Air target adaptive segmented trajectory recognition method and system based on softmax multi-classification network

Abstract

The application provides an air target adaptive segmented track recognition method and system based on a Softmax multi-classification network, which comprises the following steps: traversing a whole complex track sequence in time through a sliding window, fitting the track in the window by using a designed fitting equation to obtain equation parameters; training a Softmax classification network model based on the equation parameters, and recognizing the track pattern in the window based on the network model; and correcting the recognition result based on Haar wavelet reconstruction to eliminate discrete wrong recognition results. The application solves the problem of poor complex track pattern recognition effect and can effectively recognize the complex track pattern in an adaptive segmented manner.

Description

Technical Field

[0001] This invention belongs to the field of pattern recognition, specifically relating to an adaptive segmented trajectory recognition method and system for aerial targets based on a Softmax multi-classification network. Background Technology

[0002] Aerial target trajectory identification is a fundamental problem in analyzing target motion and a crucial component of battlefield situational awareness. In the complex and rapidly changing air combat, the rapid and accurate identification of aerial target trajectories can determine their maneuver information. Furthermore, tracking and acquiring aerial target trajectories facilitates further analysis of target behavior, is of great significance for understanding their tactical intentions, and is a prerequisite for air combat situation assessment and decision support.

[0003] For simple trajectories, where only one trajectory pattern exists, methods such as expert systems, support vector machines, Bayesian networks, Hidden Markov Models (HMMs), Dynamic Time Warping (DTW), Neural Networks (NNs), and deep learning can be used for recognition. However, for complex trajectories, where a single trajectory contains multiple trajectory patterns, the above methods perform poorly. Trajectory segmentation is crucial for complex trajectory recognition. Although there is existing research on trajectory segmentation, including feature-point-based segmentation, supervised learning-based segmentation, and unsupervised learning-based segmentation, adaptive segmentation capabilities are lacking. Summary of the Invention

[0004] To address the problem that existing aerial target trajectory recognition methods can only identify single trajectory patterns and have poor performance in recognizing complex trajectory patterns, this invention proposes an adaptive segmented trajectory recognition method and system for aerial targets based on a Softmax multi-classification network, which can achieve adaptive segmentation and pattern recognition of complex trajectories.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] An adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network is characterized by comprising:

[0007] Step 1: Perform piecewise curve fitting on the complex trajectory. Starting from the starting point, slide the window to select trajectory segments in sequence, and use the designed fitting equation to fit the trajectory within the window to obtain the equations and corresponding equation parameters of each trajectory segment of the complex trajectory.

[0008] Step 2: Train a Softmax classification network based on the obtained equation parameters, and use the trained network model to identify the trajectory patterns within the window;

[0009] Step 3: Merge continuous trajectory segments with the same identification results, and correct the identification results based on Haar wavelet reconstruction to eliminate discrete erroneous identification results.

[0010] To optimize the above technical solution, the specific measures also include:

[0011] Furthermore, in step 1, the fitting equation adopts the generalized conic section equation. The fitting equation is designed by establishing a function equation containing undetermined coefficients, calculating the sum of squared errors of the equation under a given dataset, and determining the undetermined coefficients based on the principle of minimizing the sum of squared errors, thereby obtaining the fitting equation for the given dataset.

[0012] Furthermore, the design process of the fitting equation is as follows:

[0013] Given trajectory data p i =(x i y i ), i = 1, 2, 3, ..., N, where N is the total number of points on the trajectory, and the fitting equation is:

[0014] F(x i y i ) = ax i 2 +bx i y i +cy i 2 +dx i +ey i +f (1)

[0015] Where a, b, c, d, e, and f are undetermined coefficients used to represent the curve pattern;

[0016] The above formula is processed as follows:

[0017] If f≠0, the expression for F / f is:

[0018]

[0019] Where a′, b′, c′, d′, and e′ are coefficients;

[0020] If f = 0, the curve is shifted, as shown below:

[0021] F(x i y i )+1=ax i 2 +bx i y i +cy i 2 +dxi +ey i +1 (3)

[0022] Sum of squared errors G(x) i y i ) is represented as:

[0023]

[0024] make The matrix equation is obtained as follows:

[0025]

[0026] The minimum value of the sum of squared errors is transformed into the coefficient matrix of the matrix equation. This allows us to obtain the values ​​of the five equation parameters: a, b, c, d, and e.

