A Method for Tracking Error Compensation of High-Speed Maneuvering Targets Based on Intelligent Smoothing of Time Series

Abstract

The present invention relates to a method for compensating tracking errors of high-speed maneuvering targets based on time-series intelligent smoothing, belonging to the field of target tracking. A maneuvering target motion model and a measurement model are established to obtain the true track and the measured track of the maneuvering target respectively; the measured track is smoothed and fitted respectively; a neural network is constructed, and the smoothed and fitted measured track is used as the input of the neural network, and the true track is used as the output of the neural network; the true track and the measured track are composed into training data, and the neural network is trained with the training data; the trained neural network is used to perform real-time prediction on the measured track and perform track stitching. The present invention further obtains an accurate estimate of the target state through the designed multi-scale track smoothing module and the Transformer neural network time-series prediction based on the TFoT target tracking method, improving the tracking accuracy and generalization ability of the target.

Description

Technical Field

[0001] The present invention relates to the field of target tracking, and particularly to a method for compensating tracking errors of high-speed maneuvering targets based on intelligent smoothing of time series. It is applicable to high-speed maneuvering targets with smoothly changing trajectories such as cruise missiles, unmanned aerial vehicles, and supersonic aircraft. Background Art

[0002] As an indispensable technology in both military and civilian fields, target tracking has always been widely and deeply studied by researchers from all over the world, and a large number of tracking theories and methods have been proposed. However, most of the current target tracking methods are based on state space models and rely heavily on accurate prior information about target motion. In actual target tracking tasks, especially in the military field, due to reasons such as air combat, stealth, and penetration, the random and unknown maneuvers of targets further increase the difficulty of tracking. Classical model-driven tracking methods may deteriorate rapidly due to inaccurate prior knowledge and complex real-world system models. Therefore, model-driven target tracking algorithms are facing more and more challenges in meeting actual application and requirements.

[0003] The literature "Joint smoothing and tracking based on continuous-time target trajectory function fitting" first proposed the continuous-time trajectory function (TFoT) and proved its effectiveness in target tracking. This method uses a continuous function to represent the target's motion trajectory, improving target tracking accuracy and reducing calculation time. However, the core idea based on curve fitting is limited by observation noise and measurement sampling frequency. Larger observation noise will reduce the fitting accuracy of the time trajectory function, and it is difficult to accurately capture continuous time series features at a low measurement sampling rate. Aiming at the above problems, how to reduce the influence of large-noise measurements that deviate too much from the true trajectory and accurately fill in the target trajectory between adjacent sampling intervals is the main starting point of the present invention. Summary of the Invention

[0004] The technical problem to be solved by the present invention is:

[0005] Aiming at the problems that existing classical methods rely heavily on accurate prior knowledge of target motion and TFoT is limited by observation noise and sampling rate, the present invention proposes a method for compensating tracking errors of high-speed maneuvering targets based on intelligent smoothing of time series. A multi-scale smoothing module and a neural network are used to further correct the TFoT target tracking method to obtain an accurate state estimate of the maneuvering target at the current moment using only measurement information. This method is applicable to solving the problem of tracking maneuvering targets in complex maneuvering scenarios.

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

[0007] A high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing, which is characterized by including:

[0008] Establish a maneuvering target motion model and a measurement model to obtain the true track and the measured track of the maneuvering target respectively;

[0009] Design a multi-scale moving average module to smooth the measured track;

[0010] Fit the measured track based on the continuous-time trajectory function target tracking method;

[0011] Construct a neural network, use the smoothed and fitted measured track as the input of the neural network, and use the true track as the output of the neural network; form training data with the true track and the measured track, and train the neural network with the training data; the neural network is a Transformer network, including an input module, an encoder, a decoder and an output module; the encoder includes a multi-head self-attention and a feed-forward neural network; the decoder includes a dimension-adjusting fully-connected network and a bidirectional LSTM network;

[0012] Use the trained neural network to perform real-time prediction on the measured track and perform track stitching.

[0013] A further technical solution of the present invention: The true track and the measured track include three motion model track libraries of constant velocity linear motion CV, constant velocity circular motion CT and uniformly accelerated linear motion CA, and randomly combine them to simulate the real maneuvering target track.

