Underwater maneuvering target tracking method and device

Abstract

An underwater maneuvering target tracking method comprises the following steps: establishing a nonlinear system state space model, and converting underwater maneuvering target distance and azimuth angle observation values obtained by a sonar system into a Cartesian coordinate system to form an observation trajectory sequence; inputting the observation trajectory sequence into a pre-trained prediction model, extracting global time sequence dependence characteristics of the observation trajectory sequence by the prediction model through a plurality of encoders connected in sequence, and outputting a predicted residual trajectory through a decoder; and adding the predicted residual trajectory and the observation trajectory sequence to determine a final target state prediction trajectory. The method can improve the tracking precision of the underwater maneuvering target.

Description

Technical Field

[0001] This invention relates to the field of underwater detection technology, and in particular to a method and apparatus for tracking underwater maneuvering targets. Background Technology

[0002] Sonar utilizes the propagation and reflection characteristics of sound waves in water to perform navigation and ranging through electroacoustic conversion and information processing. In the field of underwater target tracking, sonar systems need to continuously estimate and predict the target's trajectory, especially when the target is in a nonlinear maneuvering state such as high-speed turns or serpentine navigation, where real-time and high-precision estimation of the target's state is crucial. Therefore, multi-model tracking algorithms based on Bayesian theory are widely used. Among them, the Interactive Multi-Model (IMM) filtering method is widely adopted in current underwater maneuvering target tracking systems because it can fuse the estimation results of multiple motion models, possessing good target adaptability and high tracking accuracy. The IMM algorithm constructs multiple preset motion models (such as uniform velocity models, uniform acceleration models, turning models, etc.), updates model probabilities and fuses state estimates based on target observation data, making it suitable for handling unsteady target trajectories. However, a core limitation of this method is that its model switching mechanism relies entirely on posterior observation information. When the target undergoes sudden maneuvers, the update of model probabilities is significantly delayed, leading to untimely state estimation response and decreased accuracy. Furthermore, the number and combination of models within the IMM framework need to be manually set, making it difficult to dynamically cover all possible motion states and resulting in certain modeling biases. Therefore, improving the accuracy of underwater maneuvering target tracking methods has become an urgent problem to be solved. Summary of the Invention

[0003] To address the problems existing in the prior art, embodiments of this application provide a method, apparatus, computing device, computer storage medium, and product containing a computer program for tracking underwater maneuvering targets, which can improve the tracking accuracy of underwater maneuvering targets.

[0004] In a first aspect, embodiments of this application provide an underwater maneuvering target tracking method, comprising: establishing a nonlinear system state-space model; converting the distance and azimuth observations of the underwater maneuvering target acquired by the sonar system to a Cartesian coordinate system to form an observation trajectory sequence; inputting the observation trajectory sequence into a pre-trained prediction model; the prediction model extracting global temporal dependency features of the observation trajectory sequence through multiple sequentially connected encoders; and outputting the predicted residual trajectory through a decoder; and adding the predicted residual trajectory to the observation trajectory sequence to determine the final target state prediction trajectory.

[0005] In some possible implementations, the prediction model also includes an input module comprising a linear transformation layer and a position encoding layer. The method further includes: mapping the input observation trajectory sequence to a high-dimensional representation space through a learnable weight matrix and bias vector via the linear transformation layer; generating an absolute position code for each time step in the sequence via the position encoding layer, adding it to the linearly transformed sequence, and inputting the result into an encoder.

[0006] In some possible implementations, the result is represented as:

[0007]

[0008] In the formula, Characterizing the observed trajectory sequence, Characterizes the weight matrix and has d is the dimension. Characterizes the bias vector and has , Characterizing time steps, Characterized by absolute position encoding; whereby, the observed trajectory sequence In the formula, each observation vector , and The coordinates representing the x and y axes. and Characterizes the velocity along the x and y axes.

[0009] In some possible implementations, the encoder includes: a masked multi-head self-attention sublayer, a feedforward fully connected network sublayer, residual connections, and a switchable normalization layer. Extracting global temporal dependency features of the observed trajectory sequence involves: performing masked attention computation on the input sequence through the masked multi-head self-attention sublayer to capture the global dependencies of the sequence while preventing future information leakage; and performing a nonlinear transformation on the output of the masked multi-head self-attention sublayer through the feedforward fully connected network sublayer. The data processed by the masked multi-head self-attention sublayer and the feedforward fully connected network sublayer are then processed through residual connections and a switchable normalization layer.

