An underwater target track calculation method, storage medium and terminal

Abstract

The present invention discloses an underwater target track calculation method, a storage medium, and a terminal, belonging to the technical field of underwater target detection and positioning. It solves the problem that due to underwater noise, low sampling frequency, etc., the underwater target trajectory points are sparse and there are positioning errors, which in turn affect tasks such as underwater target position estimation, tracking, and trajectory prediction. The present invention first constructs a training set and a test set from the continuously collected high-frequency three-dimensional trajectory data, transforms the coordinates using the principal component analysis method, performs sample enhancement processing, then uses a multi-layer perceptron model to learn the trajectory law, and finally obtains the complete underwater target track by making multiple predictions through a sliding window and taking the mean value. The present invention uses a neural network to learn the trajectory law, and the prediction is more accurate; using PCA to transform the samples improves the model accuracy and generalization ability; enriching the samples through data enhancement; making multiple predictions through a sliding window and taking the mean value to improve the prediction accuracy.

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 an underwater target's track, 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 interfering factors, such as strong underwater noise, low sampling frequency, unstable signal quality, and frequent signal interruption problems. These adverse factors will cause the intervals between the track points of the underwater target to be too large, and there is also 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's 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 tracks 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:

[0004] 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 underwater target's track 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 information in both forward and backward directions, resulting in limited prediction accuracy.

[0005] 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 the target track conforms to a polynomial distribution. But in actual situations, the navigation track of the underwater target is complex and variable, 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 track point position.

[0006] 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's track, simply smoothing the track is far from enough. More importantly, it is necessary to extract the target's motion law from a large amount of data and then optimally estimate the track point position, which is exactly what the Bezier curve method lacks.

[0007] Machine learning / deep learning method: As a technology that relies on historical data to mine the operation 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 for specific scenarios. Only through careful design and adjustment is it possible to achieve a relatively accurate prediction of the trajectory point position, which to a certain extent limits its generality and practicality. Summary of the Invention

[0008] The present invention proposes an underwater target trajectory calculation method, a storage medium, and a 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 the 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.

[0009] An underwater target trajectory calculation method, the underwater target trajectory calculation method includes the following steps:

[0010] 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;

[0011] S200: Use the principal component analysis method to perform centering 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 axes as the axes, and generate PCA conversion samples;

[0012] S300: Generate enhanced samples by flipping and randomly scaling the PCA conversion samples;

[0013] 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;

[0014] 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.

[0015] Further, S100 includes the following steps:

[0016] 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;

[0017] S120. Divide all samples into a training set and a test set;

[0018] 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.

[0019] Further, the input feature data are sparse trajectory points under low-frequency sampling, and the output label data are trajectory points to be interpolated.

[0020] Further, S200 includes the following steps:

[0021] 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;

[0022] 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;

[0023] S230. Calculate the covariance matrix of the de-centralized input feature data;

[0024] S240. Perform eigenvalue decomposition on the covariance matrix to obtain its eigenvalues and eigenvectors;

[0025] S250. Sort the eigenvalues by size, and select the eigenvectors corresponding to the three largest eigenvalues to form an eigenvector matrix;

[0026] S260. Convert the de-centralized input feature data and output label data into the new space constituted by the eigenvector matrix;

[0027] S270. For each group of samples in the test set, adopt the same coordinate transformation method as the training set to obtain the training set and the test set after coordinate transformation.

[0028] Further, in S300, processing the PCA-transformed samples includes the following steps:

[0029] S310. Perform axisymmetric processing on the PCA-transformed samples along the three principal component axes respectively;

[0030] S320. Perform origin-symmetric processing on the PCA-transformed samples;

[0031] S330. Combine the samples after axisymmetric processing and origin-symmetric processing with the PCA-transformed samples to form an enhanced training data set.

[0032] Further, S300 also includes:

[0033] 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;

[0034] S350. Combine the samples after random scaling processing with the PCA-transformed samples to further expand the training dataset.

[0035] Further, S400 includes the following steps:

[0036] 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;

[0037] S420. The multi-layer perceptron neural network model includes at least one hidden layer and uses a non-linear activation function;

[0038] S430. Optimize the network parameters by minimizing the error between the predicted trajectory points and the real trajectory points;

[0039] S440. Use the training set processed by coordinate transformation and data augmentation to train the multi-layer perceptron neural network model.

[0040] Further, S500 includes the following steps:

[0041] S510. Input the low-frequency sparse trajectory data of the underwater target to be processed into the trained multi-layer perceptron neural network model;

[0042] S520. Adopt a sliding window mechanism to segment and predict the input data to generate intermediate trajectory points;

[0043] S530. Perform weighted fusion on the multiple prediction results generated by different windows at the same spatial position;

[0044] S540. Output a continuous and smooth underwater target trajectory curve.