[0014] A further technical solution of the present invention: The maneuvering target motion model and the measurement model are respectively:

[0015] x(k) = Fx(k - 1)+W(k)

[0016] z(k) = Hx(k)+V(x)

[0017] In the formula, x(k) represents the target state at time k; F is the state transition matrix, which characterizes the transformation of the state from the previous moment to the current moment; W(k) represents the system error (noise); z(k) represents the target measurement at time k; H represents the measurement transformation matrix; V(k) represents the measurement error (noise), and the system error and the measurement error are independent Gaussian noises.

[0018] A further technical solution of the present invention: The multi-scale moving average module is specifically:

[0019]

[0020]

[0021] where z′ 1：K is the observed track state; is the track state after smoothing processing; Padding(·) represents a padding operation to keep the sequence length unchanged; Average(·) represents a moving average operation; c1 and c2 represent weighting coefficients; kernel_size1 and kernel_size2 represent the smoothing window sizes of different scales; padding represents the padding size to ensure the sequence length remains unchanged.

[0022] A further technical solution of the present invention: It further includes normalizing the input and output labels of the neural network:

[0023]

[0024] where represents the TFoT fitting track at K moments; x 1：K represents the true track corresponding to K moments, z min , z max represent the minimum and maximum values in the measurement track respectively, x′ 1：K represent the TFoT fitting track state and the true state after normalization processing respectively, and are used as the input and output labels of the neural network respectively.

[0025] A further technical solution of the present invention: The processing process of the Transformer network includes:

[0026] Performing position encoding and sequence encoding on the input sequence;

[0027] Using the multi-head self-attention mechanism to capture the dependencies between sequence elements to globally model the target track;

[0028] Adding residual connections and layer normalization in the encoder sub-module to improve the network and enhancing the expression ability of the model through the feed-forward neural network;

[0029] Further obtaining an accurate estimate of the target state through the decoder composed of the dimension-adjusting fully connected network and the bidirectional LSTM.

[0030] A further technical solution of the present invention: Performing real-time prediction on the measurement track and splicing the tracks:

[0031]

[0032]

[0033] where Model(·) represents the trained neural network model; z′ 1：K represents the preprocessed measurement track state of the network input; represents the true state estimation output from the network; x 1：N represents the state estimations at the previous N sampling times; x 1：N+1 represents updating the state estimation at the latest sampling time to the total track state estimation; represents the state estimation of the neural network at the k-th sampling time.

[0034] A verification method for a high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing, characterized in that: taking the root mean square error RMSE as the comparison index, defining the RMSE of the target position at time t as:

[0035]

[0036] where x t and y t are the measured positions of the sensor, and are the position estimations output by the neural network.

[0037] A computer system, characterized in that it includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are caused to implement the above method.

[0038] A computer-readable storage medium, characterized in that it stores computer-executable instructions, and the instructions are used to implement the above method when executed.

[0039] The beneficial effects of the present invention are as follows:

[0040] A high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing provided by the present invention aims to further obtain an accurate estimation of the target state through a designed multi-scale track smoothing module and Transformer neural network time series prediction based on the TFoT target tracking method. Through the above method, the present invention can achieve higher-precision real-time tracking of maneuvering targets. It can significantly eliminate the influence of noise on the fitting of the motion trajectory by using the multi-scale track smoothing module, and at the same time, use the self-attention mechanism of Transformer to extract the global features of the observation sequence to achieve accurate estimation of the maneuvering target state by the TFoT target tracking method. This method can achieve higher-precision real-time tracking of targets in complex maneuvering scenarios and break through the technical bottleneck of target track update under the lack of prior knowledge. Description of the Drawings

[0041] The accompanying drawings are only for the purpose of showing specific embodiments and are not considered as limitations of the present invention. Throughout the drawings, the same reference signs denote the same components.

[0042] Figure 1 is the structural flowchart of the method of the present invention.

[0043] Figure 2 is the training data set of the method of the present invention.

[0044] Figure 3 is the neural network architecture of the method of the present invention.

[0045] Figure 4 is the simulation scenario of the method of the present invention.