[0010] In some possible implementations, the switchable normalization layer adaptively fuses batch normalization, instance normalization, and layer normalization using learnable weights, and its computation is expressed as follows:

[0011]

[0012] In the formula, For input data that needs to be normalized, , , These are learnable weight parameters. For batch normalization, all samples in each channel within a small batch are normalized. For instance normalization, normalization is performed separately for each channel. For layer normalization, each feature vector of each sample is normalized.

[0013] In some possible implementations, the computation process of the masked multi-head self-attention sublayer includes: linearly projecting the input sequence through three different sets of learnable weight matrices to generate a query matrix. Key matrix Sum matrix The output of each attention head is calculated using the following formula:

[0014]

[0015] In the formula, The scaling factor is used to prevent the inner product from becoming too large and affecting gradient calculation, and it also has... , It can be an upper triangular matrix, where M is the number of self-attention heads; the outputs of all attention heads are concatenated and linearly projected.

[0016] In some possible implementations, the decoder includes: multiple sequentially connected one-dimensional dilated convolutional layers, max pooling layers, and linear layers; the predicted residual trajectory output by the decoder includes: extracting local multi-scale details of the input global temporally dependent features through multiple one-dimensional dilated convolutional layers at different dilation rates; downsampling the feature sequence output by the dilated convolutional layers in the time dimension through max pooling layers to extract key features; and mapping the pooled features to the dimension of the residual trajectory through linear layers to output the predicted residual trajectory.

[0017] In some possible implementations, the operational formula for a one-dimensional dilated convolutional layer is:

[0018]

[0019] In the formula, Characterizing time steps, Characterizes the size of the convolution kernel. Characterize the input sequence, Characterizing the weight matrix, The weights of the convolution kernel are represented by the k-th weight of the convolution kernel. Characterizes the expansion rate.

[0020] In some possible implementations, the prediction model is trained by minimizing a weighted loss function, which is defined as:

[0021]

[0022] In the formula, Represents the true trajectory of the target. Characterizing the observed trajectory, Characterizing the predicted residuals, The weighting coefficients representing position and velocity information are taken as follows: , Characterizing the number of samples, Characterizes the time step.

[0023] Secondly, embodiments of this application provide an underwater maneuvering target tracking device, comprising: a conversion module for establishing a nonlinear system state-space model, converting the observed distance and azimuth values ​​of the underwater maneuvering target acquired by the sonar system to a Cartesian coordinate system to form an observation trajectory sequence; a processing module for inputting the observation trajectory sequence into a pre-trained prediction model, wherein the prediction model extracts global temporal dependency features of the observation trajectory sequence through multiple sequentially connected encoders, and outputs the predicted residual trajectory through a decoder; the processing module is further configured to add the predicted residual trajectory to the observation trajectory sequence to determine the final target state prediction trajectory.

[0024] Thirdly, embodiments of this application provide a computer-readable storage medium including computer-readable instructions that, when read and executed by a computer, cause the computer to perform the method as described in any of the first aspects.

[0025] Fourthly, embodiments of this application provide a computing device, including a processor and a memory, wherein the memory stores computer program instructions, which, when executed by the processor, perform the method as described in any of the first aspects.

[0026] Fifthly, embodiments of this application provide a product comprising a computer program that, when the computer program product is run on a processor, causes the processor to perform the method as described in any of the first aspects. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart illustrating an underwater maneuvering target tracking method provided in an embodiment of this application;

[0029] Figure 2This is a schematic diagram of a complete process for predicting the trajectory of a target state using a TrDCN model, provided in an embodiment of this application.

[0030] Figure 3 This is a schematic diagram of the target motion trajectory and measurement values ​​in a simulation provided by an embodiment of this application;

[0031] Figure 4 This is a comparison chart of the root mean square error of different models provided in an embodiment of this application;

[0032] Figure 5 This is a comparison chart of the root mean square error of different models provided in the embodiments of this application;

[0033] Figure 6 This application provides an embodiment of a different filter position and velocity ARMSE;

[0034] Figure 7 This is a schematic diagram of the structure of an underwater maneuvering target tracking device provided in an embodiment of this application. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0036] In this article, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The symbol " / " in this article indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0037] The terms "first" and "second," etc., used in the specification and claims herein are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0038] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0039] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0040] To facilitate understanding of the embodiments of this application, the following will provide further explanation and description with reference to the accompanying drawings and specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0041] The interactive multi-model (IMM) filtering method, which is currently widely used for underwater maneuvering target tracking, has improved its adaptability to different target motion states to some extent, but it still has key defects that limit its tracking performance and engineering application value in complex underwater environments.

