A discontinuous track association method based on long short-term memory network and residual network
By combining long short-term memory networks and residual networks, the problem of track interruption is solved, the accuracy and stability of track association are improved, and multi-target tracking is adapted to complex battlefield environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XI AN JIAOTONG UNIV
- Filing Date
- 2026-03-18
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies suffer from track interruption issues in multi-target track association, leading to increased difficulty and complexity in the association process. In particular, when targets are highly maneuvering or in formation, the mismatch between traditional algorithm models results in a decrease in association accuracy.
A discontinuous trajectory association method based on Long Short-Term Memory (LSTM) and ResNet is adopted. By extracting time-related and spatial structure information, and combining a comprehensive loss function of symmetric constraint loss and contrast loss, the association accuracy is improved.
In complex battlefield environments, it significantly improves the accuracy and robustness of track association, reduces the error and omission rates, adapts to target maneuvering and quantity changes, and outperforms traditional fuzzy TSA algorithms.
Smart Images
Figure CN122241579A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of multi-sensor information fusion and target tracking technology, and more specifically to a method for associating discontinuous tracks based on long short-term memory networks and residual networks. Background Technology
[0002] With the continuous integration and development of unmanned systems and intelligent technologies, the combat realism of UAV swarm warfare is constantly improving, gradually entering the battlefield and ushering in the era of intelligent warfare. Although the rapid development of sensor technology and information fusion technology has enabled modern multi-sensor information fusion systems to simultaneously track multiple targets in real time, track interruptions or discontinuous tracks remain a major and frequent problem when tracking multiple targets. This can easily mislead the tracker when estimating the total number of targets, reducing the tracker's overall performance. In practice, it is only possible to analyze the history of a specific target and make better tactical decisions when the target maintains a consistent track identification (ID) from detection to disappearance. However, in practical applications, track interruptions can occur at any time due to factors such as the high maneuverability of flying targets, measurement errors, radar Doppler blind spots, close-range target formations, numerous measurement errors, and long sampling intervals. Therefore, multi-target track association still faces challenges such as the increased difficulty of association due to discontinuous target tracks, and the sharp increase in association complexity with the number of targets and sensors.
[0003] The problem of discontinuous track association processing is determining whether the track before and after the interruption originates from the same continuous track for the same target. Generally, there are two main approaches to resolving track interruption issues. One is to employ high-precision, high-performance sensors and multi-sensor collaborative tracking technology to minimize track interruptions during target track filtering and tracking. The other approach is post-processing after track interruptions occur, associating the resulting interrupted tracks; this technique is generally called Track Segment Association (TSA). As a post-processing technique, TSA improves track continuity by combining or splicing track segments over a period of time. Essentially, it reduces the number of interrupted track segments by maintaining consistent track segment identifiers, thereby improving overall tracker performance.
[0004] For the correlation problem of targets in highly maneuvering or close-range formations, existing technologies have proposed two solutions. One is to fully consider prior information such as target attributes, motion characteristics, and application scenarios, and predict the trajectory based on a multi-hypothesis model to establish a fuzzy match between the predicted trajectory under maneuvering conditions and the trajectory after the interruption. The other is based on statistical double thresholds, which performs statistical double threshold hypothesis testing on the distribution of the correlation samples, helping to adapt to the correlation of interrupted trajectories in complex situations such as dense targets, overlapping or bifurcated trajectories. Existing technologies, specifically addressing the problem of trajectory interruption in passive-phase ballistic missile targets, propose an interrupted trajectory correlation algorithm based on fuzzy theory and evidence theory. By fuzzy processing the distances between feature vectors of sample points at the same moment, the correlation membership degree is obtained, which is then transformed into a basic probability assignment function in evidence theory. Finally, evidence combination is used to effectively solve the problem of discontinuity between the preceding and following trajectories caused by the trajectory interruption.
[0005] Furthermore, with the widespread application of machine learning in numerous fields, data-driven models have begun to be adopted and learned by many scholars. Existing technologies employ graph neural networks, obtaining representations of track segments and preserving irregular structural information through node-level local track point embedding and graph-level track graph embedding. Under the constraint of the loss function, track segments belonging to the same target become closer in the representation space, while track segments belonging to different targets become farther apart; therefore, the nearest neighbor embedding in the representation space is selected as the associated trajectory. In addition, existing technologies have also proposed a Track Segment Association Dual Contrast Neural Network (TSADCN) to complete the track segment association task.