[0046] Figure 5 is the simulation accuracy result of the method of the present invention. Detailed Description of the Invention

[0047] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0048] In long-term time series prediction, target motion trend modeling and seasonal modeling are the focuses of research in this field. Inspired by this, the present invention regards the noise of the target motion model as seasonal changes and pays more attention to the overall trend of target motion. Therefore, a multi-scale smoothing module is designed to be paired with the TFoT target tracking method to accurately extract the target motion time series features. Aiming at the influence of the low sampling rate on the TFoT target tracking method, the present invention starts from the perspective of strengthening the global modeling of the target and uses deep learning methods to obtain a more accurate state estimation of the track. Deep learning has achieved great success in the fields of natural language processing and computer vision. The Transformer with self-attention mechanism is considered to be the most potential model architecture due to its powerful sequence modeling ability and has been deeply studied. The present invention designs a reasonable network architecture for extracting and accurately estimating target motion time series features based on the Transformer to further compensate for the error of the TFoT method, thereby improving the tracking accuracy and generalization ability of the target.

[0049] A high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing provided by the present invention includes the following steps:

[0050] Step 1: Establish a maneuvering target track training library.

[0051] A two-dimensional trajectory generation method based on the state space model is adopted to construct trajectory libraries for three motion models, namely Constant Velocity (CV), Constant Turn (CT), and Constant Acceleration (CA), and randomly combine them to simulate the trajectories of real maneuvering targets. To ensure greater diversity of training data and avoid duplicate samples, a step size is set for the motion trajectory of a single maneuvering target to intercept K pairs of true value trajectory and measurement trajectory data at sampling moments as a single training data pair. The motion model and measurement model of the maneuvering target are as follows:

[0052] x(k) = Fx(k - 1) + W(k) (1)

[0053] z(k) = Hx(k) + V(x) (2)

[0054] In the formula, x(k) represents the target state at time k; F is the state transition matrix, representing the transformation of the state from the previous moment to the current moment; W(k) represents the system error (noise); z(k) represents the target measurement at time k; H represents the measurement transformation matrix; V(k) represents the measurement error (noise), and the system error and measurement error are independent Gaussian noises.

[0055] Among them, the state transition matrices and observation matrices of the CV, CT, and CA models are respectively:

[0056]

[0057]

[0058]

[0059] In the formula, F model , H model represent the state transition matrix and the observation matrix respectively; T represents the sampling time; ω represents the turning rate.

[0060] Step 2: Design a multi-scale moving average module to smooth the measurement trajectory.

[0061]

[0062]

[0063] In the formula, z′ 1：K is the state of the measurement trajectory; It is the track state after smoothing processing; Padding(·) represents the padding operation to keep the sequence length unchanged; Average(·) represents the moving average operation; c1 and c2 represent the weighting coefficients; kernel_size1 and kernel_size2 represent the smoothing window sizes of different scales; padding represents the padding size to ensure the sequence length remains unchanged.

[0064] Step 3: Measurement track fitting based on the TFoT target tracking method.

[0065] Step 3-1: Fitting track modeling.

[0066] x t = F(t; A) + e t

[0067] y t = h(x t ) + v t (8)

[0068] In the formula, x t represents the state of the target at time t; λ represents the continuous time function curve coefficient; F(t; λ) represents the continuous time function curve; e t represents the process error; y t represents the measurement value of the target at time t; h(·) represents the measurement function; v t represents the measurement noise.

[0069] Step 3-2: Continuous time trajectory function parameter estimation and target state estimation.

[0070] Select a polynomial order of 1 to fit the track in the corresponding time window, and estimate the coefficient parameter λ by minimizing the fitting residual:

[0071]

[0072] In the formula, |λ| is the regularization term; ρ is the regularization parameter. Obtain the state estimation at the corresponding sampling moment through the determined continuous time trajectory function order and coefficients.

[0073] Step 4: Normalization preprocessing of the neural network input and output labels.

[0074] Perform normalization processing on the training data pairs composed of the true track and the measurement track after being processed by the above steps. Take the maximum and minimum values of the corresponding original unprocessed measurement tracks as the scale to normalize the TFoT fitting track and the true track:

[0075]

[0076] In the formula, denote the TFoT fitted tracks at K moments; x 1：K denote the true tracks corresponding to the K moments, z min , z max respectively denote the minimum and maximum values in the observed track, x′ 1：K respectively denote the TFoT fitted track state and the true state after normalization processing, and are used as the input and output labels of the neural network respectively.

[0077] Step 5: Design a Transformer network to estimate and compensate the error of the smooth TFoT target tracking method.