[0042] First, model switching relies on posterior observation information and lacks feedforward prediction capabilities. This results in the system being unable to promptly perceive changes in motion patterns when the target undergoes sudden maneuvers, leading to delayed model probability updates and increased state estimation bias. Second, the IMM model set is fixed and manually configured, making it difficult to dynamically cover complex or unknown motion states that the target may exhibit, resulting in insufficient tracking robustness and generalization ability. Third, although deep learning methods such as LSTM and GRU have been introduced to enhance trajectory modeling capabilities, these methods suffer from limitations such as limited temporal modeling depth, difficulty in training convergence, and low inference efficiency, making them unsuitable for applications with high real-time requirements.

[0043] In recent years, deep learning methods have been increasingly introduced into the field of target tracking to enhance the ability to model nonlinear dynamic patterns of trajectories. Typical structures such as Long Short-Term Memory (LSTM) networks and Recurrent Neural Networks (RNNs) can capture temporal features in target trajectories for state prediction and filter initialization. While these methods improve the predictive ability of the models, they also suffer from problems such as complex training processes, insufficient depth of temporal modeling, and reliance on local history, limiting their widespread application in complex underwater environments.

[0044] Furthermore, traditional methods often directly model the target trajectory end-to-end, failing to effectively utilize the "residual signal between predicted and observed values," an important intermediate feature reflecting changes in the target state. This results in limited modeling accuracy, and inconsistent state dimensions also affect the training stability and prediction accuracy of the model.

[0045] In view of this, embodiments of this application provide an underwater maneuvering target tracking method that integrates a Transformer structure and a dilated convolutional neural network. This fully utilizes the global dependency capture capability of the Transformer network in sequence modeling to effectively represent long-term dynamic changes in the target trajectory. Simultaneously, a multi-scale dilated convolutional network (DCN) is introduced to enhance the perception of local details in the trajectory residual signal and improve the sensitivity to state changes. During the modeling process, a residual trajectory mapping mechanism is designed. By modeling the residual signal between the real trajectory and the predicted trajectory, the dynamic range of the state values ​​is effectively compressed, improving the stability and convergence speed of model training.

[0046] For example, Figure 1 A flowchart illustrating an underwater maneuvering target tracking method provided in an embodiment of this application is shown. Figure 1 As shown, the tracking method includes the following steps:

[0047] S11: Establish a state-space model of the nonlinear system, and transform the underwater maneuvering target distance and azimuth observations obtained by the sonar system into a Cartesian coordinate system to form an observation trajectory sequence.

[0048] In this embodiment, the state-space model of the nonlinear system can be used to describe the state of the underwater maneuvering target in digital language, including the state vector and the observation vector (i.e., the measurement vector). Meanwhile, considering the randomness of the target's motion (e.g., sudden acceleration, deceleration, or turning) and the interference of measurement errors, noise is added to the state-space model of the nonlinear system. The nonlinear system state-space model is represented as follows:

[0049]

[0050] In the formula, Represents the state vector. Characterizes discrete-time indexes. The state vector representing the index of the previous time step. Characterizing the state transition matrix, Characterizing the noise weighting matrix, Characterization process noise ( That is, the noise in the previous time index). Characterizing the measurement vector, Characterizing nonlinear measurement functions, Characterize measurement noise.

[0051] Wherein, the state vector , Representing the x-axis coordinate at time k, Representing the y-axis coordinate at time k, Characterizing the velocity along the x-axis at time k, Characterizing the y-axis velocity at time k, Representing a 4-dimensional vector. Measuring the vector. , Characterizes the distance to the target at time k. Characterizes the azimuth angle of the target at time k. Representing a 2D vector. Process noise. Measure noise And they are unrelated.

[0052] Assume that both process noise and measurement noise follow a Gaussian distribution, i.e., the process noise has a mean of 0 and a covariance matrix of... The distribution is Gaussian, and the measurement noise follows a mean of 0 and a covariance matrix of . If the distribution is Gaussian, then:

[0053]

[0054] In the formula, Characterizing the noise probability density distribution during the process, Characterize the probability density distribution of measurement noise. Characterizing a Gaussian distribution, Characterizing the noise covariance matrix of the process, Characterize the observation noise covariance matrix.

