An underwater sensor positioning method and system based on basis pursuit denoising

Abstract

The application provides an underwater sensor positioning method and system based on basis pursuit denoising, which is used for underwater sensor positioning based on deep learning. By means of sparse constraint property, a sparse signal L1 norm penalty term least square optimization problem is constructed, a noise-free signal is recovered by using a basis pursuit denoising algorithm, and the denoising of the signal is completed. Subsequently, positioning is performed through a neural network, so as to improve the underwater sensor positioning accuracy. It is proved by real sea trial data experiments that the underwater sensor positioning algorithm based on basis pursuit denoising proposed in the application has good performance improvement in positioning accuracy, and shows the potential of the underwater sensor based on basis pursuit denoising in underwater positioning based on deep learning.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology and relates to an underwater sensor positioning method and system based on basis tracking noise reduction. Background Technology

[0002] The underwater marine environment is a crucial foundation for safety and economic development, playing an increasingly important role in all aspects of life. A thorough understanding of the underwater marine environment is essential for the rational utilization of marine resources and the effective prevention of marine natural disasters. Research on underwater wireless sensor network (WSN) positioning technology and underwater WSNs is ongoing. Node positioning in underwater WSNs is fundamental and critical to their applications. For most application scenarios, if the location of the sensor's source cannot be determined, the collected data may be of no value.

[0003] For many underwater sensor positioning scenarios, traditional distance-based positioning techniques, including Time of Arrival (TOA), Time Difference of Arrival (TDOA), Angle of Arrival (AOA), and Received Signal Strength Indicator (RSSI), remain applicable. However, distance-based positioning heavily relies on the accuracy of the signal propagation model, and underwater environments are typically more diverse and complex, leading to the development of numerous algorithms in this field. Matched Field Positioning (MFP), a target positioning method proposed in the early 20th century, constructs a field source model using all environmental and channel parameters. This model is then compared with real-world basic array data to find the point most similar to the signal characteristics acquired during actual testing. Essentially, this method obtains target location information by modeling and seeking the correlation between the model and actual measurements. While this method yields a highly accurate signal propagation model with a wide range of applications and improved accuracy compared to previous methods, the computational burden during modeling is enormous, and the propagation model used in the calculation is easily affected by environmental parameters, thus limiting its ability to perform real-time measurements. In recent years, deep learning-based regression algorithms have begun to be applied to underwater positioning, simulated using real experimental data. The results indicate that deep learning algorithms hold promise in this field. Many machine learning algorithms, such as feedforward neural networks (FNN), support vector machines (SVM), and random forests (RF), have been widely used. The application of deep learning to the field of underwater sensor localization has received increasing attention. For example, deep neural networks (DNN), convolutional neural networks (CNN), and recurrent neural networks (RNN) have been proposed for underwater sensor localization.

[0004] Most current research on underwater sensor localization focuses on improving or replacing deep learning network models. This research primarily concentrates on deep learning itself, involving the sensor sending signals to an anchor node, extracting features from the received signals, and using a neural network to locate the sensor. However, it neglects the signal received by the anchor node itself, and research on signal preprocessing at the anchor node is insufficient. However, the underwater environment is extremely complex. The underwater acoustic channel contains numerous unpredictable noises due to various organisms and the marine environment. The raw signal received by the underwater anchor node is mixed with noise due to interference during signal propagation in the underwater acoustic channel, causing errors caused by the signal itself propagating in the underwater acoustic channel. This error is significant and cannot be ignored in the entire localization process. Using noisy data for deep learning to achieve underwater sensor localization can, in some cases, introduce significant deviations in the final localization accuracy. These deviations cannot be compensated for by improving the deep learning network because they originate from the data itself. For example, feedforward neural networks and random forests have been shown to have reduced prediction performance in classification problems when the data contains significant noise and there are variables requiring multi-class classification. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide an underwater sensor positioning method and system based on base tracking noise reduction, so as to solve the defect that underwater sensor positioning is easily affected by noise and thus the positioning effect is poor, thereby improving the performance of underwater sensor positioning.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] An underwater sensor localization method based on base tracking noise reduction includes the following steps:

[0008] S1, Receive node signals from the sensor to be located at the anchor node. The node signals consist of noise-free signals and noise signals. The noise-free signals are emitted by the underwater sensor, and the noise signals are generated in the underwater acoustic channel.