[0006] The algorithms described above generally consider prior information such as the target motion state model. They work by forward-progressing the old track to the start time of the new track, backward-progressing the new track to the end time of the old track, or forwarding the old and new tracks to a common intermediate time, and then measuring the correlation of the track data based on specific metrics. However, these methods have some shortcomings in practical applications, such as unreasonable assumptions, model mismatch, and inappropriate thresholds. Among these, model selection is a crucial step, directly affecting the quality of the association results. While IMM can effectively fuse multiple motion models, as the number of possible models increases, excessive "competition" occurs, wasting system computing resources, slowing down the operation, and reducing performance. In recent years, with the rapid development of artificial intelligence, neural networks have been widely applied in many fields. With their powerful learning and fitting capabilities, the introduction of neural networks can avoid the problems of IMM using a large number of motion models and potentially unreasonable assumptions, thereby effectively improving the association accuracy of interrupted track association algorithms.
[0007] Therefore, how to provide a method for intermittent track association based on long short-term memory networks and residual networks is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0008] In view of this, the present invention provides a discontinuous trajectory association method based on long short-term memory network and residual network. This method can effectively solve the problem of discontinuous trajectory association when the target motion model and the assumed model do not match, thereby improving the association accuracy of discontinuous trajectories in complex battlefield environments.
[0009] To achieve the above objectives, the present invention adopts the following technical solution: A method for intermittent track association based on long short-term memory networks and residual networks includes the following steps: Obtain the first and second track segments to be associated, where the first track segment is the old track segment and the second track segment is the new track segment; The first and second track segments are normalized to obtain normalized track data for the first and second track segments. The normalized first and second track segments are respectively input into the pre-trained time-related information extraction module and spatial structure information extraction module. The time-related information extraction module is built based on the Long Short-Term Memory (LSTM) network and is used to extract the time-related information of the track segments. The spatial structure information extraction module is built based on the ResNet residual network and is used to extract the spatial structure information of the track segments. The extracted time-related information and spatial structure information are fused to obtain the feature vectors of the first and second track segments; Based on the feature vectors of the first and second track segments, determine whether the two track segments originate from the same target and output the association result.
[0010] Furthermore, in Based on the start and end times of the track, all confirmed track segments are divided into two categories: old track segments and new track segments. Among them, the old track section: During this period, B represents a sliding window parameter, and the track segment for which status updates cannot be performed due to a lack of measurement data is as follows:
[0011] In the formula, Indicates the number of old track segments. These represent the old track segments. The start and end times, This represents the target state estimation vector in the old track segment; New flight path segment: In During this period, the continuation of an already terminated old track segment from the same destination, or the start of a track segment during an interruption:
[0012] In the formula, Indicates the number of new flight segments. These represent the new flight path segments. The start and end times, This represents the target state estimation vector in the new trajectory segment.
[0013] Furthermore, the normalization process includes normalizing each dimension of the state vector for the first and second track segments respectively.
[0014] Furthermore, the time-related information extraction module includes: The LSTM layer extracts the time-series features of the track segment through input gates, forget gates, output gates, and memory units. The nonlinear activation function, located after the LSTM layer, transforms the distribution of values to between -1 and 1. The specific calculation formula is as follows:
[0015] In the formula, It is a symmetric track matrix. It refers to the length of time the flight path was interrupted.
[0016] Furthermore, the spatial structure information extraction module includes multiple residual blocks and fully connected layers. Each residual block adds the input to the output after convolution and batch normalization through skip connections. The fully connected layers map the features output by the residual blocks to a high-dimensional space to obtain spatial structure information.
[0017] Furthermore, the pre-trained time-related information extraction module and spatial structure information extraction module are obtained through the following training steps: S1, Construct a training dataset, which contains multiple track pairs. Each track pair consists of an old track segment and a new track segment, and is labeled as to whether they come from the same target. S2, normalizes each track pair in the training dataset; S3, input the normalized track pairs into the time-related information extraction module and the spatial structure information extraction module to be trained, and obtain the feature vectors of the first track segment and the second track segment; S4, calculate the total loss function based on the feature vectors, the total loss function being obtained by weighting the contrastive loss function and the symmetric constraint loss function; S5 updates the network parameters using gradient descent based on the total loss function until the network converges.
[0018] Furthermore, the formula for calculating the symmetric constraint loss function is as follows:
[0019] In the formula, It is the first in the track matrix Line number Column elements, It is the first in the track matrix Line number Column elements, It refers to the length of time the flight path was interrupted.