[0055] Define the state transition matrix in the target state transition, including tracking the target using a uniform velocity (CV) model and a uniform velocity turning (CT) model. The CV model assumes that the target is moving in a straight line at a constant velocity in a two-dimensional plane, meaning that the magnitude and direction of the velocity do not change. The CT model is used to describe scenarios where the target is turning at a constant angular velocity. Then we have...

[0056]

[0057] In the formula, Characterizing the sampling time, Characterizes the turning rate at time k.

[0058] Both the CV and CT models use the same noise weighting matrix. This matrix maps the dimension of process noise to the dimension of the state vector and allocates it appropriately in state updates. The noise weighting matrix is:

[0059]

[0060] Measurement equations are used to transform from Cartesian coordinates to polar coordinates. The measurement equations can be expressed as:

[0061]

[0062] In the formula, Characterizing the random error introduced by sonar during ranging, It characterizes the random error introduced by sonar during angle measurement.

[0063] Based on this model, the sonar acquires two-dimensional observations of the target's movement: distance and azimuth. The observation trajectory is then extracted from these observations.

[0064] S12: The observed trajectory sequence is input into a pre-trained TrDCN model. This model extracts global temporal dependency features of the observed trajectory sequence through multiple sequentially connected encoders and outputs the predicted residual trajectory through a decoder. The TrDCN model consists of an input module, an encoder, and a decoder connected in sequence.

[0065] In this embodiment, the observed trajectory is transformed and positionally encoded in the input module to obtain time-series features; then it is input into a multi-layer encoder, which extracts the temporal dependencies between states through masked multi-head attention, adaptive normalization and feedforward network; next, the decoder consists of three layers of one-dimensional dilated convolution, which extracts deep features using different receptive fields, and outputs the residual trajectory after max pooling and linear mapping.

[0066] Specifically, the input module includes a positional encoding and a linear transformation to convert the raw observation trajectory data into a feature representation rich in temporal information for subsequent encoder and decoder processing. Since directly inputting observation data into the model cannot effectively utilize the temporal information of the sequence, it is necessary to first map the data to a high-dimensional space and explicitly add positional encoding. In operation, the 4-dimensional observation state vector is mapped to the higher dimension required by the model's hidden layers to improve the model's representational ability. Positional information is added to each time step in the sequence to compensate for the lack of temporal awareness inherent in the Transformer's self-attention mechanism.

[0067] In detail, the input module receives an observation trajectory sequence as input information. This sequence consists of observation vectors at T time steps, i.e. Each observation vector It contains the target's coordinates and velocity information at time k. and The coordinates representing the x and y axes. and Characterizes the velocity along the x and y axes.

[0068] A linear transformation projects the 4-dimensional observation vector onto the hidden layer dimension of the model. This is represented as... In the formula, It is a weight matrix and has d is the dimension. Let be a bias vector and have .

[0069] Because the Transformer model uses a self-attention mechanism, which processes all positions in the observed trajectory sequence in parallel, it lacks natural sequence modeling capabilities. Therefore, after the linear transformation, a positional encoding is added to explicitly incorporate positional information into each position. For each position in the sequence, an absolute positional encoding is generated using sine and cosine functions. This encoded vector is then added to the result of the linear transformation to obtain the final positional encoding. In other words, the output of the input module is represented as... . The absolute position code is generated by the following formula: , Characterizes the frequency adjustment factor, and has .

[0070] After processing the data, the input module outputs to the encoder, which consists of multiple stacked sub-layers with identical structures (i.e., multiple encoders connected sequentially). Each sub-layer contains a masked multi-head self-attention mechanism and a feedforward neural network. First, the input sequence from the input module is modeled using a masked multi-head self-attention mechanism to capture the correlations between different positions in the sequence, thereby obtaining richer representational features. This mechanism extracts information from multiple subspaces through parallel computation by multiple attention heads. However, to improve the stability and representational power of the model training, a residual connection and a switchable normalization layer are added after the attention sub-layer to alleviate gradient vanishing and accelerate convergence. Subsequently, a feedforward neural network (FFN) performs a non-linear transformation on the representation at each position to enhance feature representation. Similar to the attention sub-layer, the feedforward network is also followed by a residual connection and a switchable normalization layer.

[0071] Specifically, the encoder extracts temporal features containing positional information from the input module's output. It captures the global dependencies between any two time steps in the sequence through a self-attention mechanism, transforming the temporal feature sequence into features that better characterize the dynamic evolution of the trajectory. Each encoder includes a masked multi-head self-attention layer and a feedforward fully connected network layer, as well as residual connections and switchable normalization structures surrounding the masked multi-head self-attention layer and the feedforward fully connected network layer. The following sections will provide a detailed description of each layer and module within the encoder.