[0078] Step 5-1: Perform positional encoding and sequence encoding on the input sequence.

[0079]

[0080] In the formula, PE(·) represents the positional encoding matrix; pos represents the position of each element in the input sequence; i represents the dimension in the positional encoding matrix; d model represents the vector dimension of each position in the Transformer model.

[0081] At the same time, use a fully connected network to perform sequence encoding on the input sequence.

[0082] Step 5-2: Use the multi-head self-attention mechanism to capture the dependencies between sequence elements to globally model the target track.

[0083]

[0084]

[0085] In the formula, Q, K, and V represent the query matrix, key matrix, and value matrix respectively; d k is a parameter set to prevent the gradient from vanishing during the backpropagation of the softmax function due to too high dimensions; n is the number of attention heads.

[0086] Step 5-3: Add residual connections and layer normalization in the encoder sub-module to improve the network and enhance the expression ability of the model through a feed-forward neural network.

[0087] The residual connection mainly solves the problem that the error will become weaker and weaker when the network is very deep, such as Figure 3As shown by the dashed line of the middle encoder module, the error can return to the previous network layer through different paths to improve training. The layer normalization strategy is different from batch normalization. It calculates the mean and variance of all vectors in each layer, then normalizes them to a normal distribution, and then learns the appropriate mean and variance and performs inverse scaling again. This regularization strategy can effectively prevent the network from overfitting.

[0088] The feedforward neural network specifically consists of two linear transformations and a non-linear activation function. The first layer maps the input vector to a hidden layer through a weight matrix, the second layer maps the hidden layer to the output vector, and a ReLU activation function is used to introduce non-linear transformation between the two layers. The addition of the feedforward neural network layer enables the network to learn more complex features and better handle the noise and variations in the input.

[0089] Step 5-4: Further obtain an accurate estimate of the target state through a decoder composed of a dimension adjustment network and a bidirectional LSTM.

[0090] The dimension adjustment network is a simple fully connected network to adjust the dimension of the encoder output to adapt to the input of the bidirectional LSTM. The bidirectional LSTM is a recurrent neural network model that can effectively process time series structured data and capture long-term dependencies in the sequence. Different from the traditional unidirectional LSTM, the bidirectional LSTM considers both the forward and backward information of the input sequence at each time step. The bidirectional LSTM contains two LSTM layers, which process the input sequence from the forward and backward directions respectively and connect their outputs to form the final output, and then adjust it to the final output through the dimension adjustment network again. The decoder composed of the dimension adjustment network and the bidirectional LSTM can further improve the model's expression ability and generalization ability for time series, and obtain an accurate estimate of the target motion state.

[0091] Step 6: Train the neural network.

[0092] The present invention trains the network parameters by minimizing the average weighted root mean square error between the network output and the label.

[0093]

[0094] Where represents the state estimate of the network at the j-th sampling moment; x j represents the true state value at the j-th sampling moment; l represents the sequence length of a single training set; ||·|| represents the L2 norm; batch represents the batch size; w represents the weighted coefficient vector. During the training process, the more attention is paid to the error estimate at a certain moment, the closer the corresponding coefficient in w is to 1.

[0095] Step 7: Perform real-time prediction on the measured track and perform track stitching.

[0096]

[0097]

[0098] In the formula, Model(·) represents the trained neural network model; z' 1：K represents the preprocessed measured track state of the network input; represents the true state estimation output by the network; x 1：N represents the state estimations at the previous N sampling times; x 1：N+1 represents updating the state estimation at the latest sampling time to the total track state estimation, represents the state estimation of the neural network at the k-th sampling time.

[0099] Embodiment:

[0100] Step 1: Establish a maneuvering target track training library.

[0101] Assume that each target makes three maneuvers within a single maneuvering scenario. The starting and ending motion models of the target are CV, and the middle two maneuvers of the target are randomly switched to CT or CA.