[0009] S2 solves the sparse denoising problem by using the basis pursuit denoising algorithm to obtain a noiseless signal from the node signal;

[0010] S3. Perform a discrete Fourier transform on the noiseless signal to obtain frequency domain sound pressure data. After normalizing the frequency domain sound pressure data, obtain the sampling covariance matrix. Based on the sampling covariance matrix, obtain the data features corresponding to the noiseless signal. Input the data features into the positioning neural network model to obtain the position of the underwater sensor.

[0011] A further improvement of the present invention is that:

[0012] Preferably, in S2, the formula for the denoising problem is:

[0013]

[0014] Where λ is the coefficient, A is the N×N inverse Fourier transform matrix, y is a vector of length N, x is a vector of length N, and u is an auxiliary variable.

[0015] Preferably, the ADMM algorithm is used to obtain the auxiliary variable u by iterating through the following equation (7);

[0016]

[0017] Substitute the obtained auxiliary variable u into s(n)=Au to obtain a noiseless signal.

[0018] Preferably, after S2, the method further includes the following steps: determining whether the obtained noiseless signal meets the requirements in both the time domain and the frequency domain.

[0019] The time-domain determination method is to compare the noiseless signal and the node signal to determine whether the noiseless signal has fewer glitches compared to the node signal.

[0020] The method for determining frequency is as follows: compare the noiseless signal and the node signal, and determine whether the noiseless signal has a frequency value that becomes 0 or 1 relative to the node signal.

[0021] Preferably, in S3, the formula for data normalization is:

[0022]

[0023] Where q(f) is the frequency domain sound pressure data, f is the selected frequency point, and L is the number of anchor nodes receiving the signal.

[0024] Preferably, in S3, the real and imaginary parts of the upper triangular matrix and diagonal elements in the covariance matrix are concatenated into an L(L+1) dimensional vector to obtain the data features corresponding to the noiseless signal.

[0025] Preferably, in S3, the neural network model outputs a K-dimensional column vector, and the position of the underwater sensor is obtained through the K-dimensional column vector.

[0026] Preferably, in S3, in the K-dimensional column vector, the k-th data is 1, corresponding to the label vector i. zk , corresponding to obtain r k , which indicates the location of the underwater sensor.

[0027] Preferably, in S3, the neural network model is trained using a loss function; the loss function is obtained by comparing the underwater sensor node positions output by the neural network with the actual underwater sensor node positions; the loss function is the MSE function.

[0028] An underwater sensor positioning system based on base tracking noise reduction includes:

[0029] The acquisition unit is used to receive node signals from the sensor to be located at the anchor node. The node signals consist of noise-free signals and noise signals. The noise-free signals are emitted by the underwater sensor, and the noise signals are generated in the underwater acoustic channel.

[0030] The denoising unit is used to solve the sparse denoising problem by using the basis pursuit denoising algorithm to obtain the noiseless signal from the node signal;

[0031] The location unit is used to perform a discrete Fourier transform on the noiseless signal to obtain frequency domain sound pressure data. After normalizing the frequency domain sound pressure data, a sampling covariance matrix is ​​obtained. Based on the sampling covariance matrix, the data features corresponding to the noiseless signal are obtained. The data features are then input into the positioning neural network model to obtain the position of the underwater sensor.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] This invention proposes an underwater sensor localization algorithm based on basis pursuit denoising, applicable to deep learning-based underwater sensor localization. Compared to previous research in this field, this invention does not focus on improving the deep learning network model, but rather on the preprocessing of signal data received by the underwater anchor node, paying more attention to the signal data itself. Since the signals emitted by the underwater sensor to be located have fixed frequencies, the emitted signals are sparse in the frequency domain, and the signals received by the anchor node should also be sparse in the frequency domain. Utilizing the sparsity constraint property, a least squares optimization problem with L1 norm penalty terms for sparse signals is constructed, and the basis pursuit denoising algorithm is used to recover the noise-free signal, completing the signal denoising process. Subsequently, a neural network is used for localization to improve the underwater sensor localization accuracy. Experiments using real sea trial data demonstrate that the proposed underwater sensor localization algorithm based on basis pursuit denoising achieves significant performance improvements in localization accuracy, showcasing the potential of underwater sensors with basis pursuit denoising based on deep learning in underwater localization.