[0027] Furthermore, in step 2, the Softmax classification network consists of an input layer, a hidden layer, and an output layer. The network inputs the equation parameters of the fitted equation and outputs the probability values ​​of the trajectory patterns. The probability values ​​are calculated by nesting the SoRmax function with the results of linear regression.

[0028] Furthermore, in step 2, the training of the Sofgmax classification network based on the obtained equation parameters is specifically as follows:

[0029] The trajectory data generated by the simulation is processed by the equation parameters obtained in step 1 to form a parameter sample set. The parameter sample set is divided into a training set and a test set, and then one-hot encoded.

[0030] The encoded training samples are used as network input, and then a linear transformation is performed to output a vector of dimension K, where K is the type of trajectory to be identified. This vector is then fed into the Softmax function to obtain the probability value of each trajectory pattern.

[0031] The loss function is constructed based on the network output and input sample labels. Then, the gradient descent algorithm is used to continuously adjust the loss function towards the negative gradient of the weights and bias parameters of the hidden and output layers, so as to minimize the loss function.

[0032] Furthermore, in step 3, the process of merging consecutive trajectory segments with the same recognition result specifically involves merging these trajectory segments and outputting a single recognition result when multiple consecutive windows show the same recognition result.

[0033] Furthermore, in step 3, the correction of the recognition result based on Haar wavelet reconstruction specifically involves: when there is a significant difference between the recognition result in a certain window and the recognition result in the nearby windows, low-pass filtering is applied to the trajectory style label based on Haar wavelet.

[0034] This invention also proposes an adaptive segmented trajectory recognition system for aerial targets based on a Softmax multi-classification network, characterized by comprising:

[0035] The trajectory parameterization modeling module performs piecewise curve fitting on complex trajectories. Starting from the starting point, it sequentially slides a window to select trajectory segments and uses the designed fitting equation to fit the trajectory within the window, thereby obtaining the equations and corresponding equation parameters for each trajectory segment of the complex trajectory.

[0036] The neural network training and recognition module trains a Softmax classification network based on the obtained equation parameters, and recognizes the trajectory patterns within the window based on the trained network model.

[0037] The segmented trajectory optimization module merges continuous trajectory segments with the same recognition result and corrects the recognition result based on Haar wavelet reconstruction to eliminate discrete erroneous recognition results.

[0038] The present invention also proposes a computer-readable storage medium storing a computer program, characterized in that the computer program enables a computer to execute the above-described method for adaptive segmented trajectory recognition of aerial targets based on a Softmax multi-classification network.

[0039] The present invention also proposes an electronic device, characterized in that it includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the above-described method for adaptive segmented trajectory recognition of aerial targets based on a Softmax multi-classification network.

[0040] The beneficial effects of this invention are as follows: The segmented trajectory recognition method of this invention uses a sliding window approach to traverse the entire complex trajectory, solving the problem of complex trajectory pattern recognition. For trajectories within the window, to fully utilize the role of trajectory equation parameters in trajectory pattern recognition, a generalized trajectory equation is designed, and the corresponding equation parameters are fitted and used as recognition features. Furthermore, the equation parameters are used to train a classification model, and the recognition of unknown trajectory patterns within the window is achieved based on the trained network model. To eliminate the influence of noise and other factors on the recognition results, considering the characteristics of erroneous recognition results, Haar wavelet reconstruction is used to correct the recognition results, eliminating discrete erroneous recognition results. The results show that the method of this invention can effectively perform adaptive trajectory segmentation and recognition of complex trajectory sequences, which is beneficial for timely detection of changes in target trajectories and making corresponding judgments in battlefield environments. Attached Figure Description

[0041] Figure 1 This is a flowchart of the trajectory pattern recognition method of the present invention.

[0042] Figure 2 This is a comparison chart of the original output label data and the label data filtered by Haar wavelet filtering provided by the present invention.

[0043] Figures 3a to 3d The present invention provides four types of complex trajectory diagrams generated by simulation.

[0044] Figure 4 The flowchart for learning and testing Softmax multi-classification network provided by this invention.