[0045] A storage medium stores a computer program thereon, and when the computer program is executed by a processor, the above-mentioned underwater target trajectory calculation method is implemented.

[0046] A terminal includes: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the program to implement the above-mentioned underwater target trajectory calculation method.

[0047] Advantages of the present invention:

[0048] 1. Compared with the method that only uses linear interpolation, the model based on neural network can extract the underwater target navigation rules based on the learning of a large number of historical samples, and obtain relatively accurate prediction results.

[0049] 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, obtaining 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 the trajectory prediction model can achieve better model prediction accuracy and generalization ability with less data volume.

[0050] 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.

[0051] 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 as the final prediction result, improving the prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is the method flow chart of an underwater target track calculation method of the present invention;

[0053] Figure 2 is the schematic diagram of the underwater target track;

[0054] Figure 3 is the schematic diagram of the trajectory prediction process. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] The following will clearly and completely describe the technical solutions in the embodiments of the present invention 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. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] Referring to Figure 1 as shown, an underwater target track calculation method, the underwater target track calculation method includes the following steps:

[0057] 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 sliding windows to provide structured data for the model;

[0058] S200. Use the principal component analysis method to perform de - centering and coordinate transformation on each group of samples in the training set and the 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 - transformed samples;

[0059] S300. Generate augmented samples by flipping and randomly scaling the PCA - transformed samples;

[0060] S400. Design a multi - layer perceptron model, with the input being sparse trajectory points and the output being interpolated trajectory points, and use the PCA - transformed samples and augmented samples to train the multi - layer perceptron model to learn the trajectory pattern;

[0061] S500. Use a sliding window to predict the sparse trajectory multiple times, take the mean of the multiple prediction results for the same interpolation point as the final position, and obtain the complete interpolated trajectory.

[0062] 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 the training set and test set samples, it provides a structured data basis for the model, effectively solving the problem of sparse and noisy underwater target trajectory data. By performing de - centering and coordinate transformation on the sample data through the principal component analysis method, converting the absolute three - dimensional coordinates into a new coordinate system with the target movement direction, horizontal, and vertical axes as the axes, it not only conforms more to the physical meaning of underwater target navigation but also can improve the prediction accuracy and generalization ability of the model under the condition of less data volume. The data augmentation process of flipping and randomly scaling the PCA - transformed samples further expands the training data set and enhances the adaptability of the model to complex underwater environments. Using a multi - layer perceptron model to learn the trajectory pattern, combined with the method of multiple predictions using a sliding window and taking the mean for the same interpolation point, significantly improves the accuracy and continuity of trajectory prediction, and finally generates a smooth and accurate underwater target trajectory curve, solving tasks such as underwater target position estimation, target tracking, and trajectory prediction.

[0063] Further, S100 includes the following steps:

[0064] 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;

[0065] S120. Divide all the samples into a training set and a test set;

[0066] 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.

[0067] Specifically, for the coordinate system conversion method described in this embodiment, intelligent spatial reconstruction is performed on the underwater target trajectory data through principal component analysis technology, 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 the underwater target, effectively eliminate the deviation between the sensor coordinate system and the true movement direction of the target, and make the sparse trajectory points show a more distinct linear distribution feature in the new coordinate system. By retaining the principal components of the three directions with the largest variances, not only is the data dimension 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 the target movement law, and at the same time avoids the problem of feature confusion caused by the change of target heading in the traditional fixed coordinate system.

[0068] In the actual operating environment, high-frequency data collection is performed on the underwater target track to obtain a continuous operating trajectory. The trajectory can be regarded as consisting of three-dimensional (x, y, z) coordinate points, as Figure 2 shown.

[0069] The collected data is divided into input feature data (such as x1, x2, x3, x4) and output label data (such as y1, y2, y3, y4, y5, y6). The purpose of the present invention is to train a trajectory prediction model based on the feature and label data to achieve the calculation of the trajectory at a low sampling frequency, that is, to predict the intermediate trajectory points of the low-frequency trajectory data to obtain a continuous underwater target track.

[0070] The data preprocessing part mainly involves sample collection, division of the training set and test set (such as 4:1), and construction of input features and output label samples. The sample construction can adjust the number of trajectory points of the input and output according to needs. Assume that the length of the input sample is n, and the interval between two input samples is m, that is, the number of trajectory points input to the model is n, and the number of trajectory points predicted by the model is (n - 1)*m. Based on this, the training set and test set samples are constructed. As Figure 2 shown, the input trajectory points are (x1, x2, x3, x4), and the model predicted trajectory points are (y1, y2, y3, y4, y5, y6), then [(x1, x2, x3, x4), (y1, y2, y3, y4, y5, y6)] 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 original collected track data through a sliding window with a certain step size.