[0034] Experiments using real sea trial data demonstrate that the underwater sensor positioning method proposed in this invention achieves excellent positioning accuracy, showcasing the potential of underwater sensors based on basis tracking noise reduction in deep learning-based underwater positioning. Compared to previous research in this field, this invention does not focus on improving the deep learning network model, but rather on the preprocessing of signal data received by the underwater anchor node. It pays more attention to the signal data itself, utilizing the sparsity of the signal received by the underwater anchor node in the frequency domain to improve the positioning accuracy of the underwater sensor and reduce positioning errors by removing noise generated by the signal propagating in the underwater acoustic channel. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the feedforward neural network structure used.

[0036] Figure 2 A schematic diagram of the Swell96Ex experiment;

[0037] Figure 3 This represents the time domain of the raw signal received by the underwater sensor during the Swell96Ex experiment.

[0038] Figure 4 This represents the frequency domain of the original signal received by the underwater sensor during the Swell96Ex experiment.

[0039] Figure 5 The time domain of the signal received by the underwater sensor in the Swell96Ex experiment after denoising using the BPD algorithm;

[0040] Figure 6 The frequency domain of the signal received by the underwater sensor in the Swell96Ex experiment after noise reduction using the BPD algorithm;

[0041] Figure 7 The prediction results are shown in the figure when the selected frequency points are f = 109Hz and 198Hz.

[0042] Figure 8 The image shows the prediction results obtained after denoising the selected frequency points f = 109Hz and 198Hz using the BPD algorithm.

[0043] Figure 9 This is a flowchart of the entire algorithm. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings:

[0045] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. The terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, unless otherwise explicitly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection or a detachable connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0046] This invention proposes a basis-tracking denoising algorithm for underwater sensor localization, applicable to deep learning-based underwater sensor localization. By receiving signals from anchor nodes at known frequencies, and considering that the signals emitted by the underwater sensor to be located have fixed frequencies, the signals emitted by the underwater sensor exhibit sparse properties in the frequency domain. This means the signals received by the underwater anchor nodes should also exhibit sparse properties in the frequency domain. The signal is modeled as the sum of a noiseless signal and noise, and then processed using a basis-tracking denoising algorithm to recover the noiseless signal. Based on the known frequencies, a least-squares optimization problem with L1 norm penalty terms for the sparse signal is constructed to ultimately reconstruct the noiseless signal. In this invention, under the established underwater sensor node model, the denoising of the signals emitted by the underwater sensor to be located received by the anchor nodes is treated as a problem of sparse signal recovery and reconstruction. Leveraging the sparsity constraint property of sparse signals, a basis-tracking denoising algorithm is used to reconstruct the signals received by the sensor, ultimately completing the signal denoising process.

[0047] One embodiment of the present invention discloses an underwater sensor localization method based on basis tracking noise reduction, the method comprising the following steps:

[0048] S1, receiving the sensor node signal to be located in the anchor node; the sensor node signal has sparse properties in the frequency domain;

[0049] S2, the nodal signals of the sensor are processed by a basis pursuit denoising algorithm to obtain noise-free signals; the basis pursuit denoising algorithm is solved by the least squares method with L1 norm penalty term.

[0050] S3, input the noiseless signal into the underwater sensor positioning neural network model, and output the position of the sensor node signal through the underwater sensor positioning neural network model;

[0051] S4, the position where the output sensor receives the electrical signal.

[0052] Specifically, the specific process of S1 includes

[0053] The present invention first selects the signals transmitted by the sensor nodes to be located in the underwater sensor node dataset and received by the anchor nodes, so as to facilitate the positioning of the sensors based on the anchor nodes, which are nodes whose specific locations are known.