[0045] Figures 5a to 5d The image shows the segmentation recognition results of four complex trajectories provided by this invention.

[0046] Figures 6a to 6d The image shows the optimized segmentation recognition results for four complex trajectories provided by this invention. Detailed Implementation

[0047] 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, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0048] This invention is applicable to segmented trajectory pattern determination of complex two-dimensional trajectory data. In one embodiment, this invention proposes an adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network. The overall process of the recognition method is as follows: Figure 1 As shown, the specific steps include:

[0049] Step 1: Establish a function equation containing undetermined coefficients. By calculating the sum of squared errors of the equation under a given dataset, the undetermined coefficients are determined based on the principle of minimizing the sum of squared errors, thus obtaining the fitting equation for the given dataset. This invention uses a generalized conic section equation to fit the trajectory.

[0050] For complex two-dimensional trajectories, it is necessary to segment them in time and then identify each segment. Here, a sliding window method is used, assuming that the trajectory within each window is of the same type, and the trajectory within the window is identified.

[0051] Given trajectory data p i =(x i y i ), i = 1, 2, 3, ..., N, where N is the total number of points on the trajectory, and the fitting equation is:

[0052] F(x, y) = ax 2 +bxy+cy 2 +dx+ey+f (1)

[0053] Where a, b, c, d, e, and f are undetermined coefficients, which can represent straight lines, circles, parabolas, ellipses, and other conic section patterns.

[0054] If we directly perform least-squares fitting on the above equation, we will obtain a homogeneous linear system of equations. In this case, the coefficient matrix of the equations is very likely to become a singular matrix, making it difficult to solve. Here, we perform the following processing on the above equation:

[0055] If f≠0, the expression for F / f is:

[0056]

[0057] If f = 0, only 5 parameters are involved in the fitting. To simplify the fitting process, we can add 1 to both sides of the equation. This will not change the shape of the curve; it will only perform a translation operation on the curve, as shown below:

[0058] F(x i y i )+1=ax i 2 +bx i y i +cy i 2 +dx i +ey i +1 (3)

[0059] The right-hand sides of equations (2) and (3) have the same structure. To make the curve fitting equation best describe the motion state of the original trajectory, the sum of the distances from each point to the curve must be minimized, i.e., the sum of squared errors G(x i y i The smallest value can be represented as:

[0060]

[0061] make The matrix equation can be obtained as follows:

[0062]

[0063] The minimum value of the sum of squared errors can be transformed into solving the coefficient matrix A of the matrix equation AX = B, thereby obtaining the values ​​of the five parameters a, b, c, d, and e. At this point, the trajectory data can be parameterized as the coefficient parameters of a conic section.

[0064] Step 2: Recognition based on the Softmax multi-class network. The Softmax multi-class network consists of an input layer, hidden layers, and an output layer. The parameters of the trajectory fitting equation are input from the left side of the network, and the probability is output from the right side. The probability is calculated by nesting the Softmax function with the results of linear regression.

[0065] Neural networks are built on mathematical foundations for computation, and all feature data, regardless of its type, needs to be input into the neural network in vector form. One-hot encoding is a commonly used encoding method. When using machine learning or deep learning to solve multi-class classification problems, data is typically labeled, and these labels are one-hot encoded. This allows the model output, after softmax mapping, to directly regress the probability of the class into the one-hot encoded value; that is, the probability of the labeled position is 1, and the probability of other positions is 0. First, the trajectory data generated from the simulation is processed through step 1 to obtain the parameter sample set. The parameter sample set is then divided into a training set and a test set, and one-hot encoding is performed on each set.

[0066] The encoded training samples are used as network input, and then a linear transformation is performed to output a vector of dimension K, where K is the number of trajectory types to be identified. This vector is then fed into the Softmax function to obtain the probability value of each trajectory pattern. The mathematical expression is as follows:

[0067] z j =w j ·x+b j (6)

[0068]

[0069] Where x is the input of the fully connected layer, w j As the weight, b j For the bias term, z j This is the output of the hidden layer.