[0071] Further, the input feature data is sparse trajectory points under low-frequency sampling, and the output label data is the trajectory points to be interpolated.

[0072] Specifically, in this embodiment, it is clarified that the input feature data is sparse trajectory points under low-frequency sampling, and the output label data is the trajectory points to be interpolated. In the underwater detection scenario, affected by factors such as noise and low sampling frequency, the actually obtained trajectory data is often sparse trajectory points under low-frequency sampling. Using it as the input feature data is more in line with the real application environment. Through such input and output settings, the model of the present invention can directly process the sparse trajectory data of underwater targets. Compared with traditional methods, it no longer depends on simple assumptions about the 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 precise interpolation of the trajectory points to obtain a more accurate trajectory curve.

[0073] Further, S200 includes the following steps:

[0074] 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;

[0075] 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;

[0076] S230. Calculate the covariance matrix of the de-centralized input feature data;

[0077] S240. Perform eigenvalue decomposition on the covariance matrix to obtain its eigenvalues and eigenvectors;

[0078] S250. Sort the eigenvalues by size, and select the eigenvectors corresponding to the three largest eigenvalues to form an eigenvector matrix;

[0079] S260. Transform the de-centralized input feature data and output label data into the new space constituted by the eigenvector matrix;

[0080] 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.

[0081] 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 each group of sample input feature data in the training set, and then perform the de-centralization process, which can effectively eliminate the bias in the data and make the subsequent analysis 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 realizing 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.

[0082] 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, in the case of limited sampling data, 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 each group of sample input features 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 in the case of limited sampling data.

[0083] The steps of the PCA algorithm are as follows:

[0084] 1) Randomly sample a group of samples in the training set. Taking the example shown Figure 1 as an example, the sample input features are (x1, x2, x3, x4), and the labels are (y1, y2, y3, y4, y5, y6);

[0085] 2) Remove the mean value (i.e., de-centralize), that is, calculate the mean value of each dimension feature of the sample input features (x1, x2, x3, x4) in the three-dimensional space, and subtract the mean value from each dimension feature of the input features (x1, x2, x3, x4) and the labels (y1, y2, y3, y4, y5, y6) to obtain the de-centralized features and labels;

[0086] 3) Calculate the covariance matrix of the input features ;

[0087] 4) Use the eigenvalue decomposition method to find the covariance matrix The eigenvalues ​​and eigenvectors of

[0088] 5) Sort the eigenvalues ​​from large to small, and select the corresponding eigenvectors (row vectors) of the three largest eigenvalues ​​to form the eigenvector matrix P;

[0089] 6) Convert the decentralized feature and label data to the new space constructed by the feature vector, that is, Y=PX, to obtain the training samples (features and labels) after coordinate transformation;

[0090] 7) Traverse each group of samples in the training set and test set, repeat steps 2-6, and obtain the training set and test set after coordinate transformation.

[0091] Furthermore, in S300, the PCA conversion samples are processed, including the following steps:

[0092] S310, performing axisymmetric processing on the PCA transformed samples along three principal component axes respectively;

[0093] S320, performing origin symmetry processing on the PCA conversion samples;

[0094] S330, merging the samples after axisymmetric processing and origin symmetric processing with the PCA transformed samples to form an enhanced training data set.

[0095] Specifically, this embodiment performs axisymmetric processing on the PCA conversion samples along the three principal component axes, and performs origin symmetry processing on the PCA conversion samples, and then merges the processed samples with the PCA conversion samples to form an enhanced training data set. The motion trajectory of underwater targets is complex and changeable. The amount of data relying solely on the original PCA conversion sample may be insufficient, making it difficult for the model to fully learn various possible trajectory patterns. Through axisymmetric processing and origin symmetric processing along the principal component axis, new samples related to but different from the original samples can be created, enriching the diversity of training data. This allows the model to be exposed to more trajectory data of different forms during the training process, so as to better learn the various characteristics and laws of the underwater target track and enhance the adaptability of the model to different track conditions. In practical applications, even if the underwater target track scene is not exactly the same as the training data, the model can rely on the ability trained by these rich and diverse data to more accurately perform track calculation and prediction, thereby improving the generalization ability of the model and ensuring the accuracy and reliability of target track calculation in complex underwater environments.

