Underwater target track measuring and calculating method, storage medium and terminal

Abstract

The invention discloses an underwater target track measuring and calculating method, a storage medium and a terminal, belongs to the technical field of underwater target detection and positioning, and solves the problems that underwater target track points are sparse and positioning errors exist due to underwater noise, low sampling frequency and the like, and further tasks such as underwater target position estimation, tracking and track prediction are affected. According to the method, a training set and a test set are constructed through continuous three-dimensional trajectory data collected at high frequency, coordinates are converted through a principal component analysis method, samples are enhanced, trajectory rules are learned through a multi-layer perceptron model, a mean value is obtained through multiple times of prediction of a sliding window, and a complete underwater target trajectory is obtained. The track law is learned by using the neural network, so that the prediction is more accurate; pCA is used for converting samples, so that the model precision and generalization ability are improved; enriching samples through data enhancement; and a sliding window is used for multiple predictions to obtain an average value to improve prediction precision.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater target detection and positioning, and particularly to a method for calculating the track of an underwater target, a storage medium, and a terminal. Background Art

[0002] In the field of underwater detection and tracking, accurately mastering the track of an underwater target is of crucial significance for key tasks such as target positioning, continuous tracking, and track prediction. The underwater environment is extremely complex, with many interference factors, such as strong underwater noise, low sampling frequency, unstable signal quality, and frequent signal interruption problems. These adverse factors will cause the interval between track points of the underwater target to be too large, and there will also be a certain degree of positioning error. This makes it extremely difficult to accurately draw the track curve, and the sparse distribution of track points will ultimately have a negative impact on the optimal estimation of the underwater target position, resulting in difficult to obtain ideal results in subsequent tasks such as target tracking and track prediction.

[0003] Currently, the existing methods for calculating the track mainly include the Kalman filtering method, the polynomial interpolation method, the Bezier curve method, and the machine learning / deep learning method. However, these traditional methods all have certain limitations in practical applications: Kalman filtering / particle filtering method: This method is usually used to optimally estimate the system state from a series of measurement data containing noise. However, when accurately predicting the track of an underwater target based on sparse track points, its effect is not good. This is because it generally infers the optimal state at the next moment based on the state at the previous moment, without making full use of the bidirectional information before and after, resulting in limited prediction accuracy.

[0004] Polynomial interpolation method: This method interpolates the sparse track points by constructing a polynomial, mainly aiming to smooth the track. However, it has a key assumption, that is, it assumes that the target track conforms to the polynomial distribution. But in actual situations, the navigation track of the underwater target is complex and changeable, and it is difficult to fully meet the polynomial distribution. In addition, the polynomial interpolation method cannot effectively consider the influence of speed changes on the interval between track points, which further reduces the accuracy of predicting the position of track points.

[0005] Bezier curve method: Bezier curves are often used for parametric modeling of curves and perform well in smoothing curves. However, for the actual calculation of the underwater target track, simply smoothing the track is far from enough. More importantly, it is necessary to mine the motion law of the target from a large amount of data and then optimally estimate the position of the track points, which is exactly what the Bezier curve method lacks.

[0006] Machine learning / deep learning method: As a technology that relies on historical data to mine the operating rules of targets, the machine learning / deep learning method has certain application potential in trajectory calculation based on data. However, this method has a significant drawback, that is, its prediction effect depends to a large extent on various data augmentation operations and complex algorithm designs carried out for specific scenarios. Only through careful design and adjustment is it possible to achieve relatively accurate prediction of the positions of trajectory points, which to a certain extent limits its generality and practicality. Summary of the Invention

[0007] The present invention proposes an underwater target trajectory calculation method, storage medium and terminal. For sparse trajectory data of underwater targets affected by noise, the machine learning / deep learning method is used to interpolate and smooth the trajectory data to obtain a relatively accurate trajectory curve, thereby solving the problem that underwater target trajectory points are sparse and have positioning errors due to underwater noise, low sampling frequency, etc., which in turn affects tasks such as underwater target position estimation, tracking and trajectory prediction.

[0008] An underwater target trajectory calculation method, the underwater target trajectory calculation method includes the following steps: S100. Divide the continuously collected high-frequency three-dimensional trajectory data into input feature data and output label data, and construct training set and test set samples through a sliding window to provide structured data for the model; S200. Use the principal component analysis method to perform decentralization and coordinate transformation on each group of samples in the training set and test set, convert the absolute three-dimensional coordinates into a new coordinate system with the target movement direction, horizontal and vertical axes as the axes, and generate PCA conversion samples; S300. Generate enhanced samples by flipping and randomly scaling the PCA conversion samples; S400. Design a multi-layer perceptron model, with sparse trajectory points as the input and interpolated trajectory points as the output, and use the PCA conversion samples and enhanced samples to train the multi-layer perceptron model to learn the trajectory rules; S500. Use a sliding window to predict the sparse trajectory multiple times, and take the mean of the multiple prediction results for the same interpolation point as the final position to obtain a complete interpolated trajectory.