[0070] A loss function is constructed based on the network output and input sample labels. Then, the gradient descent algorithm is used to continuously adjust the loss function towards the negative gradients of the weights and biases of the hidden and output layers, minimizing the loss function. The loss function used in this invention is the cross-entropy loss function, defined as follows:

[0071]

[0072] Where M is the number of categories, y ic p is a symbolic function ic Let be the probability that the i-th observed sample belongs to category c.

[0073] Step 3: The sliding window recognition result can be obtained through the neural network. Typically, the trajectory pattern should be the same over a continuous period. When the recognition results are the same in multiple consecutive windows, these trajectory segments are merged, and a single recognition result is output. When the recognition result in a certain window differs significantly from the recognition results in nearby windows, there may be discrete recognition errors. In this case, low-pass filtering of the pattern labels can be applied based on Haar wavelets.

[0074] Wavelet analysis is a multi-resolution analysis method that generates a family of functions, derived from the scaling function φ(x) and the wavelet function ψ(x), that can be used to decompose and reconstruct signals. The scaling function and wavelet function at different resolution scales correspond to different frequency components; therefore, wavelet analysis can be used to decompose and reconstruct signals to filter them and obtain the desired signal.

[0075] The scaling function in Haar wavelet analysis is determined by equation (9):

[0076]

[0077] The wavelet function at the same resolution is determined by equation (10):

[0078] ψ(x)=φ(2x)-φ(2x-1) (10)

[0079] Based on the above formula, we can obtain the scaling function and wavelet function for other resolutions, φ(2 j xk) determined a Haar wavelet at a resolution of 2. j The scaling function under the given conditions, ψ(2) j xk) determined a Haar wavelet at a resolution of 2. j The wavelet function at the specified resolution. Furthermore, the scaling function and wavelet function at adjacent resolutions satisfy the following equation:

[0080]

[0081]

[0082] Based on the above formula, we can obtain the decomposition and reconstruction method of Haar wavelet analysis.

[0083] Furthermore, for any function f j (x) can be written in a resolution of 2 j The form of the scaling function is as follows: Then f j (x) can be decomposed into:

[0084] f j =w j-1 +f j-1 (13)

[0085] in:

[0086]

[0087]

[0088]

[0089]

[0090] By continuously updating the above process, the signal f can be... j (x) is decomposed as follows:

[0091] f j =w j-1 +w j-2 +…+w0+f0 (18)

[0092] The above equation shows that the signal can be decomposed into signals at different scales (frequency) using the Haar wavelet decomposition method.

[0093] Suppose that the signal f after filtering out high frequencies can be expressed as:

[0094] f = w m-1 +w m-2 +…+w0+f0 (19)

[0095] in:

[0096]

[0097]

[0098] Then the original signal can be reconstructed:

[0099]

[0100] in:

[0101]

[0102] The recognition results from the neural network consist of numbers 1, 2, 3...K, where K represents the types of trajectory patterns. If the recognition results are considered as a time signal, discrete recognition errors will manifest as high-frequency noise in a square wave signal when there are errors in the pattern category. Therefore, to recover the ideal pattern category square wave signal, the Haar wavelet is used to first decompose the pattern label, discarding the high-resolution components, and then reconstructing the signal to obtain the desired pattern signal. Figure 2 As shown.

[0103] The implementation steps of the trajectory recognition method proposed in this invention have been described above. To verify the effectiveness of this method, simulation experiments are conducted below. This paper considers two-dimensional trajectory data and simulates the generation of four complex trajectories, such as... Figures 3a to 3d As shown.

[0104] In the simulation, the distance to the radar is approximately 30 km, and the azimuth error is approximately 0.5°. The Softmax multi-classification network is a fully connected network consisting of one input layer, three hidden layers, and one output layer. The input layer consists of five neurons, corresponding to the five coefficient parameters generated by the fitting. The three hidden layers have 32, 64, and 32 neurons respectively, and the activation function is the sigmoid function. Since both the training labels and the test output are one-hot encoded, the number of neurons in the output layer corresponds to the number of classification categories, which is set to 4 here.

[0105] To train the Softmax multi-class network parameters, 40,000 noisy conic section data points were randomly generated. Curve fitting was performed as described in step 1 to generate five corresponding coefficient parameters, thus creating the multi-class network training set. The network learning and testing process is as follows: Figure 4 As shown.