[0072] The masked multi-head self-attention layer extracts features from different subspaces using multiple attention heads to model the dependencies between positions in a sequence. Furthermore, in target tracking, a masking mechanism is introduced to constrain attention and prevent the acquisition of future information. The masked multi-head self-attention layer linearly projects the input sequence through three different sets of learnable weight matrices to generate a query matrix. Key matrix Sum matrix The similarity score between each query and all keys is obtained by calculating the dot product of Q and K. These similarity scores are then scaled and softmax normalized to form weight coefficients. These weight coefficients are multiplied by V and summed to obtain the weighted output for the current position. Assuming this mechanism contains M self-attention heads, then:

[0073]

[0074] In the formula, All are linear projection matrices.

[0075] Next, the output of single-head attention can be calculated:

[0076]

[0077] In the formula, The scaling factor is used to prevent the inner product from becoming too large and affecting gradient calculation, and it also has... , It can be an upper triangular matrix, and triangular matrices can be used to implement masks.

[0078] Because it involves multiple heads, the computation is performed in parallel on M sets of Q, K, and V. Each head uses a different projection matrix, allowing it to focus on information from different subspaces of the input sequence. The outputs of the single-head attention are fused through a concatenation operation and projected onto the final dimension to compute the output of the multi-head attention mechanism.

[0079] .

[0080] Feedforward fully connected network (FFN) layers can perform independent nonlinear transformations on features at each time step. The two-layer fully connected structure enhances information abstraction capabilities, improving the model's feature representation and nonlinear modeling abilities. It complements the self-attention mechanism, enabling the Transformer to not only capture global dependencies in the sequence but also improve information processing capabilities at individual time steps. In the two-layer fully connected structure, the first layer is a linear transformation that expands the dimension, followed by a ReLU activation function; the second layer is a linear transformation that compresses back to the original dimension. The formula is as follows:

[0081]

[0082] In the formula, For the input of FFN, To expand the dimensions of the weight matrix, To compress the weight matrix back to its original dimensions, , For learnable parameters, This is the ReLU activation function.

[0083] Residual connections and switchable normalization structures are used to ensure the stability and efficiency of training. Residual connections directly pass information through skip connections, preventing gradient vanishing, accelerating convergence, and preserving input features while reducing information loss. Switchable normalization normalizes features at each time step, stabilizing data distribution, accelerating convergence, and improving generalization ability. Furthermore, switchable normalization considers batch normalization, instance normalization, and layer normalization results simultaneously, fusing them through learnable weights to enhance the model's adaptability to different tasks. Switchable normalization is implemented according to the following formula:

[0084]

[0085] In the formula, For input data that needs to be normalized, , , For the weight parameters of the science department, For batch normalization, all samples in each channel within a small batch are normalized. For instance normalization, normalization is performed separately for each channel. For layer normalization, each feature vector of each sample is normalized.

[0086] Residual connectivity and switchable normalized structures are performed according to the following formula:

[0087]

[0088] In the formula, Characterizing the input of this sublayer, Characterizes the output of the sublayer. The representation can switch normalization. This is the residual operation, which is followed by switchable normalization.

[0089] After being encoded by multiple encoders, the encoded results are input into the decoder for processing, resulting in the predicted residual trajectory. The decoder is used for feature compression and residual prediction. It receives the feature sequence containing global contextual information from the encoder output, extracts the local details and multi-scale patterns of these features, and outputs the residual trajectory between the observed trajectory and the true trajectory. Unlike the encoder, which uses a self-attention mechanism to capture long-range dependencies, the decoder is based on a convolutional neural network, efficiently capturing local correlations and patterns. Specifically, the decoder module consists of multiple (three are used as an example in this embodiment) 1D dilated convolutional layers, a max pooling layer, and a linear transformation layer. First, the input sequence passes through three dilated convolutional layers sequentially, expanding the receptive field layer by layer, thereby efficiently capturing long-range dependency information while maintaining temporal resolution. Compared with standard convolution, dilated convolution introduces spacing between convolutional kernels, enabling the modeling of a wider range of contextual relationships without increasing the number of parameters. Subsequently, a max pooling operation is used to compress the temporal dimension to extract key features and reduce computational complexity. Subsequently, the pooled features are input into the Linear Transformation Layer to obtain the residual mapping between the observed trajectory and the output trajectory.