[0009] Further, S100 includes the following steps: S110. Perform sliding window interception on the continuously collected high-frequency three-dimensional trajectory data to construct multiple groups of samples, and each group of samples includes input feature data and output label data; S120. Divide all samples into a training set and a test set; S130. Control the interpolation density by adjusting the proportional relationship between the number of trajectory points of the input feature data and the number of trajectory points of the output label data.

[0010] Further, the input feature data are sparse trajectory points under low-frequency sampling, and the output label data are trajectory points to be interpolated.

[0011] Further, S200 includes the following steps: S210. Calculate the mean of each dimension feature of the input feature data of each group of samples in the training set in three-dimensional space; S220. Subtract the mean from each dimension feature of the input feature data and the corresponding output label data to achieve the centering process; S230. Calculate the covariance matrix of the centered input feature data; S240. Perform eigenvalue decomposition on the covariance matrix to obtain its eigenvalues and eigenvectors; S250. Sort the eigenvalues by magnitude, and select the eigenvectors corresponding to the three largest eigenvalues to form an eigenvector matrix; S260. Transform the centered input feature data and output label data into the new space constituted by the eigenvector matrix; S270. For each group of samples in the test set, use the same coordinate transformation method as the training set to obtain the training set and test set after coordinate transformation.

[0012] Further, in S300, the PCA-transformed samples are processed, including the following steps: S310. Perform axisymmetric processing on the PCA-transformed samples along the three principal component axes respectively; S320. Perform origin-symmetric processing on the PCA-transformed samples; S330. Combine the samples after axisymmetric processing and origin-symmetric processing with the PCA-transformed samples to form an enhanced training data set.

[0013] Further, S300 also includes: S340. Multiply the PCA-transformed samples by a random scaling factor to obtain the samples after random scaling processing, and the random scaling factor is sampled from a preset probability distribution; S350. Combine the samples after random scaling processing with the PCA-transformed samples to further expand the training data set.

[0014] Further, S400 includes the following steps: S410. Construct a multi-layer perceptron neural network model, whose input layer receives the sparse trajectory point data after principal component analysis transformation, and the output layer generates the interpolated trajectory point data; S420. The multi-layer perceptron neural network model includes at least one hidden layer and adopts a non-linear activation function; S430. Optimize the network parameters by minimizing the error between the predicted trajectory points and the true trajectory points; S440. Use the training set processed by coordinate system transformation and data augmentation to train the multi-layer perceptron neural network model.

[0015] Further, S500 includes the following steps: S510. Input the low-frequency sparse trajectory data of the underwater target to be processed into the trained multi-layer perceptron neural network model; S520. Adopt a sliding window mechanism to segment and predict the input data to generate intermediate trajectory points; S530. Perform weighted fusion on the multiple prediction results generated by different windows at the same spatial position; S540. Output a continuous and smooth underwater target track curve.

[0016] A storage medium stores a computer program thereon, and when the computer program is executed by a processor, the above-mentioned underwater target track calculation method is implemented.

[0017] A terminal includes: a memory, a processor, and a computer program stored on the memory and operable on the processor, and the processor executes the program to implement the above-mentioned underwater target track calculation method.

[0018] Advantages of the present invention: 1. Compared with the method that only uses linear interpolation, the model based on neural network of the present invention can learn from a large number of historical samples, extract the navigation rules of underwater targets, and obtain relatively accurate prediction results.

[0019] 2. The present invention uses the PCA algorithm for each group of samples to perform coordinate transformation on the trajectory points in the original three-dimensional space to obtain three mutually orthogonal principal components, which can approximately represent the forward direction, lateral direction, and longitudinal direction, and are more in line with the physical meaning of the actual underwater target navigation. Compared with directly using the sparse samples in the original three-dimensional coordinate space for learning, using the samples transformed by PCA to construct a trajectory prediction model can achieve better model prediction accuracy and generalization ability with less data volume.

[0020] 3. The present invention uses data augmentation methods such as flipping and random scaling to further ensure the model accuracy and generalization ability in the case of limited data volume.