[0106] The trajectory data fitting window has a length of 32 points and a sliding step size of 1. Starting from the starting point, 32 points are sequentially selected for equation fitting until the entire trajectory is traversed. The parameters fitted for each segment are then fed into a trained neural network for pattern recognition. The results of segmented trajectory recognition are as follows: Figures 5a to 5d As shown.

[0107] according to Figures 5a to 5d As can be seen, the trajectory pattern data directly output by the Softmax multi-classification network is not the ideal, clearly segmented trajectory pattern. If the corresponding trajectory pattern is plotted, it appears as a rectangular wave containing a significant amount of high-frequency clutter. After applying a Haar wavelet low-pass filter to this signal, the integrated trajectory pattern signal is obtained, and the trajectory recognition result is as follows. Figures 6a to 6d As shown, the method of the present invention can perform adaptive segmented trajectory pattern recognition for complex trajectory sequences.

[0108] The result after Haar wavelet low-pass filtering exhibits the desired segmented pattern and has high accuracy. Based on the method of this invention, four trajectories were identified, and the identification results are shown in Table 1.

[0109] Table 1 shows the recognition results for the four trajectories.

[0110] Trajectory 1 Track 2 Track 3 Track 4 Points 123 398 207 193 accuracy 0.846 0.919 0.759 0.917

[0111] In the simulation experiment, the recognition accuracy of each point reached 86%.

[0112] In another embodiment, the present invention provides an adaptive segmented trajectory recognition system for aerial targets based on a Softmax multi-classification network, which corresponds to the adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network described in Embodiment 1, and includes:

[0113] The trajectory parameterization modeling module performs piecewise curve fitting on complex trajectories. Starting from the starting point, it sequentially slides a window to select trajectory segments and uses the designed fitting equation to fit the trajectory within the window, thereby obtaining the equations and corresponding equation parameters for each trajectory segment of the complex trajectory.

[0114] The neural network training and recognition module trains a Softmax classification network based on the obtained equation parameters, and recognizes the trajectory patterns within the window based on the trained network model.

[0115] The segmented trajectory optimization module takes into account in-window recognition errors and features, merges continuous trajectory segments with the same recognition results, and corrects the recognition results based on Haar wavelet reconstruction to eliminate discrete error recognition results.

[0116] Furthermore, the segmented trajectory optimization module includes:

[0117] The same recognition style merging unit should typically exhibit the same trajectory style within a continuous period of time. When the recognition results are the same in multiple consecutive windows, the trajectory segments with the same style are merged and the same result is output.

[0118] The error identification pattern filtering unit can correct discrepancy results when there is a significant difference between the identification result in a certain window and the identification result in the nearby windows. This is because there may be discrete identification errors. The pattern label can be low-pass filtered based on Haar wavelet to correct the identification result.

[0119] The specific working details of each module in the adaptive segmented trajectory recognition system for aerial targets based on the Softmax multi-classification network are consistent with the recognition method in Example 1, so they will not be described again.

[0120] In another embodiment, the present invention also proposes a computer-readable storage medium storing a computer program, characterized in that the computer program causes a computer to execute the adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network as described in Embodiment 1.

[0121] In another embodiment, the present invention also proposes an electronic device, characterized in that it includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network as described in Embodiment 1.

[0122] In the embodiments disclosed in this application, a computer storage medium may be a tangible medium that may contain or store programs for use by or in conjunction with an instruction execution system, apparatus, or device. The computer storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of computer storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0123] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0124] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. An adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network, characterized in that, include: Step 1: Perform piecewise curve fitting on the complex trajectory. Starting from the starting point, slide the window to select trajectory segments in sequence, and use the designed fitting equation to fit the trajectory within the window to obtain the equations and corresponding equation parameters of each trajectory segment of the complex trajectory. Step 2: Train a Softmax classification network based on the obtained equation parameters, and use the trained network model to identify the trajectory patterns within the window; Step 3: Merge continuous trajectory segments with the same identification results, and correct the identification results based on Haar wavelet reconstruction to eliminate discrete erroneous identification results.