[0020] Furthermore, the formula for calculating the contrast loss function is as follows:
[0021] In the formula, It is a binary tag when the old and new track segments come from the same target. ,on the contrary ; This represents the distance threshold, which is the shortest distance in high-dimensional space between the feature vectors extracted from new and old track segments from different targets. It is the Euclidean distance between two eigenvectors in a high-dimensional space.
[0022] Furthermore, the formula for calculating the total loss function is as follows:
[0023] In the formula, and These are the symmetric constraint loss function and the contrastive loss function, respectively.
[0024] Furthermore, in the training dataset, the training set contains 6144 track pairs, and the validation set contains 2048 track pairs; the batch size during training is 256, the learning rate is 0.015, the training cycle is 150 times, and the weight optimization adopts the stochastic gradient descent method.
[0025] As can be seen from the above technical solution, compared with the prior art, this invention provides a discontinuous track association method based on Long Short-Term Memory (LSTM) networks and residual networks. By introducing deep learning technology, it effectively solves the problem of decreased association accuracy in traditional algorithms when the model is mismatched. Its beneficial effects are as follows: First, by extracting time-related information through the LSTM module and combining it with the ResNet module to extract spatial structure information, it can fully mine the deep features of track data, overcoming the limitations of traditional methods that rely on manually set motion models. Second, a comprehensive loss function integrating symmetric constraint loss and contrastive loss is designed, effectively improving the discriminativeness of the feature space. This ensures that the average correct association rate remains stable even in complex scenarios such as target height maneuvering, changes in interruption time, or an increase in the number of targets, while the error association rate and missed association rate are controlled at extremely low levels. Furthermore, this method exhibits excellent robustness to changes in interruption duration and the number of targets, significantly outperforming traditional fuzzy TSA algorithms and improved TSA algorithms, providing reliable technical support for multi-target tracking in complex battlefield environments. Attached Figure Description
[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0027] Figure 1 The overall structure diagram of the TSALR neural network provided by this invention; Figure 2 The basic unit structure diagram of LSTM provided by this invention; Figure 3 The structural diagram of the TSALR time-related information extraction module provided by this invention; Figure 4 The structural diagram of the TSALR spatial structure information extraction module provided by this invention; Figure 5 The network training loss and the change curves of accuracy on the training set and validation set are provided for the present invention. Figure 6 A comparison chart of the average correct correlation rates of different algorithms under different track interruption times provided by this invention; Figure 7 A comparison chart of the average correct correlation rates of different algorithms under different numbers of flying targets provided by this invention; Figure 8 This is a schematic diagram of the discontinuous flight track association method provided by the present invention. Detailed Implementation
[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0029] See Figure 8 This invention discloses a method for associating discontinuous flight paths based on long short-term memory networks and residual networks, comprising the following steps: Obtain the first and second track segments to be associated, where the first track segment is the old track segment and the second track segment is the new track segment; The first and second track segments are normalized to obtain normalized track data. The normalized first and second track segments are respectively input into the pre-trained time-related information extraction module and spatial structure information extraction module. The time-related information extraction module is built based on the Long Short-Term Memory (LSTM) network and is used to extract the time-related information of the track segments. The spatial structure information extraction module is built based on the ResNet residual network and is used to extract the spatial structure information of the track segments. The extracted time-related information and spatial structure information are fused to obtain the feature vectors of the first and second track segments; Based on the feature vectors of the first and second track segments, determine whether the two track segments originate from the same target and output the association result.
[0030] Specifically, in actual combat scenarios, due to factors such as the high maneuverability of flying targets, measurement errors, radar Doppler blind spots, close-range target formations, numerous measurement errors, and long sampling intervals, track interruptions are inevitable. The method of this invention first trains network parameters based on metric learning. Then, it pairs new and old track segments as input to the network, using time-related information extraction and spatial structure information extraction modules for feature abstraction and extraction. A similarity measurement is performed in the classifier module to determine whether a track is associated, thereby improving the accuracy of associating interrupted track links.
[0031] See Figure 1First, the trajectory data is normalized by normalizing each dimension to obtain standardized, dimensionless training data, which is convenient for neural network processing. Then, time-related information is extracted by constructing a time-related information extraction module based on a Long Short Term Memory (LSTM) network to extract time-related information from both new and old trajectory segments. Simultaneously, spatial structure information is extracted by constructing a spatial structure information extraction module based on a Residual Network (ResNet) to extract spatial structure information from both new and old trajectory segments. Next, the loss function is calculated by combining a symmetric constraint loss function and a contrastive loss function with certain weights to obtain the total loss function. Finally, performance testing is performed by training the network and applying the trained TSALR network to the test set.