[0021] 4. During the prediction process, the present invention uses overlapping sliding windows to predict the trajectory points and takes the mean of the multiple prediction data at the same moment to represent the final prediction result, improving the prediction accuracy. Description of the Drawings

[0022] Figure 1 is the method flow chart of a method for calculating the underwater target track of the present invention; Figure 2 is the schematic diagram of the underwater target track; Figure 3 is the schematic diagram of the trajectory prediction process. Specific embodiments

[0023] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0024] Refer to Figure 1 As shown, a method for calculating the underwater target track, the method for calculating the underwater target track includes the following steps: S100. Divide the continuously collected high-frequency three-dimensional trajectory data into input feature data and output label data, and construct training set and test set samples through a sliding window to provide structured data for the model; S200. Use the principal component analysis method to perform de-centralization and coordinate transformation on each group of samples in the training set and test set samples, convert the absolute three-dimensional coordinates into a new coordinate system with the target movement direction, horizontal, and vertical as axes, and generate PCA conversion samples; S300. Generate enhanced samples by flipping and randomly scaling the PCA conversion samples; S400. Design a multi-layer perceptron model, with sparse trajectory points as the input and interpolated trajectory points as the output, and use the PCA conversion samples and enhanced samples to train the multi-layer perceptron model to learn the trajectory law; S500. Use a sliding window to predict the sparse trajectory multiple times, and take the mean of the multiple prediction results of the same interpolation point as the final position to obtain a complete trajectory after interpolation.

[0025] Specifically, for the underwater target trajectory calculation method proposed by the present invention, by dividing the continuously collected high-frequency three-dimensional trajectory data into input feature data and output label data, and using a sliding window to construct training set and test set samples, a structured data basis is provided for the model, effectively solving the problem of sparse and noisy underwater target trajectory data. Through the principal component analysis method, the sample data is decentralized and coordinate-transformed, converting the absolute three-dimensional coordinates into a new coordinate system with the target movement direction, lateral direction, and longitudinal direction as axes. This not only conforms more to the physical meaning of underwater target navigation but also improves the prediction accuracy and generalization ability of the model under the condition of less data volume. Data augmentation processing of flipping and random scaling is performed on the PCA-transformed samples, further expanding the training data set and enhancing the model's adaptability to complex underwater environments. The multi-layer perceptron model is used to learn the trajectory law, and by combining multiple predictions with a sliding window and taking the average value of the same interpolation point, the accuracy and continuity of trajectory prediction are significantly improved, and finally a smooth and accurate underwater target trajectory curve is generated, solving tasks such as underwater target position estimation, target tracking, and trajectory prediction.

[0026] Further, S100 includes the following steps: S110. Perform sliding window interception on the continuously collected high-frequency three-dimensional trajectory data to construct multiple groups of samples, and each group of samples includes input feature data and output label data; S120. Divide all samples into a training set and a test set; S130. Control the interpolation density by adjusting the proportional relationship between the number of trajectory points of the input feature data and the number of trajectory points of the output label data.

[0027] Specifically, for the coordinate system conversion method described in this embodiment, through the principal component analysis technology, the intelligent spatial reconstruction of underwater target trajectory data is carried out, converting the traditional absolute coordinate system into a dynamic local coordinate system based on the main direction of target movement. This adaptive coordinate conversion method based on data characteristics of the present invention can automatically capture the actual movement trend of underwater targets, effectively eliminating the deviation between the sensor coordinate system and the true movement direction of the target, making the sparse trajectory points show a more obvious linear distribution feature in the new coordinate system. By retaining the principal components of the three largest variance directions, not only the data dimension is compressed, but also the three most critical movement components for navigation analysis, namely the target forward direction, lateral offset, and longitudinal undulation, are highlighted, providing more physically meaningful input features for the subsequent neural network model. This coordinate conversion method is particularly suitable for the analysis of irregular movement trajectories of underwater targets, can significantly improve the model's ability to capture target movement laws, and at the same time avoids the problem of feature confusion caused by changes in target heading under the traditional fixed coordinate system.

[0028] Under actual operating conditions, high-frequency data collection of the underwater target track is carried out to obtain a continuous operating track. The track can be regarded as consisting of three-dimensional (x, y, z) coordinate points, as Figure 2 shown.

[0029] The collected data is divided into input feature data (such as x 1 , x 2 , x 3 , x 4 ) and output label data (such as y 1 , y 2 ,y 3 , y 4 , y 5 , y 6 ). The purpose of the present invention is to train a track prediction model based on the feature and label data to realize the measurement of the track at a low sampling frequency, that is, to predict the intermediate track points of the low-frequency track data to obtain a continuous underwater target track.