[0090] For one-dimensional dilated convolutional layers, traditional one-dimensional convolutional neural networks require stacking a large number of layers due to the slow growth of the receptive field, leading to increased computational costs. To address this issue, this embodiment employs dilated convolution, introducing a dilation within the convolutional kernel to expand the receptive field without increasing the number of parameters. The calculation formula is as follows:

[0091]

[0092] In the formula, Characterizing time steps, Characterizes the size of the convolution kernel. Characterize the input sequence, Characterizing the weight matrix, Represents the kernel weights (the k-th weight of the kernel). Characterizes the expansion rate.

[0093] The max-pooling layer and the linear layer together constitute the feature compression and mapping module at the back end of the decoder. The max-pooling layer effectively compresses feature length, reduces computational complexity, and highlights salient features by selecting local maxima in the time dimension, thus focusing on key temporal information. The linear layer further maps the pooled features to the output space to obtain the final residual trajectory. The calculation formula is as follows:

[0094]

[0095] In the formula, This is the residual trajectory output by the decoder. This is the weight matrix, used to map the high-dimensional feature space to the 4-dimensional residual output space. For maximum pooling processing, This is the bias vector, used to provide translation offset for linear transformations.

[0096] S13: Add the predicted residual trajectory to the observed trajectory sequence to determine the final target state prediction trajectory.

[0097] In this embodiment, the final target state prediction trajectory is obtained by adding the residual trajectory predicted by the TrDCN model to the observed trajectory.

[0098] For example, Figure 2 A complete flowchart illustrating the target state trajectory prediction using the TrDCN model is shown. Figure 2 As shown, the observed trajectory is processed through an input module, which performs linear transformations and adds positional encoding to inject sequential information into the sequence data. The processed data is then fed into an encoder module, which consists of a multi-layered stacked structure. Each layer includes a masked multi-head self-attention mechanism and a feedforward neural network, and is stably trained using residual connections and switchable normalization layers to capture long-range global temporal dependencies in the observed trajectory sequence. The feature sequence output by the encoder is then fed into a decoder module, which consists of three layers of one-dimensional dilated convolutions. The decoder aims to extract local details and multi-scale features from the sequence using different receptive fields. Feature compression is then performed using a max-pooling layer, and finally, a linear layer maps the predicted residual trajectory. The predicted residual trajectory obtained from the decoder is added to the original input observed trajectory to obtain the final output target predicted trajectory.

[0099] The above describes overshoot using the TrDCN model. The TrDCN model will be introduced next.

[0100] In some possible implementations, the TrDCN model employs residual modeling during training.

[0101] In this embodiment, due to the significant variation in amplitude of the target trajectory, direct modeling can easily lead to difficulties in training convergence. Therefore, this embodiment employs a residual modeling strategy, estimating the residual portion of the target trajectory to reduce the range of numerical variation and improve model convergence. Furthermore, considering the order-of-magnitude differences in the accuracy requirements of position and velocity in practical applications, this embodiment further introduces a weighting mechanism to adjust the importance of different components in the loss function, thereby achieving a more refined modeling effect. The loss function is defined as follows:

[0102]

[0103] In the formula, Represents the true trajectory of the target. Characterizing the observed trajectory, Characterizing the predicted residuals, The weighting coefficients representing position and velocity information are taken as follows: , Characterizing the number of samples, Characterizes the time step.

[0104] In a specific example, the Transformer network was trained using 200,000 sets of target motion trajectories during the TrDCN model training. The experimental parameters are shown in Table 1 below. The model training lasted for 100 epochs, with each batch containing 128 training samples. The loss function was the function proposed in Section 3.5, the optimizer was ADAM, the initial learning rate was set to 0.001, and the learning rate decay coefficient for each epoch was 0.02.

[0105] Table 1 content scope distance [0,5km] speed [5m / s, 10m / s] Turning speed [-5° / s, 5° / s] Distance noise deviation [5m, 10m] Azimuth noise deviation [0.5°，1°]

[0106] The total sampling time for this simulation was 100 seconds, with a sampling interval of T=2 seconds. The target trajectory and measured values ​​at different times are as follows: Figure 3 As shown. The noise covariance matrix during the simulation. Measurement noise covariance matrix Initial target state information The settings are as follows:

[0107]

[0108] Furthermore, this application compares the performance of this method for underwater maneuvering target tracking with that of using RNN and LSTM. In the comparison, the root mean square error (RMSE) of position and velocity, and the average RMSE (ARMSE) are selected as performance metrics to evaluate the accuracy and consistency of the algorithm.