[0032] Specifically, in Based on the start and end times of the track, all confirmed track segments are divided into two categories: old track segments and new track segments. (1) Old track segment: in (B is the sliding window parameter) During this period, track segments that cannot be updated due to lack of measurement data.
[0033]
[0034] In the formula, Indicates the number of old track segments. These represent the old track segments. The start and end times, This represents the target state estimation vector in the old track segment.
[0035] (2) New track segment: in During this period, it may be a continuation of an old track segment that has been terminated from the same target, or a track segment that begins during an interruption.
[0036]
[0037] In the formula, Indicates the number of new flight segments. These represent the new flight path segments. The start and end times, This represents the target state estimation vector in the new trajectory segment.
[0038] In step one, a new track segment is selected from the training dataset. and an old track section To form a pair of flight paths For the new flight path segment and old track section Normalization is performed separately to obtain standardized dimensionless training data. The normalization formula is:
[0039] In the formula, They represent Current old flight path segment and new flight path One dimension of the state vector, These represent the old track segments. and new flight path The maximum value of the dimension of the state vector during the existence of the track. These represent the old track segments. and new flight path The minimum value of the state vector dimension during the existence of the track.
[0040] In step two, a time-related information extraction module based on LSTM is constructed to transform the shape of the input track vector from... Change to And extract time-related information. The specific calculation formula for LSTM is as follows: See Figure 2 Suppose there is There are hidden units, and the batch size is [number]. The input number is Therefore, the input is The hidden state at the previous time step was Accordingly, The time gate is defined as: the input gate is The Gate of Oblivion is The output gate is Their mathematical expressions are as follows:
[0041] in, and These are weight parameters. It is a bias parameter.
[0042] The computation of candidate memories is similar to that of the three gates, but uses... The function, as an activation function, has the following properties: The mathematical expression for time is:
[0043] in, and These are weight parameters. It is a bias parameter.
[0044] The memory elements and hidden states passed to the next moment are and The calculation method is as follows:
[0045] Among them, memory element Mainly affected by input gate And the Gate of Oblivion Control: Input Gate Control how much from candidate memory cells to use New data, Forgot Gate Control how much memory from the past is retained Information, This indicates element-wise multiplication. Hidden state. Mainly affected by the output gate Influence.
[0046] In step two, the time-related information extraction module is added after the LSTM. A non-linear activation function transforms the distribution of values to between -1 and 1. The specific calculation formula is as follows:
[0047] In the formula, It is a symmetric track matrix. This refers to the duration of the track interruption; tanh(x) is a function. See the structure diagram of the time-related information extraction module. Figure 3 .
[0048] In step three, a ResNet-based spatial structure information extraction module is constructed to extract spatial structure information. The calculation formula for the residual block is as follows:
[0049] In the formula, It is the output of the residual block. It goes through two layers The output of the convolutional layer after batch normalization. Introduced The output of the residual connections of the convolutional layer.
[0050] In step three, the spatial structure information extraction module uses a fully connected (FC) layer for high-dimensional mapping. The output of the fully connected layer is the track vector in high-dimensional space.
[0051] in, It is the output of the fully connected layer. These are the learnable parameters of the fully connected layer. It is the bias of the fully connected layer. This is the output of the 5th residual block. See the diagram for the spatial structure information extraction structure. Figure 4 .
[0052] In step four, the total loss function is obtained by combining the symmetric constraint loss function and the contrastive loss function according to certain weights.
[0053] The symmetry-constrained loss function is used to maintain the symmetry of the track matrix and minimize the difference between values at symmetric positions in the track matrix. The formula for calculating the symmetry-constrained loss function is as follows:
[0054] In the formula, It is the first in the track matrix Line number Column elements, It is the first in the track matrix Line number Column elements, It refers to the length of time the flight path was interrupted.
[0055] The formula for calculating the contrastive loss function is as follows:
[0056] In the formula, It is a binary tag that indicates when new and old track segments originate from the same destination. ,on the contrary . This represents the distance threshold, which is the shortest distance in high-dimensional space between the feature vectors extracted from new and old track segments from different targets. It is the Euclidean distance between two eigenvectors in a high-dimensional space.