[0030] The data preprocessing part mainly involves sample collection, division of the training set and the test set (such as 4:1), and construction of input feature and output label samples. The sample construction can adjust the number of track points of the input and output according to needs. Assuming that the length of the input sample is n and the interval between two input samples is m, that is, the number of track points input to the model is n, and the number of track points predicted by the model is (n - 1)*m. Based on this, the samples of the training set and the test set are constructed. As Figure 2 shown, the input track points are (x 1 , x 2 , x 3 , x 4 ), and the track points predicted by the model are (y 1 , y 2 , y 3 , y 4 , y 5 , y 6 ). Then [(x 1 , x 2 , x 3 , x 4 ), (y 1 , y 2 , y 3 , y 4 , y 5 ,y 6 )] can be regarded as a set of samples, and the sample set consists of a large number of sets of samples. Each set of samples can be intercepted from the originally collected track data through a sliding window with a certain step size.

[0031] Further, the input feature data are sparse trajectory points under low-frequency sampling, and the output label data are trajectory points to be interpolated.

[0032] Specifically, in this embodiment, it is clarified that the input feature data are sparse trajectory points under low-frequency sampling, and the output label data are trajectory points to be interpolated. In an underwater detection scenario, due to factors such as noise and low sampling frequency, the actually obtained trajectory data are often sparse trajectory points under low-frequency sampling. Using them as input feature data is more in line with the real application environment. Through such input-output settings, the model of the present invention can directly process underwater target sparse trajectory data. Compared with traditional methods, it no longer relies on simple assumptions about data distribution. For example, the polynomial interpolation method assumes that the target trajectory conforms to a polynomial distribution. This setting enables the model to focus on mining the motion law of the target from sparse trajectory points, and then achieve accurate interpolation of trajectory points to obtain a more accurate trajectory curve.

[0033] Further, S200 includes the following steps: S210. Calculate the mean value of each dimension feature of the input feature data of each group of samples in the training set in three-dimensional space; S220. Subtract the mean value from each dimension feature of the input feature data and the corresponding output label data to achieve the de-centralization process; S230. Calculate the covariance matrix of the de-centralized input feature data; S240. Perform eigenvalue decomposition on the covariance matrix to obtain its eigenvalues and eigenvectors; S250. Sort the eigenvalues by magnitude, and select the eigenvectors corresponding to the three largest eigenvalues to form an eigenvector matrix; S260. Convert the de-centralized input feature data and output label data into the new space constituted by the eigenvector matrix; S270. For each group of samples in the test set, use the same coordinate transformation method as the training set to obtain the training set and test set after coordinate transformation.

[0034] Specifically, this embodiment elaborates in detail the application steps of the principal component analysis (PCA) method in underwater target trajectory calculation. First, calculate the mean value of each dimension feature in the three-dimensional space for the input feature data of each group of samples in the training set, and then perform the de-centralization process, which can effectively eliminate the bias in the data and enable subsequent analysis to focus on the core features of the data. Next, calculate the covariance matrix and perform eigenvalue decomposition, and select the eigenvectors corresponding to the three largest eigenvalues to form a matrix, thereby achieving coordinate transformation and converting the absolute three-dimensional coordinates into a new coordinate system with the target movement direction, lateral direction, and longitudinal direction as the axes. This transformation conforms to the physical meaning of underwater target navigation and can more accurately reflect the target movement characteristics. Compared with directly using sparse samples for learning in the original three-dimensional coordinate space, the samples after PCA transformation can effectively improve the model prediction accuracy and generalization ability with less data volume, enabling the model to more accurately learn the underwater target trajectory law. At the same time, perform the same coordinate transformation process on the test set using the eigenvector matrix determined by the training set, ensuring the consistency and comparability of the data in the training set and the test set, and further optimizing the model performance.

[0035] In reality, underwater target trajectory data can be regarded as a point set in a three-dimensional space coordinate system (x, y, z). Due to the large and sparse sampling space, when the sampling data is limited, the accuracy of establishing a trajectory prediction model in the original three-dimensional space is relatively low. The present invention innovatively uses the principal component analysis (PCA) method. The function of this method is not to reduce the dimension of the features, but to transform the coordinates of the input features of each group of samples in the original three-dimensional space, converting the trajectory points in the absolute coordinate system into representations in the relative coordinate system. After PCA, three mutually orthogonal principal components with the largest variances are still retained, which can approximately represent the forward direction, lateral direction, and longitudinal direction of the underwater target, and are more in line with the physical meaning of actual underwater target navigation. Using the PCA method to transform the discrete three-dimensional sparse space trajectory into a motion space representation can greatly improve the model prediction accuracy when the sampling data is limited.