[0096] Furthermore, S300 also includes:

[0097] 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;

[0098] S350. Combine the samples after random scaling processing with the PCA-transformed samples to further expand the training dataset.

[0099] Specifically, in this embodiment, the PCA-transformed samples are multiplied by a random scaling factor sampled from a preset probability distribution, and then combined with the PCA-transformed samples to further expand the training dataset. When calculating the underwater target track, due to the complex underwater environment, the target movement trajectory may have various scale changes. By randomly scaling the PCA-transformed samples, the target track situations at different scales are simulated, providing more diverse data for the model. This enables the model to learn the characteristics and laws of the track at different scales, enhancing the model's adaptability to track changes. When the model faces actual underwater target track data, even if the data is different in scale from the training data, it can more accurately calculate and predict the track relying on the knowledge learned from the randomly scaled data. In addition, the expanded training dataset allows the model to come into contact with more data with different characteristics during training, helping the model better capture the potential patterns in the data and further improving the model's generalization ability.

[0100] 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 track calculation scenario include flipping and random scaling. Flipping is to perform axial symmetry processing and origin symmetry processing on the PCA-transformed samples (features and labels) along the three principal component axes to obtain the augmented samples; random scaling is to multiply the PCA-transformed samples 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 (PCA-transformed samples) and the augmented samples (flipping and random scaling) are used together for the training of the trajectory prediction model, which improves the prediction accuracy and generalization ability of the trajectory point positions in the case of limited sample quantity.

[0101] Furthermore, S400 includes the following steps:

[0102] S410. Construct a multi-layer perceptron neural network model, whose input layer receives the sparse track point data after principal component analysis transformation, and the output layer generates the interpolated track point data;

[0103] S420. The multi-layer perceptron neural network model includes at least one hidden layer and adopts a non-linear activation function;

[0104] S430. Optimize the network parameters by minimizing the error between the predicted trajectory points and the actual trajectory points;

[0105] S440. Use the training set processed by coordinate system transformation and data augmentation to train the multi-layer perceptron neural network model.

[0106] Specifically, this embodiment details the construction and training process of the multi-layer perceptron neural network model. The multi-layer perceptron neural network model is constructed. The input layer receives the sparse trajectory point data after principal component analysis transformation, and the output layer 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 underwater targets is affected by various factors and is not a simple linear relationship. The use of the non-linear activation function enables the model to more accurately depict these complex relationships and uncover the deep-seated laws behind the data. Optimize the network parameters by minimizing the error between the predicted trajectory points and the actual trajectory points to ensure that the model continuously adjusts in a more accurate direction during training, improving the accuracy of prediction. Use the training set processed by coordinate system transformation and data augmentation to train the model, making full use of the data advantages processed in the previous steps. The data after coordinate system transformation is more in line with physical meaning, 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.

[0107] In actual use, the trajectory prediction model preferably uses the simplest multi-layer perceptron (MLP). The activation function can use the Relu function, and a single-hidden layer or double-hidden layer network can be used. Assume that the length of the input sample is n, the interval between two input samples is m, and the feature dimension of the trajectory points 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 (x1, x2, x3, x4), and the model-predicted trajectory points are (y1, y2, y3, y4, y5, y6). 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. Use this model to train the PCA-transformed samples and the data-augmented samples to obtain the underwater target track prediction model.

[0108] Furthermore, S500 includes the following steps:

[0109] S510. Input the low-frequency sparse trajectory data of the underwater target to be processed into the trained multi-layer perceptron neural network model;

[0110] S520. Use a sliding window mechanism to segment and predict the input data to generate intermediate trajectory points;

[0111] S530. Perform weighted fusion on the multiple prediction results generated by different windows at the same spatial position;

[0112] S540. Output a continuous and smooth underwater target trajectory curve.

[0113] Specifically, this embodiment details the prediction and output process of the trajectory calculation method. Input the low-frequency sparse trajectory data of the underwater target to be processed into the trained multi-layer perceptron neural network model, which lays a foundation for accurately predicting the trajectory by leveraging the learning results of the underwater target trajectory pattern accumulated in the previous training. Use a sliding window mechanism to segment and predict the input data and generate intermediate trajectory points. This method can fully utilize the local information in the data and analyze the trajectory change trend from different local perspectives. Due to the complex movement trajectory of the underwater target, the sliding window can flexibly capture the features of different segments and avoid missing important information. Perform weighted fusion on the multiple prediction results generated by different windows at the same spatial position, comprehensively considering the advantages and reliability of different window predictions, and reducing the error and uncertainty of single-window prediction. Compared with relying only on single prediction, the fusion of multiple prediction results can more accurately reflect the true situation of the target at this position. Finally, output a continuous and smooth underwater target trajectory curve, providing high-quality data support for subsequent tasks such as target positioning, tracking, and trajectory prediction, and enhancing the accuracy and reliability of analyzing the target movement state in a complex underwater environment.