[0057] Since the value of the symmetric constraint loss function is too small, it needs to be multiplied by the weight coefficients to make the network more convergent. The formula for calculating the total loss function is as follows:
[0058] In the formula, and These are the symmetric constraint loss function and the contrastive loss function, respectively.
[0059] In step five, during neural network training, 6144 track pairs are used as the training set, 2048 track pairs as the validation set, and the number of track pairs used in the test set is the square of the target number, which varies with the number of targets. The batch size in the neural network is 256, the learning rate is 0.015, the training epochs are 150, and the weight optimization method is stochastic gradient descent.
[0060] See Figure 5 The blue line represents the network loss curve, while the red and black lines represent the accuracy change curves of the training set and the validation set, respectively. This shows that the accuracy of the TSALR neural network continuously improves and the network loss continuously decreases during the training process, indicating that the neural network can gradually converge.
[0061] See Figure 6 The TSALR algorithm proposed in this invention, even under the assumption of model mismatch, achieves a higher average correct correlation rate compared to the improved TSA algorithm. The accuracy rate remained high at around 97%, showing no significant decline, and remained stable even with increasing track interruption time, demonstrating the good applicability of neural networks. The average correct association rate of the discontinuous track association algorithm based on fuzzy mathematics first decreased, then increased, and then decreased again with increasing interruption time, reaching a maximum of 78% when the track interruption time was 10 seconds. Although, under the assumption of model mismatch, the fuzzy TSA algorithm still maintained a more stable average correct association rate (between 65% and 80%) compared to the traditional TSA algorithm, even without knowing the target's motion model during the track interruption, its overall association judgment performance was only average.
[0062] Referring to Tables 1 and 2, both the TSALR algorithm and the fuzzy TSA algorithm proposed in this invention have low average missed association rates, which do not change much with the increase of interruption time, basically remaining between 1% and 2%. The difference in the association accuracy of the two algorithms is mainly reflected in the erroneous associations. The fuzzy TSA algorithm has consistently had a high average erroneous association rate, fluctuating around 20% to 30%, while the TSALR algorithm fluctuates around 1% to 2%. It is worth noting that the average erroneous association rate of the fuzzy TSA algorithm is as high as 30.72% when the track interruption time is 6 seconds. This is because as the interruption time increases, the prediction error of the track prediction algorithm continuously increases, leading to a corresponding increase in the probability of erroneous associations. Therefore, the average erroneous association rate increases from 24.06% when the interruption time is 4 seconds to 30.72%. However, the average error correlation rate was lowest when the track interruption time was 10s, at only 20.44%. This is because the upper and lower limit thresholds of the error of each fuzzy factor set by the fuzzy TSA algorithm are based on the prediction error when the interruption time is 10s. Therefore, compared with the average error correlation rate of 30.72% when the interruption time is 6s, the average error correlation rate of 10s is significantly lower.
[0063] Table 1. Comparison of average missed correlation rates under different track interruption times.
[0064] Table 2 Comparison of average error correlation rates under different track interruption times
[0065] See Figure 7 The TSALR algorithm proposed in this invention, even under the assumption of model mismatch, shows a slight overall improvement in average correct association rate compared to the improved TSA algorithm. In fact, with 6 flying targets, the average correct association rate reaches 100%, and even with an increased number of flying targets, it remains around 97%, showing no significant decline in association judgment performance. In contrast, the fuzzy TSA algorithm, despite not knowing the target's motion model, shows a more significant improvement in average correct association rate compared to the traditional TSA algorithm, with a slight decrease in the rate of decline from 88% to 66%.
[0066] Referring to Tables 3 and 4, the average missed association rate and average false association rate of the TSALR algorithm proposed in this invention remain at a low level, with the highest reaching only 1.52% and 1.74% respectively, and the lowest even reaching 0%. The average missed association rate of the fuzzy TSA algorithm also remains at a low level, fluctuating between 1% and 3%. However, its average false association rate inevitably begins to rise rapidly with the increase of the number of flying targets. Although the rate of increase in average false association rate is suppressed when the number of flying targets increases to a certain extent, overall, it is still affected by the large number of flying targets.