[0036] The steps of the PCA algorithm are as follows: 1) Randomly sample a group of samples in the training set. Taking the example shown below, the sample input features are (x Figure 1 , x 1 , x 2 , x 3 , x 4 ), and the labels are (y 1 , y 2 , y 3 , y 4 , y 5 , y 6 ); 2) Remove the mean value (i.e., de-centralize), that is, calculate the sample input features (x 1 , x 2 , x3 , x 4 ), the mean value of each dimension feature in three-dimensional space, and for the input feature (x 1 , x 2 , x 3 , x 4 ), and the label (y 1 , y 2 , y 3 , y 4 , y 5 , y 6 ), subtract the mean value of each dimension feature to obtain the de-centered feature and label; 3) Calculate the covariance matrix of the input feature ; 4) Use the eigenvalue decomposition method to find the eigenvalues and eigenvectors of the covariance matrix ; 5) Sort the eigenvalues from largest to smallest, and select the eigenvectors (row vectors) corresponding to the three largest eigenvalues to form the eigenvector matrix P; 6) Transform the de-centered feature and label data into the new space constructed by the eigenvectors, that is, Y = PX, to obtain the training samples (features and labels) after coordinate transformation; 7) Traverse each group of samples in the training set and the test set, and repeat steps 2-6 to obtain the training set and test set after coordinate transformation.

[0037] Furthermore, in S300, process the PCA-transformed samples, including the following steps: S310. Perform axisymmetric processing on the PCA-transformed samples along the three principal component axes respectively; S320. Perform origin-symmetric processing on the PCA-transformed samples; S330. Combine the samples after axisymmetric processing and origin-symmetric processing with the PCA-transformed samples to form an enhanced training data set.

[0038] Specifically, in this embodiment, the PCA-transformed samples are subjected to axisymmetric processing along three principal component axes respectively, and origin-symmetric processing is performed on the PCA-transformed samples. Subsequently, the processed samples are combined with the PCA-transformed samples to form an enhanced training data set. The movement trajectories of underwater targets are complex and variable. Relying solely on the original PCA-transformed sample data volume may be insufficient, making it difficult for the model to fully learn various possible trajectory patterns. Through axisymmetric processing along the principal component axes and origin-symmetric processing, new samples that are related to but different from the original samples can be created, enriching the diversity of the training data. This enables the model to come into contact with more different forms of trajectory data during the training process, thereby better learning various characteristics and laws of underwater target trajectories and enhancing the model's adaptability to different trajectory situations. In practical applications, even when encountering underwater target trajectory scenarios that are not exactly the same as the training data, the model can, relying on the capabilities trained with this rich and diverse data, more accurately perform trajectory calculation and prediction, thereby improving the model's generalization ability and ensuring the accuracy and reliability of target trajectory calculation in complex underwater environments.

[0039] Further, S300 further includes: S340. Multiply the PCA-transformed samples by a random scaling factor to obtain samples after random scaling processing, where the random scaling factor is sampled from a preset probability distribution; S350. Combine the samples after random scaling processing with the PCA-transformed samples to further expand the training data set.

[0040] Specifically, in this embodiment, the PCA-transformed samples are multiplied by a random scaling factor sampled from a preset probability distribution and combined with the PCA-transformed samples to further expand the training data set. When calculating underwater target trajectories, due to the complex underwater environment, the target movement trajectories may have various scale changes. By randomly scaling the PCA-transformed samples, the target trajectory situations at different scales are simulated, providing the model with more rich and diverse data. This enables the model to learn the characteristics and laws of trajectories at different scales and enhances the model's adaptability to trajectory changes. When the model faces actual underwater target trajectory data, even if the data is different from the training data in scale, it can, relying on the knowledge learned from the randomly scaled data, more accurately perform trajectory calculation and prediction. In addition, the expanded training data set enables the model to come into contact with more data with different characteristics during the training process, helping the model better capture the potential patterns in the data and further improving the model's generalization ability.