[0054] The raw signal received by the anchor node is modeled as follows:

[0055] y(n)=s(n)+w(n) (1)

[0056] Where y(n) is the original signal received by the anchor node, w(n) is the noise signal in the underwater acoustic channel, and s(n) is the noise-free signal.

[0057] The noiseless signal s(n) has a sparse representation in the frequency domain, which can be represented and modeled as:

[0058] s=Ax (2)

[0059] Therefore, the noisy signal can be represented as:

[0060] y = Ax + w (3)

[0061] Where y is a vector of length N, x is a vector of length N, where only a few positions in x are non-zero, and the rest are zero; x is the vector of the sparse signal in the frequency domain, meaning that x contains only a few frequency components, and only these frequencies have values ​​in the frequency domain; A is an N×N inverse Fourier transform matrix.

[0062]

[0063] Where j represents the description, and p and q represent the row and column numbers of the element in the matrix.

[0064] Specifically, the process of S2 is as follows:

[0065] S201, the signal is transmitted from the sensor to be located to the anchor node for reception. The entire process of propagation in the underwater acoustic channel is considered to have large noise interference. Since the signal has sparse properties in the frequency domain, the basis pursuit denoising method is used to denoise the original signal received by the anchor node. Therefore, this denoising problem is a sparse denoising problem, which can be solved by the basis pursuit denoising algorithm (BPD algorithm).

[0066] The problem of recovering the noiseless signal s(n) from the noisy signal y(n) received from the underwater anchor node is transformed into a least squares problem with L1 norm penalty terms:

[0067]

[0068] By splitting the variables, the optimization problem can be written as:

[0069]

[0070] Where λ is a coefficient, the first term in the formula is to minimize the error between the original signal and the recovered signal, the second term is to constrain the sparsity of x, that is, x should contain only a few frequency components, and u is an auxiliary variable used to represent the L1 norm of x.

[0071] Using the ADMM algorithm, the optimization in the above formula is performed alternately between x and u, and the algorithm will still converge to the global minimum.

[0072] By iterating over the following equation (7),

[0073]

[0074] Where μ is a regularization parameter used to control sparsity, which helps in feature selection; d is a Lagrange multiplier used to introduce a penalty for the constraint problem ux = 0.

[0075] When the error is less than a set threshold or when the number of iterations reaches a certain number, u is finally solved, and the noiseless signal s(n) = Au can be obtained for subsequent steps.

[0076] S202: Verify the denoising effect of the BPD algorithm on the signal received by the underwater anchor node. Analysis is performed from both the time and frequency domains, comparing the signal without BPD denoising with the signal denoised by BPD.

[0077] In the time domain, observe whether the signal denoised by the BPD algorithm has fewer glitches compared to the signal without BPD denoising. In the frequency domain, observe whether the values ​​of the signal denoised by the BPD algorithm become 0 or decrease at certain frequency points compared to the signal without BPD denoising. This verifies the denoising effect of the BPD algorithm in underwater sensor positioning scenarios. If the requirements are not met, modify the parameters and number of iterations in the optimization problem and repeat step 201.

[0078] Specifically, the process of S3 is as follows:

[0079] S301, after obtaining the noise-free signal, the underwater sensor localization problem is solved as a deep learning classification problem. The noise-free signal is subjected to a discrete Fourier transform to obtain the frequency domain sound pressure data q(f)=[q1(f),…,q L (f)] Tf is the selected frequency point, L is the number of anchor nodes receiving the signal, and the frequency domain sound pressure data is divided by its norm to normalize the data.

[0080]

[0081] We obtain an L×L sampling covariance matrix:

[0082]

[0083] The sampling covariance matrix reflects the intensity of all noiseless signals received by the anchor nodes at the selected frequency *f*, and also reflects the phase characteristics of the noiseless signals received by each anchor node, thus reflecting the spatial distribution characteristics of the noiseless signals. Since the obtained sampling covariance matrix is ​​symmetric along its diagonal, the real and imaginary parts of the upper triangular matrix and the elements on the diagonal are taken and concatenated into a column vector. Each column vector represents a noiseless signal, resulting in an L(L+1) dimensional column vector, thus obtaining the data characteristics corresponding to the noiseless signals. The real and imaginary parts, combined, reflect the signal power and phase characteristics received by the anchor nodes, as well as the phase relationship between the positions of the sensors.

