A method for adaptive filtering of non-stationary noise of radar tide level data

Abstract

The application provides a radar tide level data non-stationary noise adaptive filtering method, and belongs to the technical field of radar tide level.The original echo signal of the radar tide level is subjected to segmented time-frequency domain joint analysis to extract a time-varying noise characteristic vector, a spectrum clustering algorithm is used to identify and remove abnormal noise nodes, and then cubic spline interpolation repair is carried out, the pretreated signal is input into a frequency domain adaptive denoising model, the model uses a frequency domain convolution acceleration mechanism and a parallel branch to extract multi-frequency noise characteristics, adaptive filter coefficients are calculated according to noise estimation results, the filter update step is dynamically adjusted according to the noise energy change rate, and the residual signal energy is monitored and iteratively optimized until the accuracy requirement is met, so that the technical problem that a fixed parameter filter cannot accurately track the instantaneous change of noise due to the time-varying of non-stationary noise characteristics is solved.

Description

Technical Field

[0001] This invention belongs to the field of radar tide level technology, and more specifically, relates to a method for adaptive filtering of non-stationary noise in radar tide level data. Background Technology

[0002] Radar tide level measurement systems acquire tide level data by emitting electromagnetic waves and receiving sea surface echo signals. Traditional tide level data denoising methods mainly employ frequency domain filtering using fixed-window Fourier transforms or wavelet transforms, separating signals and noise by setting fixed frequency thresholds. However, in actual marine environments, radar tide level data is interfered with by various noise sources such as wave clutter, atmospheric turbulence, and equipment nonlinear distortion. The frequency components and energy distribution of these noises exhibit significant non-stationary characteristics with changes in sea state, with their instantaneous frequencies and amplitudes changing drastically within a short period. Traditional fixed-parameter filters maintain constant frequency response and filter coefficients during processing, failing to dynamically adjust filtering strategies based on the instantaneous characteristics of the noise. When noise energy suddenly increases or frequency drifts, fixed-parameter filters may either over-suppress, leading to distortion of the effective tide level signal, or under-filter, resulting in residual noise affecting measurement accuracy. In other words, existing technologies suffer from the technical problem that the time-varying non-stationary noise characteristics prevent fixed-parameter filters from accurately tracking instantaneous noise changes. Summary of the Invention

[0003] In view of this, the present invention provides a method for adaptive filtering of non-stationary noise in radar tide data, which can solve the technical problem in the prior art where the time-varying characteristics of non-stationary noise cause fixed parameter filters to be unable to accurately track the instantaneous changes in noise.

[0004] This invention is implemented as follows: It provides a method for adaptive filtering of non-stationary noise in radar tide data. The method involves acquiring raw radar tide echo signals and processing them in segments. For each time window, a joint time-frequency domain analysis is performed to extract time-varying noise feature vectors. These feature vectors are mapped to graph-structured nodes, and a spectral clustering algorithm is used to cluster and identify abnormal noise nodes. Abnormal data points are removed, and cubic spline interpolation is used to repair them, resulting in a preprocessed radar tide signal. This preprocessed signal is then input into a frequency-domain adaptive denoising model. A frequency-domain convolution acceleration mechanism is used to extract noise pattern features and output noise estimation results. Adaptive filter coefficients are calculated based on the noise estimation results. The update step size of the adaptive filter coefficients is dynamically adjusted according to the noise energy change rate. The preprocessed radar tide signal is then filtered to obtain denoised tide data. The residual signal energy between the denoised tide data and the preprocessed radar tide signal is calculated. When the residual signal energy is greater than a residual threshold, the update step size is increased, and filtering is repeated. When the residual signal energy is less than the residual threshold, the denoised tide data is output.

[0005] Specifically, the time-frequency domain joint analysis step involves performing a short-time Fourier transform on the original radar tide echo signal within the time window to obtain a time-frequency matrix, calculating instantaneous high-energy frequency points along the time axis, calculating the instantaneous frequency drift rate along the frequency axis, and combining the frequency value, amplitude value, and instantaneous frequency drift rate of the instantaneous high-energy frequency points to form a time-varying noise feature vector.

[0006] The instantaneous high-energy frequency point refers to a frequency point where the instantaneous amplitude value is greater than 1.5 times the average amplitude value, and the instantaneous frequency drift rate refers to the rate of change of the frequency centroid over time.

[0007] Specifically, the step of mapping to graph structure nodes involves taking the time-varying noise feature vector corresponding to each time window as a graph structure node, calculating the Euclidean distance between any two graph structure nodes, using the reciprocal of the Euclidean distance as the edge weight, and setting the edge weight to zero when the Euclidean distance is greater than the distance threshold, thereby constructing an undirected weighted graph.