[0109] The formula for the root mean square error of position is:

[0110]

[0111] The formula for the root mean square error of velocity is:

[0112]

[0113] The formula for the root mean square error of the location is:

[0114]

[0115] The formula for the root mean square error of velocity is:

[0116]

[0117] In the formula, M represents the number of Monte Carlo simulations, with a value of 1000, and N represents the number of tracking steps in each Monte Carlo simulation.

[0118] Figure 4 A comparison chart of the root mean square errors of the three methods is shown. Figure 5 A comparison chart of root mean square error of velocity is shown. Figure 6 The position and velocity RMSE of different filters are shown. It can be seen that the TrDCN model has lower RMSE for both position and velocity than the RNN and LSTM models; moreover, the error curve of TrDCN is more stable, indicating that the model in this application has better robustness. Extensive Monte Carlo simulations have verified that this application significantly outperforms traditional tracking methods such as RNN, LSTM, and IMM in terms of position and velocity RMSE.

[0119] The above describes the underwater maneuvering target tracking method provided in this application. It uses a deep learning framework that integrates the Transformer model and dilated convolutional neural networks to predict residuals. Specifically, the Transformer's multi-head self-attention mechanism fully models the global temporal dependency features of the observed trajectory, overcoming the dependency decay and efficiency bottlenecks of RNNs and LSTMs in long-sequence learning. Combined with multi-scale dilated convolution, it extracts local residual dynamic features while maintaining temporal resolution, improving the tracking accuracy for highly maneuverable targets. The predicted trajectory of the target is obtained by combining the residual trajectory with the observed trajectory. Introducing a residual mapping between the observed and true trajectories in target state modeling reduces the numerical dynamic range and improves the convergence and stability of the network. The residual strategy significantly reduces the bias introduced by directly predicting the absolute trajectory, enhancing estimation accuracy. Switchable normalization is used in each sub-layer of the encoder, combining Batch Normalization, Instance Normalization, and Layer Normalization to automatically learn weighted combinations of different normalization methods, enhancing the model's adaptability to different tasks and data distributions. To address the differences in the dimensions of position and velocity, weighted coefficients are designed to differentiate the loss function, thereby improving the estimation accuracy for different physical quantities. This loss function helps resolve the imbalance between position and velocity accuracy, enhancing overall tracking performance under high-dynamic underwater conditions. This method is applicable to various complex underwater target motion scenarios, exhibiting significant advantages, particularly in typical environments involving high maneuverability and long-sequence trajectory estimation.

[0120] It is understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. Furthermore, in some possible implementations, each step in the above embodiments may be selectively executed according to actual circumstances; it may be partially or fully executed, without limitation here. All or part of any feature of any embodiment of this application can be freely and arbitrarily combined without contradiction. The combined technical solutions are also within the scope of this application.

[0121] Based on the methods in the above embodiments, this application also provides an underwater maneuvering target tracking device. For example, this application provides a schematic diagram of the structure of an underwater maneuvering target tracking device. Figure 7 As shown, the underwater maneuvering target tracking device 700 includes a conversion module 701 and a processing module 702.

[0122] Among them, the conversion module 701 is used to establish a state-space model of the nonlinear system, converting the underwater maneuvering target distance and azimuth observation values ​​obtained by the sonar system to the Cartesian coordinate system to form an observation trajectory sequence.

[0123] The processing module 702 is used to input the observed trajectory sequence into a pre-trained prediction model. The prediction model extracts the global temporal dependency features of the observed trajectory sequence through multiple encoders connected in sequence, and outputs the predicted residual trajectory through a decoder.

[0124] The processing module 702 is also used to add the predicted residual trajectory to the observed trajectory sequence to determine the final target state prediction trajectory.

[0125] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0126] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0127] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0128] It is understood that the processor in the embodiments of this application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor may be a microprocessor or any conventional processor.

[0129] The method steps in the embodiments of this application can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0130] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0131] It is understood that the various numerical designations used in the embodiments of this application are merely for descriptive convenience and are not intended to limit the scope of the embodiments of this application.

Claims

1. A method for tracking underwater maneuvering targets, characterized in that, The method includes: A state-space model of the nonlinear system is established, and the distance and azimuth observations of underwater maneuvering targets acquired by the sonar system are transformed into a Cartesian coordinate system to form an observation trajectory sequence; The observed trajectory sequence is input into a pre-trained prediction model, which extracts global temporal dependency features of the observed trajectory sequence through multiple sequentially connected encoders and outputs the predicted residual trajectory through a decoder. The predicted residual trajectory is added to the observed trajectory sequence to determine the final target state prediction trajectory.