[0041] In reality, data augmentation can improve the accuracy and generalization ability of the model, especially when the number of samples is limited. The data augmentation methods used in this underwater target trajectory calculation scenario include flipping and random scaling. Flipping performs axisymmetric processing and origin-symmetric processing on the samples (features and labels) after PCA transformation along the three principal component axes to obtain the augmented samples; random scaling multiplies the samples after PCA transformation by a random scaling factor to obtain the augmented samples, and the random factor can be sampled from a distribution with a mean of μ and a standard deviation of σ (such as a mean of 1 and a standard deviation of 0.5). The original samples (samples after PCA transformation) and the augmented samples (flipping and random scaling) are used together for the training of the trajectory prediction model to improve the prediction accuracy and generalization ability of the trajectory point positions in the case of limited sample quantity.

[0042] Furthermore, S400 includes the following steps: S410. Construct a multi-layer perceptron neural network model, whose input layer receives the sparse trajectory point data after principal component analysis transformation, and the output layer generates the interpolated trajectory point data; S420. The multi-layer perceptron neural network model includes at least one hidden layer and adopts a non-linear activation function; S430. Optimize the network parameters by minimizing the error between the predicted trajectory points and the true trajectory points; S440. Use the training set processed by coordinate system transformation and data augmentation to train the multi-layer perceptron neural network model.

[0043] Specifically, this embodiment details the construction and training process of a multi-layer perceptron neural network model. The multi-layer perceptron neural network model is constructed with an input layer that receives the sparse trajectory point data after principal component analysis transformation, and an output layer that generates the interpolated trajectory point data. This structural design is specifically for the underwater target track calculation task, enabling the model to directly process the effective data after PCA transformation, improving the pertinence and effectiveness of data processing. The model contains at least one hidden layer and uses a non-linear activation function, endowing the model with a powerful non-linear mapping ability to learn the complex non-linear relationships in the underwater target track. The movement trajectory of an underwater target is affected by various factors and is not a simple linear relationship. The use of a non-linear activation function allows the model to more accurately depict these complex relationships and uncover the deep-seated laws behind the data. By minimizing the error between the predicted trajectory points and the real trajectory points, the network parameters are optimized to ensure that the model continuously adjusts in a more accurate direction during training, improving the accuracy of prediction. The model is trained using a training set that has undergone coordinate system transformation and data augmentation, making full use of the advantages of the processed data in the previous steps. The data after coordinate system transformation is more physically meaningful, and data augmentation increases the diversity and richness of the data. The combination of the two enables the model to learn more comprehensive and accurate track laws during training, and thus can output more accurate interpolated trajectory points when actually calculating the underwater target track.

[0044] In practical use, the trajectory prediction model preferably uses the simplest multi-layer perceptron (MLP), and the activation function can use the Relu function. A single hidden layer or a double hidden layer network can be used. Assuming the length of the input sample is n, the interval between two input samples is m, and the feature dimension of the trajectory point is 3, then the input feature dimension of the model is 3*n, and the output feature dimension of the model is 3*(n - 1)*m. As Figure 2 shown in the example, the input trajectory points are (x 1 , x 2 , x 3 , x 4 ), and the predicted trajectory points of the model are (y 1 , y 2 , y 3 , y 4 ,y 5 , y 6 ). Then the input dimension of the model is 3*4, that is, 12, and the output dimension of the model is 3*(4 - 1)*2, that is, 18. This model is used to train the PCA transformation samples and the data-augmented samples to obtain an underwater target track prediction model.

[0045] Furthermore, S500 includes the following steps: S510. Input the low-frequency sparse trajectory data of the underwater target to be processed into the trained multi-layer perceptron neural network model; S520. Segment and predict the input data using a sliding window mechanism to generate intermediate trajectory points; S530. Perform weighted fusion on multiple prediction results generated by different windows at the same spatial position; S540. Output a continuous and smooth underwater target trajectory curve.

[0046] Specifically, this embodiment details the prediction and output processes of the trajectory calculation method. The low-frequency sparse trajectory data of the underwater target to be processed is input into the trained multi-layer perceptron neural network model, leveraging the learning results of the underwater target trajectory patterns accumulated during the previous training, laying a foundation for accurate trajectory prediction. The sliding window mechanism is used to segment and predict the input data to generate intermediate trajectory points. This approach can fully utilize the local information in the data and analyze the trajectory change trends from different local perspectives. Due to the complex movement trajectory of the underwater target, the sliding window can flexibly capture the characteristics of different segments, avoiding missing important information. The weighted fusion of multiple prediction results generated by different windows at the same spatial position comprehensively considers the advantages and reliability of different window predictions, reducing the errors and uncertainties of single-window predictions. Compared with relying solely on single predictions, the fusion of multiple prediction results can more accurately reflect the true situation of the target at that position. Finally, a continuous and smooth underwater target trajectory curve is output, providing high-quality data support for subsequent tasks such as target positioning, tracking, and trajectory prediction, enhancing the accuracy and reliability of analyzing the target's motion state in a complex underwater environment.