[0008] Specifically, the steps of the spectral clustering partitioning algorithm are as follows: calculate the Laplacian matrix based on the edge weight matrix of the undirected weighted graph, extract eigenvectors by eigenvalue decomposition of the Laplacian matrix, use the eigenvectors as the embedded representation of the graph structure nodes, and use the K-means clustering algorithm to partition them into normal noise clusters and abnormal noise clusters. Graph structure nodes whose distance is greater than the mean distance within the cluster plus twice the standard deviation are marked as abnormal noise nodes.

[0009] The Laplacian matrix is ​​calculated by subtracting the edge weight matrix from the degree matrix and then performing symmetric normalization.

[0010] Specifically, the steps of the cubic spline interpolation method are as follows: select three normal data points before and after the abnormal data point as interpolation reference points, construct a cubic spline function, determine the coefficients of the cubic spline function by solving a system of tridiagonal matrix equations, and substitute the time of the abnormal data point into the cubic spline function to calculate the interpolation result as the repaired data value.

[0011] The frequency domain adaptive denoising model includes a fast Fourier transform layer, a frequency domain convolutional feature extraction layer, a frequency domain pointwise multiplication layer, a frequency domain fusion layer, a noise estimation branch, a signal estimation branch, and an inverse fast Fourier transform layer. The frequency domain convolutional feature extraction layer contains three parallel frequency domain convolutional branches that extract low-frequency component features, mid-frequency component features, and high-frequency component features, respectively.

[0012] The fusion weights of the frequency domain fusion layer are dynamically calculated through an attention mechanism. The attention mechanism maps the outputs of the three frequency domain convolution branches to query vectors, key vectors, and value vectors, respectively. The dot product of the query vector and the key vector is calculated and normalized to obtain the attention weights. The attention weights are multiplied by the value vectors and summed to obtain the weighted fusion features.

[0013] The implementation principle of the frequency domain convolution acceleration mechanism is that the convolution kernel parameters are defined and optimized directly in the frequency domain. The time domain signal is converted to the frequency domain through fast Fourier transform, complex point-by-point multiplication is performed in the frequency domain, and the signal is converted back to the time domain through inverse fast Fourier transform. For long sequence signals, the overlapping preservation method is used for segmented processing.

[0014] The adaptive filter coefficients are calculated using the Wiener filtering principle. The power spectral density of the noise is calculated based on the noise estimation results. The power spectral density of the noise is divided by the power spectral density of the preprocessed radar tide signal to obtain the power ratio of the noise to the signal. The optimal filter frequency response is calculated based on the power ratio of the noise to the signal. The time-domain adaptive filter coefficients are obtained by performing an inverse Fourier transform on the optimal filter frequency response.

[0015] The noise energy change rate is calculated by dividing the difference between the noise energy of the current window and the noise energy of the previous window by the noise energy of the previous window. When the absolute value of the noise energy change rate is greater than 0.3, the update step size is set to 0.05; when the absolute value of the noise energy change rate is less than 0.1, the update step size is set to 0.01; and when the noise energy change rate is between 0.1 and 0.3, the update step size is set to 0.03.

[0016] The residual threshold is set by using the 95th percentile of the residual signal energy on the statistical validation set as the initial value, and dynamically adjusting the residual threshold based on the statistical characteristics of the residual signal energy over 100 consecutive time windows.

[0017] The time window is set to a length of 2 seconds, with an overlap of 1 second between adjacent time windows. When sea conditions are severe, the time window length is shortened to 1 second, and when sea conditions are calm, the time window length is extended to 4 seconds.

[0018] The frequency domain adaptive denoising model is trained by using a weighted sum of time domain mean square error loss and frequency domain spectral distance loss as the loss function. The adaptive moment estimation optimization algorithm is used to update the model parameters. 32 training samples are randomly selected in the training batch. Training is stopped and the model parameters are saved when the performance of the validation set no longer improves after 20 consecutive training cycles.

[0019] The distance threshold is determined by calculating the Euclidean distance between the time-varying noise feature vectors corresponding to all adjacent time windows in the training dataset, and multiplying the median of the Euclidean distance by 1.5 to obtain the distance threshold.