[0084] The range of the sensor location to be located is divided into K grids, where K is determined based on the minimum error required for positioning. The K grids are K parallel long strip grids. A horizontal position of a sound source corresponds to a marker vector i. n Each vector has only one element that is 1, meaning there are a total of K marker vectors corresponding to the grids of the K sensor locations. This marker vector i n Corresponding to the data features of a noiseless signal above, a data feature column vector can correspond to a grid, but a grid may correspond to multiple column vectors, that is, there may be multiple sets of received data features from the same grid, which means that there may be multiple sensors emitting corresponding signals in a grid.

[0085]

[0086] Where z = 1, ..., N are the indices of the input samples, and r k (k = 1, ..., K) represents the pre-labeled sensor locations, and r is the located position. Therefore, the label vector i for each input sample is... z Each corresponds to a position r k This is how we obtain the labels for the data.

[0087] S302, after inputting the data features into the neural network, the output is a K-dimensional column vector, where each column vector contains only one value of 1 and the rest are 0. If the k-th data point in this vector is 1, it corresponds to the label vector i. zkIt belongs to the k-th class, that is, the k-th grid i zk Then, corresponding to r k Above, r k This refers to the specific location. The value 'r' primarily comes into play when dividing the system into K grids. Each grid corresponds to a region containing multiple sensors at different locations. 'r' represents the position of each sensor, but the final localization can only pinpoint the location within that grid, thus determining the final sensor position. For example, if the final location is i... zk This corresponding grid, that is, the specific location obtained by the final positioning, is r. k r k It's up to you to decide, but generally you take the center point of this grid area.

[0088] In some embodiments of the present invention, the neural network is trained, see [link to relevant documentation]. Figure 9 The specific training process is as follows:

[0089] The original data is mapped to features and labels, and randomly divided into training and testing sets. The training set is input into a neural network for training. The neural network obtains the underwater sensor node position corresponding to each feature data. The calculated position is compared with the actual underwater sensor node position corresponding to that feature data to obtain a loss function. When the loss function meets the set requirements or the training reaches a certain number of iterations, the neural network training ends, and the obtained network model parameters are saved. The original dataset includes the anchor node position, the actual position of the node to be located, and the signal received by the anchor node.

[0090] The underwater sensor positioning neural network model used in this invention is a three-layer feedforward neural network model. Figure 1 This is a diagram of the feedforward neural network structure used in this invention. The network input size is N×L(L+1), meaning there are N samples, and the feature dimension of each sample is L(L+1). The number of neurons in layers 1, 2, and 3 varies depending on the dataset. This can be determined based on the specific circumstances. The neural network localization test set is a randomly generated test set based on the original dataset used in this invention to verify its localization performance.

[0091] Using the MSE function as the loss function for the FNN, the network directly outputs the target's coordinates. The Adam optimizer is used, with an initial learning rate of 0.01. L2 loss is used for weight decay, and its value is set to 5 × 10⁻⁶. -4 Furthermore, to mitigate the risk of neuron death, the ReLU function was used for the activation of each neuron in each layer, while the Softmax function was selected for the output layer.

[0092] Performance verification phase. The test set data is input into the network model saved in step 4 to obtain the category corresponding to the predicted location of the underwater sensor. Then, the predicted location of the underwater sensor is obtained by reverse calculation according to the classification criteria and compared with the actual location.

[0093] To facilitate the analysis of the positioning accuracy of underwater sensors, this invention posits that the sensor's position prediction is accurate when the absolute or relative error between the predicted and actual positions is less than a certain value *l*. The determination of the value of *l* depends on the specific application scenario and is made according to the specific circumstances. Steps 3, 4, and 5 above were performed on signals without BPD denoising and signals denoised using BPD, respectively. The prediction accuracy and prediction error were then obtained, and the two results were compared and analyzed to verify the performance improvement of the BPD algorithm for underwater sensor positioning. The results show that the underwater sensor positioning effect obtained by using the described basis tracking denoising method is better.