[0047] In reality, after model training, the obtained trajectory prediction model is used for subsequent interpolation processing of sparse trajectories. The actual prediction process can use sliding prediction, and finally, the mean value is taken as the final trajectory point prediction result. As Figure 3 shown, assuming the input window length is 4 and the sliding step size is 1, the mean value of multiple prediction results is taken as the prediction of the interpolation point position.

[0048] A storage medium stores a computer program thereon, and when the computer program is executed by a processor, it implements the above-mentioned underwater target trajectory calculation method.

[0049] Specifically, for the storage medium proposed in this embodiment, when the computer program stored thereon is executed by a processor, it can implement the underwater target trajectory calculation method. First, it realizes the effective storage and convenient reuse of this trajectory calculation method. When scientific researchers or relevant technical personnel need to perform underwater target trajectory calculation in different application scenarios, there is no need to rewrite complex codes or repeat the entire algorithm process. They only need to call the computer program in the storage medium to quickly carry out the calculation work, greatly saving time and labor costs. Second, the existence of the storage medium ensures the stability and consistency of the algorithm. No matter on which device the program runs, as long as the processor can execute it correctly, it can be processed according to the established underwater target trajectory calculation method, avoiding calculation errors and result deviations caused by human operation or environmental differences. This is crucial for some underwater detection tasks with extremely high accuracy requirements, such as military reconnaissance and marine resource exploration. In addition, it provides strong support for the popularization and application of underwater target trajectory calculation technology. Different research teams or enterprises can conduct secondary development and optimization based on this storage medium to further expand the application scope and functions of this method.

[0050] A terminal includes: a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the program to implement the above-mentioned underwater target trajectory calculation method.

[0051] Specifically, the terminal involved in this embodiment has a memory, a processor, and a related executable computer program. The terminal integrates the hardware and software resources required to implement the trajectory calculation method, and can quickly respond and process underwater target trajectory data in actual scenarios. The processor executes the program, enabling the terminal to efficiently complete the entire trajectory calculation process from data preprocessing to model operation. The memory can store a large amount of historical trajectory data and model parameters, which is convenient to be called at any time during the calculation process to ensure the coherence of data processing. In a complex underwater operation environment, the real-time processing ability of the terminal is crucial. It can analyze the collected low-frequency sparse trajectory data in a timely manner and quickly output a continuous and smooth trajectory curve, providing strong support for the real-time monitoring, precise positioning, and continuous tracking of underwater targets. Moreover, the existence of this terminal makes it possible to develop the integration and miniaturization of underwater detection and positioning systems, which is convenient for scientific researchers and engineers to carry and use during actual operations, improving the efficiency and convenience of the entire underwater target detection work, and enhancing the adaptability and practicality of the system in different application scenarios.

[0052] The innovation of the present invention is mainly reflected in the combination of principal component analysis (PCA) and data augmentation technology. A complete solution for track calculation is proposed for the characteristics of sparse trajectory data of underwater targets. By using a sliding window to divide the input features and output labels, training samples suitable for neural network model processing are constructed; innovatively, PCA coordinate transformation is independently performed on each group of samples, converting the absolute coordinate system into a dynamic local coordinate system based on the main direction of target movement, making the data more conform to the actual movement law of underwater targets; a dual data augmentation strategy including symmetric processing and random scaling is designed, which not only expands the sample diversity through geometric transformation but also simulates the speed change through probability perturbation; a multi-layer perceptron model is used to learn the track law, and the method of taking the average value by combining multiple predictions of the sliding window effectively improves the continuity and accuracy of track prediction.

[0053] The present invention solves the problem of insufficient accuracy of traditional underwater target trajectory calculation methods under sparse data conditions. The PCA coordinate transformation highlights the main feature components of target movement, enabling the neural network to more effectively learn the track law; the application of data augmentation technology significantly improves the generalization ability of the model under limited sample conditions; the method of sliding window prediction and result fusion effectively reduces random errors, making the generated track curve smoother and more reliable. The method described in the present invention is particularly suitable for the common low-frequency sampling scenarios in underwater target detection, and can reconstruct a continuous and accurate navigation path from sparse track points, providing a reliable technical means for applications such as underwater target tracking, behavior analysis, and trajectory prediction, and having important practical value in the fields of marine environmental monitoring, underwater security, etc.