2. The adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network as described in claim 1, characterized in that: In step 1, the fitting equation adopts the generalized conic section equation. The fitting equation is designed by establishing a function equation with undetermined coefficients, calculating the sum of squared errors of the equation under a given dataset, and determining the undetermined coefficients based on the principle of minimizing the sum of squared errors, thereby obtaining the fitting equation for the given dataset.

3. The method for adaptive segmented trajectory recognition of aerial targets based on a Softmax multi-classification network as described in claim 2, characterized in that: The design process of the fitting equation is as follows: Given trajectory data p i =(x i y i ), i = 1, 2, 3, ..., N, where N is the total number of points on the trajectory, and the fitting equation is: F(x i ,y i )=ax i 2 +bx i y i +cy i 2 +dx i +ey i +f (1) Where a, b, c, d, e, and f are undetermined coefficients used to represent the curve pattern; The above formula is processed as follows: If f≠0, the expression for F / f is: Where a′, b′, c′, d′, and e′ are coefficients; If f = 0, the curve is shifted, as shown below: F(x i ,y i )+1=ax i 2 +bx i y i +cy i 2 +dx i +ey i +1 (3) Sum of squared errors G(x) i y i ) is represented as: make The matrix equation is obtained as follows: The minimum value of the sum of squared errors is transformed into the coefficient matrix of the matrix equation. This allows us to obtain the values ​​of the five equation parameters: a, b, c, d, and e.

4. The method for adaptive segmented trajectory recognition of aerial targets based on Softmax multi-classification network as described in claim 1, characterized in that: In step 2, the Softmax classification network consists of an input layer, a hidden layer, and an output layer. The network inputs the equation parameters of the fitted equation and outputs the probability values ​​of the trajectory patterns. The probability values ​​are calculated by nesting the Softmax function with the results of linear regression.

5. The method for adaptive segmented trajectory recognition of aerial targets based on Softmax multi-classification network as described in claim 4, characterized in that: In step 2, the training of the Softmax classification network based on the obtained equation parameters is specifically as follows: The trajectory data generated by the simulation is processed by the equation parameters obtained in step 1 to form a parameter sample set. The parameter sample set is divided into a training set and a test set, and then one-hot encoded. The encoded training samples are used as network input, and then a linear transformation is performed to output a vector of dimension K, where K is the type of trajectory to be identified. This vector is then fed into the Softmax function to obtain the probability value of each trajectory pattern. The loss function is constructed based on the network output and input sample labels. Then, the gradient descent algorithm is used to continuously adjust the loss function towards the negative gradient of the weights and bias parameters of the hidden and output layers, so as to minimize the loss function.

6. The method for adaptive segmented trajectory recognition of aerial targets based on a Softmax multi-classification network as described in claim 1, characterized in that: In step 3, the process of merging consecutive trajectory segments with the same recognition result is as follows: when the recognition results are the same in multiple consecutive windows, these trajectory segments are merged and a single recognition result is output.

7. The method for adaptive segmented trajectory recognition of aerial targets based on a Softmax multi-classification network as described in claim 1, characterized in that: In step 3, the correction of the recognition results based on Haar wavelet reconstruction is specifically as follows: when there is a significant difference between the recognition results in a certain window and the recognition results in nearby windows, the trajectory style label is low-pass filtered based on Haar wavelet.

8. An adaptive segmented trajectory recognition system for aerial targets based on a Softmax multi-classification network, characterized in that, include: The trajectory parameterization modeling module performs piecewise curve fitting on complex trajectories. Starting from the starting point, it sequentially slides a window to select trajectory segments and uses the designed fitting equation to fit the trajectory within the window, thereby obtaining the equations and corresponding equation parameters for each trajectory segment of the complex trajectory. The neural network training and recognition module trains a Softmax classification network based on the obtained equation parameters, and recognizes the trajectory patterns within the window based on the trained network model. The segmented trajectory optimization module merges continuous trajectory segments with the same recognition result and corrects the recognition result based on Haar wavelet reconstruction to eliminate discrete erroneous recognition results.

9. A computer-readable storage medium storing a computer program, characterized in that, The computer program causes the computer to execute the adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network as described in any one of claims 1-7.

10. An electronic device, characterized in that, include: The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the adaptive segmented trajectory recognition method for aerial targets based on a Softmax multi-classification network as described in any one of claims 1-7.

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