[0094] Example 1

[0095] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0096] The dataset used in the experiment was the SWell96Ex experiment, a 75-minute underwater acoustic experiment conducted by the Marine Physical Laboratory and other institutions in the waters near San Diego. The test vessel towed a sensor from one side of the VLA array to the other at a constant speed. Throughout the experiment, the sensor continuously emitted signals at several frequencies, all within the range of 0–400 Hz. A total of four sensor arrays with known locations were deployed to receive the signals; these were the anchor nodes: VLA, TLA, HLANorth, and HLASouth. All four arrays had a sampling frequency of 1500 Hz, satisfying the Nyquist sampling theorem. Figure 2 This is a schematic diagram of the experiment. The dataset also includes signals emitted by the sound sources received by these four sensor arrays. This example uses data received by the vertical array VLA, which contains a total of 21 sensor elements, i.e., L=21 in step 3.

[0097] We selected any 1 second of data from the experiment to perform a performance analysis of the BPD algorithm for denoising. Figure 3 and Figure 4 This is a time-domain plot. By comparison, we can see the denoising effect of the BPD algorithm in the time domain of the signal. We can see that the signal is smoother and the noise is reduced. Figure 5 and Figure 6This is a frequency domain plot, showing the denoising effect of the BPD algorithm in the signal frequency domain. It can be seen that most of the noise has been eliminated, with the values ​​at the frequency points becoming 0, leaving the useful signal frequencies in the denoised spectrum. It can be seen that the BPD algorithm has good denoising performance for signals received by underwater anchor nodes.

[0098] The underwater sensor positioning performance was analyzed using 3000 seconds of data from the 9th to the 59th minute of the entire process. For each second of data, steps 2 and 3 were performed, selecting frequencies of 109Hz and 198Hz, resulting in a 462-dimensional neural network input vector for step 4. Since the ship's route was fixed in this experiment, the ship's position, i.e., the position of the sensor to be located, could be determined based on the distance from the ship to the VLA sensor array. Therefore, the distance from the ship to the VLA sensor array was divided into 300 categories, resulting in 300 output layer neurons. The position at each time point was mapped to a category, thus obtaining a total of 3000 data sets.

[0099] The aforementioned 3000 sets of data were randomly divided into a training set and a test set, with 90% allocated to the training set and the remaining 10% to the test set. The training set was input into the feedforward neural network for training, and the model parameters were saved after training. The localization performance was then validated using the test set.

[0100] To compare performance, the above steps were performed on both signals without BPD denoising and signals denoised using the BPD algorithm to verify the effectiveness of the basis tracking denoising method in improving the underwater sensor positioning performance. For ease of analysis of positioning accuracy, this invention considers a predicted distance from the anchor node to be between 90% and 110% of the actual distance to the anchor node as an accurate prediction, indicating successful underwater sensor positioning. Distances outside this range are considered prediction errors, i.e., positioning failures. Furthermore, the absolute distance error is calculated by comparing the predicted distance from the anchor node at the moment of positioning failure with the actual distance at that moment. The sum of the absolute errors from all positioning failures is then divided by the number of failures to obtain the average absolute error. This average absolute error is also used as a reference for evaluating the improvement in underwater sensor positioning performance achieved by the basis tracking denoising method.

[0101] Figure 7 The prediction result is the signal without BPD denoising. If the signal is within the shaded area, the prediction is considered accurate; if it is outside the shaded area, the prediction is considered incorrect. Figure 7 The prediction accuracy rate was 70%, and the mean absolute error for the time of prediction error was 3.47 km; Figure 8 The prediction result is the signal after BPD denoising. Figure 8The prediction accuracy rate was 77%, and the average absolute error of the time of prediction error was 1.73 km.