[0020] This invention extracts instantaneous frequency and amplitude features of noise through joint time-frequency domain analysis to construct a time-varying noise feature vector. A spectral clustering algorithm is then used to identify anomalous noise patterns for preprocessing. Next, a frequency-domain adaptive denoising model is employed, using parallel frequency-domain convolutional branches to capture low-frequency, mid-frequency, and high-frequency noise components. Adaptive filter coefficients are dynamically calculated based on the noise estimation results, and the filter parameter update step size is adjusted in real-time according to the noise energy change rate, enabling the filter to quickly respond to instantaneous noise changes. This mechanism solves the problem that fixed-parameter filters cannot track non-stationary noise characteristics. In the case of noise frequency drift and energy abrupt changes, the filter continuously monitors the residual signal energy and iteratively optimizes the filter coefficients, achieving accurate suppression of time-varying noise without losing effective information from the tide level signal. In summary, this invention solves the technical problem mentioned in the background art where the time-varying non-stationary noise characteristics prevent fixed-parameter filters from accurately tracking instantaneous noise changes. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 This is the time-domain waveform of the original radar tide level signal.

[0023] Figure 3 This is a spatial clustering distribution diagram of the node embedding in the graph structure.

[0024] Figure 4 This is a diagram illustrating the iterative convergence process of the residual signal energy.

[0025] Figure 5 A curve showing the comparison of tide level data before and after noise reduction. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0027] like Figure 1 The diagram shown is a flowchart of an adaptive filtering method for non-stationary noise in radar tide data provided by the present invention. This method includes the following steps:

[0028] S01. Acquire the original radar tide level echo signal, segment the original radar tide level echo signal, divide the continuous time series into multiple time windows, and record the start and end times of each time window.

[0029] S02. Perform joint time-frequency domain analysis on the original radar tide level echo signal within each time window, extract instantaneous frequency feature parameters and instantaneous amplitude feature parameters, and construct a time-varying noise feature vector;

[0030] S03. Map the time-varying noise feature vector to graph structure nodes, calculate the feature distance between adjacent graph structure nodes as edge weights, use the spectral clustering partitioning algorithm to cluster and group the graph structure nodes, identify abnormal noise nodes and mark them as abnormal data points.

[0031] S04. The marked abnormal data points are removed, and the data at the removed locations is repaired using cubic spline interpolation to obtain the preprocessed radar tide signal.

[0032] S05. Input the preprocessed radar tide signal into the frequency domain adaptive denoising model. The frequency domain adaptive denoising model extracts noise pattern features through a frequency domain convolution acceleration mechanism and outputs noise estimation results and signal spectrum components.

[0033] S06. Calculate the adaptive filter coefficients based on the noise estimation results. The update step size of the adaptive filter coefficients is dynamically adjusted according to the noise energy change rate. Filter the preprocessed radar tide signal to obtain denoised tide data.

[0034] S07. Calculate the residual signal energy between the denoised tide level data and the preprocessed radar tide level signal. When the residual signal energy is greater than the set residual threshold, increase the update step size of the adaptive filter coefficients by 20% and repeat step S06. When the residual signal energy is less than the residual threshold, output the denoised tide level data as the final result.

[0035] The specific steps of performing joint time-frequency domain analysis on the original radar tide echo signal within each time window include: performing a short-time Fourier transform on the original radar tide echo signal within the time window to obtain a time-frequency spectrum matrix; calculating the instantaneous amplitude value of each frequency point along the time axis of the time-frequency spectrum matrix, and recording the frequency points whose instantaneous amplitude value is greater than 1.5 times the average amplitude value as instantaneous high-energy frequency points; calculating the frequency centroid of each moment along the frequency axis of the time-frequency spectrum matrix, and recording the rate of change of the frequency centroid with time as the instantaneous frequency drift rate; and combining the frequency value of the instantaneous high-energy frequency point, the amplitude value of the instantaneous high-energy frequency point, and the instantaneous frequency drift rate to form a time-varying noise feature vector.

[0036] The step of mapping the time-varying noise feature vector to graph structure nodes specifically includes: using the time-varying noise feature vector corresponding to each time window as a graph structure node; calculating the Euclidean distance between any two graph structure nodes, and using the reciprocal of the Euclidean distance as the edge weight connecting the two graph structure nodes; when the Euclidean distance between two graph structure nodes is greater than a distance threshold, setting the corresponding edge weight to zero, indicating that the two graph structure nodes are not connected; and constructing an undirected weighted graph containing all graph structure nodes and edge weights.

[0037] The specific steps of clustering graph structure nodes using the spectral clustering partitioning algorithm include: calculating the Laplacian matrix based on the edge weight matrix of the undirected weighted graph; performing eigenvalue decomposition on the Laplacian matrix to extract the eigenvectors corresponding to the first few smallest eigenvalues; using the eigenvectors as the embedding representation of the graph structure nodes, and using the K-means clustering algorithm in the embedding space to divide the graph structure nodes into normal noise clusters and abnormal noise clusters; calculating the distance between each graph structure node and the center of its cluster, and marking graph structure nodes whose distance is greater than the mean distance within the cluster plus twice the standard deviation as abnormal noise nodes.