[0067] Table 3. Comparison of average missed correlation rates under different numbers of flying targets
[0068] Table 4. Comparison of average error correlation rates under different numbers of flying targets
[0069] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0070] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for correlated discontinuous flight paths based on long short-term memory networks and residual networks, characterized in that, Includes the following steps: Obtain the first and second track segments to be associated, where the first track segment is the old track segment and the second track segment is the new track segment; The first and second track segments are normalized to obtain normalized track data for the first and second track segments. The normalized first and second track segments are respectively input into the pre-trained time-related information extraction module and spatial structure information extraction module. The time-related information extraction module is built based on the Long Short-Term Memory (LSTM) network and is used to extract the time-related information of the track segments. The spatial structure information extraction module is built based on the ResNet residual network and is used to extract the spatial structure information of the track segments. The extracted time-related information and spatial structure information are fused to obtain the feature vectors of the first and second track segments; Based on the feature vectors of the first and second track segments, determine whether the two track segments originate from the same target and output the association result.
2. The discontinuous track association method based on long short-term memory network and residual network according to claim 1, characterized in that, exist Based on the start and end times of the track, all confirmed track segments are divided into two categories: old track segments and new track segments. Among them, the old track section: During this period, B represents a sliding window parameter, and the track segment for which status updates cannot be performed due to a lack of measurement data is as follows: In the formula, Indicates the number of old track segments. These represent the old track segments. The start and end times, This represents the target state estimation vector in the old track segment; New flight path segment: In During this period, the continuation of an already terminated old track segment from the same destination, or the start of a track segment during an interruption: In the formula, Indicates the number of new flight segments. These represent the new flight path segments. The start and end times, This represents the target state estimation vector in the new trajectory segment.
3. The discontinuous track association method based on long short-term memory network and residual network according to claim 1, characterized in that, The normalization process includes normalizing each dimension of the state vector for the first and second track segments respectively.
4. The discontinuous track association method based on long short-term memory network and residual network according to claim 1, characterized in that, The time-related information extraction module includes: The LSTM layer extracts the time-series features of the track segment through input gates, forget gates, output gates, and memory units. The nonlinear activation function, located after the LSTM layer, transforms the distribution of values to between -1 and 1. The specific calculation formula is as follows: In the formula, It is a symmetric track matrix. It refers to the length of time the flight path was interrupted.
5. The discontinuous track association method based on long short-term memory network and residual network according to claim 1, characterized in that, The spatial structure information extraction module includes multiple residual blocks and fully connected layers. Each residual block adds the input to the output after convolution and batch normalization through skip connections. The fully connected layers map the features output by the residual blocks to a high-dimensional space to obtain spatial structure information.
6. The discontinuous track association method based on long short-term memory network and residual network according to claim 1, characterized in that, The pre-trained time-related information extraction module and spatial structure information extraction module are obtained through the following training steps: S1, Construct a training dataset containing multiple track pairs. Each track pair consists of an old track segment and a new track segment, and is labeled as to whether they come from the same target. S2, normalizes each track pair in the training dataset; S3, input the normalized track pairs into the time-related information extraction module and the spatial structure information extraction module to be trained, and obtain the feature vectors of the first track segment and the second track segment; S4, calculate the total loss function based on the feature vectors, the total loss function being obtained by weighting the contrastive loss function and the symmetric constraint loss function; S5 updates the network parameters using gradient descent based on the total loss function until the network converges.
7. The discontinuous track association method based on long short-term memory network and residual network according to claim 6, characterized in that, The formula for calculating the symmetric constraint loss function is as follows: In the formula, It is the first in the track matrix Line number Column elements, It is the first in the track matrix Line number Column elements, It refers to the length of time the flight path was interrupted.
8. The discontinuous track association method based on long short-term memory network and residual network according to claim 6, characterized in that, The formula for calculating the contrastive loss function is as follows: In the formula, It is a binary tag when the old and new track segments come from the same target. ,on the contrary ; This represents the distance threshold, which is the shortest distance in high-dimensional space between the feature vectors extracted from new and old track segments from different targets. It is the Euclidean distance between two eigenvectors in a high-dimensional space.
9. The discontinuous track association method based on long short-term memory network and residual network according to claim 6, characterized in that, The formula for calculating the total loss function is as follows: In the formula, and These are the symmetric constraint loss function and the contrastive loss function, respectively.
10. The discontinuous track association method based on long short-term memory network and residual network according to claim 6, characterized in that, The training dataset contains 6144 track pairs in the training set and 2048 track pairs in the validation set. The batch size during training is 256, the learning rate is 0.015, the training cycle is 150 times, and the weight optimization uses the stochastic gradient descent method.