[0054] The specific embodiments of the invention have been described in detail above, but they are only examples, and the present invention is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications and substitutions to the invention are also within the scope of the present invention. Therefore, all equivalent transformations and modifications made without departing from the spirit and scope of the present invention should be covered within the scope of the present invention.

Claims

1. A method for calculating underwater target track, characterized in that: The underwater target track calculation method comprises the following steps: S100, dividing the high-frequency collected continuous three-dimensional trajectory data into input feature data and output label data, constructing training set and test set samples through sliding windows, and providing structured data for the model; S200, using principal component analysis to decentralize and transform coordinates of each group of samples in the training set and the test set, transforming the absolute three-dimensional coordinates into a new coordinate system with the target movement direction, horizontal direction, and vertical direction as axes, and generating PCA transformation samples; S300, generating enhanced samples by flipping and randomly scaling the PCA transformed samples; S400, designing a multi-layer perceptron model, with sparse trajectory points as input and interpolated trajectory points as output, and using the PCA conversion samples and enhanced samples to train the multi-layer perceptron model to learn trajectory rules; S500, using a sliding window to predict the sparse trajectory multiple times, taking the average of multiple prediction results for the same interpolation point as the final position, and obtaining a complete trajectory after interpolation.

2. The underwater target track calculation method according to claim 1, characterized in that: S100 includes the following steps: S110, performing sliding window interception on the continuous three-dimensional trajectory data collected at a high frequency to construct multiple groups of samples, each group of samples including input feature data and output label data; S120, dividing all samples into a training set and a test set; S130 , controlling the interpolation density by adjusting the proportional relationship between the number of trajectory points of the input feature data and the number of trajectory points of the output label data.

3. The underwater target track calculation method according to claim 2, characterized in that: The input feature data are sparse trajectory points under low-frequency sampling, and the output label data are trajectory points to be interpolated.

4. The underwater target track calculation method according to claim 3, characterized in that: S200 includes the following steps: S210, for each set of input feature data of samples in the training set, calculate the mean of each dimension feature in the three-dimensional space; S220, subtracting the mean from each dimension feature of the input feature data and the corresponding output label data to achieve decentralized processing; S230, calculating the covariance matrix of the decentralized input feature data; S240, performing eigenvalue decomposition on the covariance matrix to obtain its eigenvalues ​​and eigenvectors; S250, sorting the eigenvalues ​​by size, and selecting the eigenvectors corresponding to the three largest eigenvalues ​​to form an eigenvector matrix; S260, converting the decentralized input feature data and output label data into a new space formed by the feature vector matrix; S270. For each group of samples in the test set, the same coordinate transformation method as that of the training set is used to obtain a training set and a test set after coordinate transformation.

5. The underwater target track calculation method according to claim 4, characterized in that: In S300, the PCA conversion samples are processed, including the following steps: S310, performing axisymmetric processing on the PCA transformed samples along three principal component axes respectively; S320, performing origin symmetry processing on the PCA conversion samples; S330, merging the samples after axisymmetric processing and origin symmetric processing with the PCA transformed samples to form an enhanced training data set.

6. The underwater target track calculation method according to claim 5, characterized in that: The S300 also includes: S340, multiplying the PCA transformed sample by a random scaling factor to obtain a sample after random scaling, wherein the random scaling factor is sampled from a preset probability distribution; S350, merging the samples after random scaling processing with the PCA conversion samples to further expand the training data set.

7. The underwater target track calculation method according to claim 6, characterized in that: S400 includes the following steps: S410, constructing a multi-layer perceptron neural network model, wherein the input layer receives the sparse trajectory point data converted by principal component analysis, and the output layer generates the interpolated trajectory point data; S420, the multi-layer perceptron neural network model includes at least one hidden layer and adopts a nonlinear activation function; S430, optimizing network parameters by minimizing the error between the predicted trajectory points and the actual trajectory points; S440: training the multi-layer perceptron neural network model using the training set that has been processed with coordinate system transformation and data enhancement.

8. The underwater target track calculation method according to claim 7, characterized in that: S500 includes the following steps: S510, inputting the low-frequency sparse trajectory data of the underwater target to be processed into a trained multi-layer perceptron neural network model; S520, using a sliding window mechanism to perform segmented prediction on the input data to generate intermediate trajectory points; S530, performing weighted fusion on multiple prediction results generated by different windows at the same spatial position; S540: Output a continuous and smooth underwater target track curve.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the underwater target track calculation method described in any one of claims 1 to 8 is implemented.

10. A terminal, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the underwater target track estimation method according to any one of claims 1 to 8.

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