[0102] The parameter settings for a single maneuvering scenario are as follows:

[0103] Sampling time t s = 0.5 s, the total track duration t all = 80 s, the duration of a single motion model is randomly taken in the range 15 s ≤ t single ≤ 25 s, the initial track position ini_position = (0, 0), the initial track speed is randomly taken in the range 100 m / s ≤ v ≤ 200 m / s, the initial track motion direction 0° ≤ ini_direction ≤ 360°, the maximum target motion speed limit v max = 300 m / s, the acceleration of the CA model is randomly taken in the range -5 m / s 2 ≤ a ≤ 5 m / s 2 , the turning rate of the CT model is randomly taken in the range -10° ≤ turn_rate ≤ 10°, the position process noise standard deviation and the velocity process noise standard deviation pos_pnsd = 10 m, vel_pnsd = 50 m, the position observation noise standard deviation pos_onsd = 50 m. Process the single-scenario target track, set the step size kernel_size = 5, the sampling time window seq_len = 10, and intercept the true track and the observed track data pairs as training data. Using the above parameters, 1000 motion scenarios are randomly generated, and a total of 30,000 training data pairs are generated. Among them, 500 true tracks are selected and shown as Figure 2 shown.

[0104] Step 2: Use the multi-scale moving average module to smooth the measurement track and perform motion state estimation using the TFoT target tracking method.

[0105] The parameters of the multi-scale moving average module are set as follows: the sliding window step size stride = 1, the smoothing window sizes kernel_size1 = 2 and kernel_size2 = 3, and the sequence padding length is set to 1 accordingly.

[0106] Apply the TFoT target tracking method to the smoothed track for target motion state estimation.

[0107] Step 3: Preprocess the input and output labels of the neural network and set the network parameters for network training.

[0108] Step 3-1: Perform scale normalization on the TFoT state estimation and the target true state according to the maximum and minimum values of the corresponding measurement track, and use them as the input and output labels of the neural network respectively.

[0109] Step 3-2: Set the network parameters and perform network training.

[0110] The details of the adopted neural network architecture are as Figure 3 shown, where the vector dimension of the Transformer position encoding module is set to d model = 128, the fully connected network of the input sequence encoding module is set with input_size = 10, output_size = 128, the number of multi-head attentions is set to num_head = 8, the parameters of the feed-forward neural network are set with input_size = 128, output_size = 256, the parameters of the bidirectional LSTM time series extraction module are set with input_size = output_size = 256, seq_len = 10, num_layers = 2, and the parameters of the deep fully connected network in the output dimension adjustment module are set with input_size = 256, output_size = 2.

[0111] During the network training process, the weight vector of the weighted mean square error loss function is set to w = [0.1, 0.1, 0.1, 0.1, 0.2, 0.3, 0.4, 0.6, 0.8, 1] / 3.7, the network training optimizer is set to the Adam optimizer, the initial learning rate is set to 0.0001, the regularization coefficient is set to 0.0001, the training batch size is set to batch_size = 256, the number of training epochs is set to epochs = 1500, the training framework used is pytorch1.13.1, and the graphics card used is GeForce RTX4090.

[0112] Step 4: Simulation scenario setup.

[0113] The simulation scenario is set in a two - dimensional coordinate system. Initially, the target moves in a uniform straight - line motion with \(t_1 = 20s\), \(v = 150m / s\), and the motion direction is horizontally to the right. Then, it maneuvers and starts to move in a uniform circular motion with \(t_2 = 20s\) and \(turn_rate = 6°\). Then, it maneuvers again and starts to move in a uniform circular motion with \(t_3 = 20s\) and \(turn_rate = 3°\). Finally, it maneuvers again and starts to move in a uniform accelerated straight - line motion with \(t_4 = 20s\) and \(a = 2m / s\) 2 The maneuvering target trajectory is generated by a two - dimensional trajectory generation method based on state space. Among them, the standard deviation of the position process noise and the standard deviation of the velocity process noise are \(pos_pnsd = 10m\) and \(vel_pnsd = 5m / s\), and the standard deviation of the position observation noise is \(pos_onsd = 50m\). The simulation trajectory is as Figure 4 shown.

[0114] Step 5: Target state estimation.

[0115] Using the trained neural network model, the sliding window step size is set to 1. The observed trajectory values of the maneuvering target at \(K = 10\) sampling times are intercepted, and the accurate estimation of the target state is obtained by the method proposed in the present invention, and the complete trajectory is updated in real - time.

[0116] Step 6: Performance index comparison.