2. The method according to claim 1, characterized in that, The prediction model further includes an input module, which comprises a linear transform layer and a position encoding layer. The method further includes: Through the linear transformation layer, the input observation trajectory sequence is mapped to a high-dimensional representation space using a learnable weight matrix and bias vector; The position coding layer generates an absolute position code for each time step in the sequence, adds it to the linearly transformed sequence, and inputs the result into the encoder.

3. The method according to claim 2, characterized in that, The obtained result is expressed as follows: In the formula, Characterizing the observed trajectory sequence, Characterizes the weight matrix and has d is the dimension. Characterizes the bias vector and has , Characterizing time steps, Characterized by absolute position encoding; whereby, the observed trajectory sequence In the formula, each observation vector , and The coordinates representing the x and y axes. and Characterizes the velocity along the x and y axes.

4. The method according to claim 1, characterized in that, The encoder includes: a masked multi-head self-attention sublayer, a feedforward fully connected network sublayer, residual connections, and a switchable normalization layer. The extraction of global temporal dependency features of the observed trajectory sequence includes: By using a masked multi-head self-attention sublayer, masked attention computation is performed on the input sequence to capture the global dependencies of the sequence while preventing information leakage in the future. The output of the masked multi-head self-attention sublayer is nonlinearly transformed by a feedforward fully connected network sublayer. The data processed by the masked multi-head self-attention sub-layer and the feedforward fully connected network sub-layer are processed through residual connections and switchable normalization layers.

5. The method according to claim 1, characterized in that, The switchable normalization layer adaptively fuses batch normalization, instance normalization, and layer normalization using learnable weights, and its calculation is expressed as follows: In the formula, For input data that needs to be normalized, , , These are learnable weight parameters. For batch normalization, all samples in each channel within a small batch are normalized. For instance normalization, normalization is performed separately for each channel. For layer normalization, each feature vector of each sample is normalized.

6. The method according to claim 4, characterized in that, The calculation process of the masked multi-head self-attention sublayer includes: The input sequence is linearly projected through three different sets of learnable weight matrices to generate the query matrix. Key matrix Sum matrix , The output of each attention head is calculated using the following formula: In the formula, The scaling factor is used to prevent the inner product from becoming too large and affecting gradient calculation, and it also has... , It can be an upper triangular matrix, where M is the number of self-attention heads; The outputs of all attention heads are concatenated and linearly projected.

7. The method according to claim 1, characterized in that, The decoder includes: multiple sequentially connected one-dimensional dilated convolutional layers, max-pooling layers, and linear layers; the residual trajectory predicted by the decoder output includes: Local multi-scale detail information of the input global temporal dependent features is extracted by using multiple one-dimensional dilated convolutional layers with different dilation rates; Key features are extracted by downsampling the feature sequence output by the dilated convolutional layer in the time dimension using a max pooling layer. The pooled features are mapped to the dimension of the residual trajectory through a linear layer, and the predicted residual trajectory is output.

8. The method according to claim 7, characterized in that, The formula for operating a one-dimensional dilated convolutional layer is: In the formula, Characterizing time steps, Characterizes the size of the convolution kernel. Characterize the input sequence, Characterizing the weight matrix, The weights of the convolution kernel are represented by the k-th weight of the convolution kernel. Characterizes the expansion rate.

9. The method according to claim 1, characterized in that, The prediction model is trained by minimizing a weighted loss function, which is defined as: In the formula, Represents the true trajectory of the target. Characterizing the observed trajectory, Characterizing the predicted residuals, The weighting coefficients representing position and velocity information are taken as follows: , Characterizing the number of samples, Characterizes the time step.

10. An underwater maneuvering target tracking device, characterized in that, The device includes: The conversion module is used to establish a state-space model of the nonlinear system, converting the distance and azimuth observations of underwater maneuvering targets acquired by the sonar system to the Cartesian coordinate system to form an observation trajectory sequence. The processing module is used to input the observed trajectory sequence into a pre-trained prediction model. The prediction model extracts the global temporal dependency features of the observed trajectory sequence through multiple encoders connected in sequence, and outputs the predicted residual trajectory through a decoder. The processing module is also used to add the predicted residual trajectory to the observed trajectory sequence to determine the final target state prediction trajectory.

Images