[0102] The results show that the basis pursuit denoising algorithm significantly improves the underwater sensor positioning effect. It reduces the error caused by noise by denoising the signal received by the anchor node. In the case of prediction failure, the absolute error after the BPD algorithm is smaller than the absolute error without the BPD algorithm. This result verifies that the underwater sensor positioning effect obtained by using the basis pursuit denoising method is better.

[0103] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for underwater sensor localization based on base tracking noise reduction, characterized in that, Includes the following steps: S1, Receive node signals from the sensor to be located at the anchor node. The node signals consist of noise-free signals and noise signals. The noise-free signals are emitted by the underwater sensor, and the noise signals are generated in the underwater acoustic channel. S2 solves the sparse denoising problem by using the basis pursuit denoising algorithm to obtain a noiseless signal from the node signal; The formula for the denoising problem is: (6) Where λ is the coefficient, and A is the N×N inverse Fourier transform matrix. y It is a vector of length N. x It is a vector of length N. u As an auxiliary variable, Here, is the regularization parameter, and d is the Lagrange multiplier; Using the ADMM algorithm, the auxiliary variables are obtained by iterating through equation (7). u ; (7) The obtained auxiliary variables u , bring into To obtain a noise-free signal; S3. Perform a discrete Fourier transform on the noiseless signal to obtain frequency domain sound pressure data. After normalizing the frequency domain sound pressure data, obtain the sampling covariance matrix. Based on the sampling covariance matrix, obtain the data features corresponding to the noiseless signal. Input the data features into the positioning neural network model to obtain the position of the underwater sensor.

2. The underwater sensor localization method based on basis tracking noise reduction according to claim 1, characterized in that, After S2, the following steps are also included: determining whether the obtained noiseless signal meets the requirements in both the time domain and the frequency domain. The time-domain determination method is to compare the noiseless signal and the node signal to determine whether the noiseless signal has fewer glitches compared to the node signal. The method for determining frequency is as follows: compare the noiseless signal and the node signal, and determine whether the noiseless signal has a frequency value that becomes 0 or 1 relative to the node signal.

3. The underwater sensor localization method based on basis tracking noise reduction according to claim 1, characterized in that, In S3, the formula for data normalization is: (8) in, For frequency domain sound pressure data, The selected frequency point is L, and the number of anchor nodes receiving the signal is L.

4. The underwater sensor localization method based on base tracking noise reduction according to claim 1, characterized in that, In S3, the real and imaginary parts of the upper triangular matrix and diagonal elements in the covariance matrix are concatenated into an L(L+1) dimensional vector to obtain the data features corresponding to the noiseless signal.

5. The underwater sensor localization method based on base tracking noise reduction according to claim 1, characterized in that, In S3, the neural network model outputs a K-dimensional column vector, and the position of the underwater sensor is obtained through the K-dimensional column vector.

6. The underwater sensor localization method based on basis tracking noise reduction according to claim 5, characterized in that, In S3, in a K-dimensional column vector, the k-th data is 1, and the corresponding label vector is... i zk , corresponding to obtain r k , which indicates the location of the underwater sensor.

7. The underwater sensor localization method based on basis tracking noise reduction according to claim 1, characterized in that, In S3, the neural network model is trained using a loss function; the loss function is obtained by comparing the underwater sensor node positions output by the neural network with the actual underwater sensor node positions; the loss function is the MSE function.

8. An underwater sensor positioning system based on basis tracking noise reduction for implementing the underwater sensor positioning method of claim 1, characterized in that, include: The acquisition unit is used to receive node signals from the sensor to be positioned at the anchor node. The node signals consist of noise-free signals and noise signals. The noiseless signal is emitted by the underwater sensor, while the noise signal is generated in the underwater acoustic channel. The denoising unit is used to solve the sparse denoising problem by using the basis pursuit denoising algorithm to obtain the noiseless signal from the node signal; The location unit is used to perform a discrete Fourier transform on the noiseless signal to obtain frequency domain sound pressure data. After normalizing the frequency domain sound pressure data, a sampling covariance matrix is ​​obtained. Based on the sampling covariance matrix, the data features corresponding to the noiseless signal are obtained. The data features are then input into the positioning neural network model to obtain the position of the underwater sensor.

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