[0117] To show the superiority of the method proposed in the present invention, the comparison methods are selected as existing target tracking methods, including polynomial - time trajectory function fitting (the fitting orders are the first - order and the second - order respectively) and the interacting multiple model (IMM) target tracking algorithm (the motion models are CV, CT, and CA models). Taking the root mean square error (RMSE) as the comparison index, the RMSE of the target position at time \(t\) is defined as:

[0118]

[0119] where \(x\) t and \(y\) t are the measured positions of the sensor, and are the position estimates output by the neural network.

[0120] The simulation of the maneuvering target tracking position error between this method and other methods is as Figure 5As shown, it can be seen that this method has achieved significantly better results when tracking CV and CA models. The error increases when tracking the CT motion model with a relatively high turning rate, and the error at the model switching node is significantly smaller than that of other methods. The experimental results prove the effectiveness of this patent in maneuvering target tracking.

[0121] As described above, the above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should be covered within the protection scope of the present invention.

Claims

1. A method for compensating the tracking error of a high-speed maneuvering target based on intelligent smoothing of time series, characterized in that Including: Establish a maneuvering target motion model and a measurement model to obtain the true track and the measured track of the maneuvering target respectively; Design a multi-scale moving average module to smooth the measured track; The multi-scale moving average module is specifically: wherein, is the observed track state; is the track state after smoothing; represents a padding operation to keep the sequence length unchanged; represents a moving average operation; represents a weighting coefficient; represents the smoothing window size at different scales; represents the padding size to ensure the sequence length remains unchanged; Fit the measured track based on the continuous-time trajectory function target tracking method; Construct a neural network, use the smoothed and fitted measured track as the input of the neural network, and use the true track as the output of the neural network; Combine the true track and the measured track to form training data, and use the training data to train the neural network; The neural network is a Transformer network, including an input module, an encoder, a decoder and an output module; The encoder includes a multi-head self-attention and a feed-forward neural network; The decoder includes a dimension-adjusting fully-connected network and a bidirectional LSTM network; Use the trained neural network to perform real-time prediction on the measured track and perform track splicing.

2. A high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing according to claim 1, characterized in that The true track and the measured track include three motion model track libraries of constant velocity linear motion CV, constant velocity circular motion CT and uniformly accelerated linear motion CA, and randomly combine them to simulate the true maneuvering target track.

3. A high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing according to claim 1, characterized in that The maneuvering target motion model and the measurement model are respectively: In the formula, represents the target state at the moment; is the state transition matrix, characterizing the transformation of the state from the previous moment to the current moment; represents the system error; represents the target measurement at the moment; represents the measurement transformation matrix; represents the measurement error, and the system error and the measurement error are independent Gaussian noises.

4. A method for compensating tracking error of a high-speed maneuvering target based on time series intelligent smoothing according to claim 1, characterized in that It also includes normalizing the input and output labels of the neural network: In the formula, represents the TFoT fitting track at corresponding true tracks at respectively represent the minimum and maximum values in the measurement track, respectively represent the TFoT fitting track state and the true state after normalization processing, and are used as the input and output labels of the neural network respectively.

5. A high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing according to claim 1, characterized in that The processing process of the Transformer network includes: Perform position encoding and sequence encoding on the input sequence; Use the multi-head self-attention mechanism to capture the dependencies between sequence elements to globally model the target track; Add residual connections and layer normalization in the encoder sub-module to improve the network and enhance the expression ability of the model through a feed-forward neural network; Further obtain an accurate estimate of the target state through a decoder composed of a dimension-adjusting fully-connected network and a bidirectional LSTM.

6. The high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing according to claim 1, wherein The real-time prediction of the measured track and the track splicing: In the formula, represents the trained neural network model; represents the preprocessed measurement track state of the network input; represents the true state estimation output by the network; represents the previous state estimations at sampling times; represents updating the state estimation at the latest sampling time to the total track state estimation; represents that the neural network estimates the state at the k th sampling time.

7. A verification method for the high-speed maneuvering target tracking error compensation method based on time series intelligent smoothing according to claim 1, characterized in that: Taking the root mean square error RMSE as the comparison index, it is defined that the RMSE of the target position at time In the formula, and are the sensor measurement positions, and are the position estimations output by the neural network.

8. A computer system, characterized in that Including: One or more processors, a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method according to claim 1.

9. A computer-readable storage medium, characterized in that Store computer-executable instructions, which are used to implement the method according to claim 1 when executed.

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