the above-described embodiments are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0053] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0054] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0055] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of the embodiments of this application, depending on actual needs.

[0056] In addition, each functional unit in the various embodiments of this application can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0057] Alternatively, if the integrated units described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause the device automatic test line to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROMs, magnetic disks, or optical disks.

[0058] The methods disclosed in the several method embodiments provided in this application can be arbitrarily combined without conflict to obtain new method embodiments.

[0059] The features disclosed in the several method or device embodiments provided in this application can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0060] The above description is merely an embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A radar track target classification method based on statistical knowledge and neural networks, characterized in that, The method includes: Raw track data of low-altitude airspace targets are collected by a passive radar system, and abnormal track data in the raw track data are labeled and removed to obtain a standard track dataset. Based on all track points in each track in the standard track dataset, kinematic features, bistatic radar cross section features, and track morphology features are extracted to construct the original feature set. For each feature in the original feature set, feature weights are learned based on the neighborhood component analysis method to obtain the importance weights of each feature dimension, and then filtered according to a preset weight threshold to obtain an effective feature subset. The effective feature subset is statistically distributed according to the target category to determine the significant features of each target category, and a significant feature threshold range is set for each significant feature. Obtain the effective feature vector of the track to be classified, determine the discriminant function value of each significant feature in each target category, and combine the discriminant functions of each significant feature according to the preset logical combination rules to obtain the category discriminant function value of each target category. Based on the category discriminant function value of each target category, determine whether the track to be classified can be classified, output the classification result of easy-to-classify samples, and pass the difficult-to-classify samples to the backpropagation neural network classifier. Build and train a neural network model. Input the feature vectors of the hard-to-distinguish samples into the trained neural network model to perform forward propagation calculations. Output the probability values ​​of each target category and take the target category with the highest probability value as the final classification result.

2. The method according to claim 1, characterized in that, The original track data includes general aviation aircraft track data, bird track data, and other target track data. The annotation and removal of abnormal track data from the original track data yields a standard track dataset, including: The original track data is initially labeled using automatic dependent surveillance broadcast signals, and track data not associated with automatic dependent surveillance broadcast signals is categorized through long-term observation and manual discrimination to distinguish general aviation aircraft, birds and other targets. Unreliable and redundant track data are removed from the labeled track data to obtain the standard track dataset, which includes the feature vector and corresponding category label for each track.

3. The method according to claim 1, characterized in that, Based on all track points in each track in the standard track dataset, kinematic features, bistatic radar cross section features, and track morphology features are extracted to construct an original feature set, including: For each track in the standard track dataset, six kinematic features are calculated for the distance, velocity, and acceleration of each track point in each track: mean, variance, interquartile range, equivalent mode, skewness, and kurtosis. These features are then combined with the six statistical features corresponding to the distance, velocity, and acceleration to construct an 18-dimensional kinematic feature sub-vector. The bistatic radar cross section (BRS) of each track point is calculated based on the bistatic radar equation. For each BRS, six bistatic radar cross section features are calculated: mean, variance, interquartile range, equivalent mode, skewness, and kurtosis. A 6-dimensional bistatic radar cross section feature sub-vector is constructed. Calculate the jitter and clustering of the trajectory, and combine the jitter and clustering to construct a 2D morphological feature sub-vector; The original feature set is generated by concatenating the 18-dimensional kinematic feature vector, the 6-dimensional bistatic radar cross section feature vector, and the 2-dimensional morphological feature vector.

4. The method according to claim 1, characterized in that, For each feature in the original feature set, feature weights are learned based on neighborhood component analysis to obtain the importance weights of each feature dimension. Then, a subset of effective features is obtained by filtering based on a preset weight threshold, including: The original feature set is subjected to minimax normalization for each feature dimension to obtain normalized features. A diagonal weighted matrix is ​​defined, and a weighted distance metric is defined based on the diagonal weighted matrix. Each diagonal element of the diagonal weighted matrix represents the weight of the corresponding feature dimension. The weighted distance metric transforms the hard discrimination in traditional nearest neighbor classification into a probability-based soft discrimination, determines the nearest neighbor probability of each sample being selected as a nearest neighbor by the other samples, and determines the probability of each sample being correctly classified based on the nearest neighbor probability. An objective function is constructed based on the nearest neighbor probability, and an L2 regularization term is introduced into the objective function. The objective function with the L2 regularization term is optimized by the gradient ascent algorithm to obtain the importance weights of each feature dimension. The objective function aims to maximize the expected number of all samples that are correctly classified. Based on a preset weight threshold, features with importance weights higher than the preset weight threshold are selected from the original feature set to form an effective feature subset.

5. The method according to claim 1, characterized in that, The step of performing statistical distribution analysis on the effective feature subset according to the target category to determine the significant features of each target category, and setting a significant feature threshold range for each significant feature, includes: The training dataset is divided into multiple subsets according to the target category, with each subset corresponding to a target category; For each feature in the effective feature subset, the distribution statistics of each feature are calculated on a subset of each target category. The distribution statistics include the median, upper quartile, and lower quartile. Based on the median, the upper quartile, and the lower quartile, the box plot range of each feature under each target category is calculated. Determine the degree of overlap of the box plot ranges for each feature across different target categories, and filter out salient features that have high discriminative power for specific target categories; For each significant feature determined for each target category, a corresponding significant feature threshold interval is set, which is determined based on the statistical distribution range of the corresponding significant feature under the corresponding target category; For each target category, a correspondence list of salient features and salient feature threshold intervals is constructed, and a discrimination rule base for a statistical knowledge classifier is constructed based on the correspondence list.

6. The method according to claim 5, characterized in that, The easily distinguishable and difficult-to-distinguish samples are determined through the following process: Based on the list of significant features corresponding to each target category, calculate the discriminant sub-function value for each significant feature, and determine whether the feature measurement value is within the significant feature threshold range based on the discriminant sub-function value. The discriminant function values ​​of all salient features of each target category are combined according to a preset logical combination rule to obtain the category discriminant function value of each target category; The classification of a track is determined based on the class discriminant function value of each target category. The track is considered easy to classify if and only if the class discriminant function value of one target category is true. If there is no target category or the class discriminant function values ​​of multiple target categories are true, the track is marked as difficult to classify. The classification result of the easily classifiable sample is output, which is the target category corresponding to the easily classifiable sample, and the difficult-to-classify sample is passed to the backpropagation neural network classifier.

7. The method according to claim 1, characterized in that, The process involves constructing and training a neural network model, inputting the feature vectors of difficult-to-distinguish samples into the trained neural network model to perform forward propagation calculations, outputting the probability values ​​of each target category, and taking the target category with the highest probability value as the final classification result, including: Construct a neural network model, wherein the input vector of the neural network model is a subset of effective features, and the output vector is the probability distribution of each target category; The feature vectors of hard-to-distinguish samples are input into the neural network model to perform forward propagation calculation. Through nonlinear transformation of the weight matrix, bias vector and activation function between layers, the probability distribution is output. The error between the output of the neural network model and the true label is calculated by a preset loss function, which is the cross-entropy loss function. The gradient of the preset loss function with respect to the parameters of each layer is calculated by backpropagation algorithm, and the network weights and bias parameters are updated based on gradient descent. In addition, the model training process adopts an early stopping strategy, and training is terminated when the preset loss function value on the validation set no longer decreases. The trained neural network model performs a single forward propagation calculation on the feature vectors of hard-to-classify samples, outputs the probability value of each target category, and takes the target category with the highest probability value as the final classification result.

8. An electronic device comprising a memory and a processor, the memory storing a computer program executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 7.

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