[0114] 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 take the mean value of the results as the final trajectory point prediction result. As Figure 3 shown, assume that the input window length is 4, the sliding step is 1, and the mean value of multiple prediction results is taken as the prediction of the interpolation point position.

[0115] 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.

[0116] Specifically, the storage medium proposed in this embodiment can realize the underwater target track calculation method when the computer program stored thereon is executed by the processor. First, it realizes the effective storage and convenient reuse of the track calculation method. When researchers or relevant technical personnel need to perform underwater target track calculation in different application scenarios, there is no need to rewrite complex codes or repeatedly design the entire algorithm process. They only need to call the computer program in the storage medium to quickly carry out the calculation work, which greatly saves time and labor costs. Secondly, the existence of the storage medium ensures the stability and consistency of the algorithm. No matter what device the program is run on, as long as the processor can execute it correctly, it can be processed according to the established track 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, marine resource exploration, etc. In addition, it provides strong support for the promotion and application of underwater target track calculation technology. Different research teams or enterprises can carry out secondary development and optimization based on the storage medium to further expand the application scope and function of the method.

[0117] A terminal comprises: 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.

[0118] Specifically, the terminal involved in this embodiment has a memory, a processor, and an executable related computer program. The terminal integrates the hardware and software resources required to implement the track calculation method, and can quickly respond to and process underwater target track data in actual scenarios. The processor executes the program, so that the terminal can efficiently complete the entire track calculation process from data preprocessing to model calculation. The memory can store a large amount of historical track data and model parameters, which is convenient for calling at any time during the calculation process to ensure the consistency of data processing. In a complex underwater operating environment, the real-time processing capability of the terminal is crucial. It can timely analyze the collected low-frequency sparse track data, quickly output a continuous and smooth track curve, and provide strong support for real-time monitoring, precise positioning and continuous tracking of underwater targets. Moreover, the existence of the terminal provides the possibility for the integrated and miniaturized development of underwater detection and positioning systems, which is convenient for scientific researchers and engineers to carry and use in actual operations, improves the efficiency and convenience of the entire underwater target detection work, and enhances the adaptability and practicality of the system in different application scenarios.

[0119] 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. The multi-layer perceptron model is used to learn the trajectory law, and the method of taking the mean by combining multiple predictions of the sliding window effectively improves the continuity and accuracy of track prediction.

[0120] 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 trajectory 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 trajectory 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.

[0121] 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. An underwater target trajectory calculation method, characterized in that, The underwater target trajectory calculation method includes the following steps: S100. Divide the continuously acquired 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, lateral, and longitudinal axes as axes, and generate PCA transformation samples. S200 includes the following steps: S210. For the input feature data of each group of samples in the training set, calculate the mean value of each dimension feature in the 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 decentralization processing; S230. Calculate the covariance matrix of the decentralized input feature data; S240. Perform eigenvalue decomposition on the covariance matrix to obtain its eigenvalues and eigenvectors; S250. Sort the eigenvalues in descending order, and select the eigenvectors corresponding to the three largest eigenvalues to form an eigenvector matrix; S260. Convert the decentralized 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; S300. Generate enhanced samples by flipping and randomly scaling the PCA transformation samples. The processing of the PCA transformation samples includes the following steps: S310. Perform axisymmetric processing on the PCA transformation samples along the three principal component axes respectively; S320. Perform central symmetry processing on the PCA transformation samples; S330. Combine the samples after axisymmetric processing and central symmetry processing with the PCA transformation samples to form an enhanced training data set; S340. Multiply the PCA transformation 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 transformation samples to further expand the training data set; 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 transformation 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 value of the multiple prediction results of the same interpolation point as the final position to obtain the complete trajectory after interpolation.

2. The underwater target track calculation method according to claim 1, characterized in that S100 includes the following steps: S110. Perform sliding window interception on the continuously acquired 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.

3. The underwater target track calculation method according to claim 2, wherein 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 1, characterized in that 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 uses 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.

5. The underwater target track calculation method according to claim 4, characterized in that 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 trajectory curve.

6. A storage medium, on which a computer program is stored, characterized in that, When the computer program is executed by a processor, it implements the underwater target trajectory calculation method according to any one of claims 1-5.

7. A terminal, characterized in that, Comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the program to implement the underwater target trajectory calculation method according to any one of claims 1-5.

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