[0038] The structure of the frequency-domain adaptive denoising model is as follows: the input layer receives the preprocessed radar tide level signal time-domain sequence; the fast Fourier transform layer performs a frequency domain transformation on the preprocessed radar tide level signal time-domain sequence to obtain a frequency domain complex representation; the frequency domain convolutional feature extraction layer contains three parallel frequency domain convolutional branches, and the convolution kernel parameters of each frequency domain convolutional branch are defined in the frequency domain, respectively used to extract low-frequency component features, mid-frequency component features, and high-frequency component features; the frequency domain pointwise multiplication layer performs pointwise complex multiplication operations on the frequency domain representation of the convolution kernel parameters and the frequency domain complex representation; the frequency domain fusion layer performs weighted fusion of the outputs of the three frequency domain convolutional branches, and the fusion weights are dynamically calculated through an attention mechanism; the noise estimation branch and the signal estimation branch extract the noise spectrum and signal spectrum from the fused features, respectively; the inverse fast Fourier transform layer transforms the frequency domain results back to the time domain and outputs the noise estimation result and the denoised signal estimation result.

[0039] The steps for establishing the training dataset for the frequency domain adaptive denoising model specifically include: collecting radar tide level measurement data under different sea state conditions, including calm sea surface data, moderate sea state data, and severe sea state data; manually labeling the radar tide level measurement data, marking the actual tide level change curves and noise interference areas; dividing the labeled radar tide level measurement data into training and validation sets at an 8:2 ratio; performing data augmentation processing on the training set data, including adding Gaussian white noise of different intensities, adding impulse noise, performing time axis stretching transformation, and time axis compression transformation; extracting frequency domain features for each training sample, calculating the power spectral density distribution and frequency distribution feature parameters, and using them as input features for the training dataset; and using the manually labeled actual tide level change curves as label data for the training dataset.

[0040] The specific steps for training the frequency domain adaptive denoising model include: initializing the convolution kernel parameters of the frequency domain convolutional feature extraction layer to a random Gaussian distribution; setting the loss function as a weighted sum of the time domain mean square error loss and the frequency domain spectral distance loss, wherein the frequency domain spectral distance loss calculates the difference between the predicted signal spectrum and the true signal spectrum; updating the frequency domain adaptive denoising model parameters using an adaptive moment estimation optimization algorithm, setting the initial learning rate to 0.001, and decaying the learning rate to 0.9 times the original value every 10 training cycles; randomly selecting 32 training samples in each training batch, inputting the training samples into the frequency domain adaptive denoising model for forward propagation to calculate the loss value, calculating the gradient through the backpropagation algorithm and updating the frequency domain adaptive denoising model parameters; evaluating the performance of the frequency domain adaptive denoising model on the validation set every 5 training cycles, recording the mean square error and signal-to-noise ratio improvement on the validation set; stopping training and saving the frequency domain adaptive denoising model parameters when the validation set performance no longer improves after 20 consecutive training cycles.

[0041] The implementation principle of the frequency domain convolution acceleration mechanism is as follows: Traditional time-domain convolution operations require multiplication and accumulation operations between the signal at each time step and each position of the convolution kernel parameters, and the computational complexity increases linearly with the length of the convolution kernel parameters. According to the convolution theorem, time-domain convolution operations are equivalent to point-by-point multiplication operations in the frequency domain. By using Fast Fourier Transform (FFT) to simultaneously convert the time-domain signal and the convolution kernel parameters to the frequency domain, complex point-by-point multiplication is performed in the frequency domain, and then the signal is converted back to the time domain by Inverse Fast Fourier Transform (IFFT), significantly reducing the computational complexity of the entire process. In the frequency-domain adaptive denoising model, the convolution kernel parameters are directly defined and optimized in the frequency domain, eliminating the step of frequency domain conversion of the convolution kernel parameters and further improving computational efficiency. For long sequence signals, an overlap preservation method is used to segment the signal for processing. Each segment retains an overlapping region at the boundary to avoid boundary distortion caused by cyclic convolution and ensure the continuity and accuracy of the filtering results.

[0042] The technical effects of the frequency domain convolution acceleration mechanism are reflected in the following aspects: the improved computational efficiency reduces the computation time of the frequency domain adaptive denoising model to less than one-tenth of the traditional time domain convolution method when processing long-term radar tide data, meeting the requirements of real-time processing; the parameterized design in the frequency domain makes the features learned by the frequency domain adaptive denoising model more closely match the frequency characteristics of the signal, and has a stronger ability to capture time-varying frequency components of non-stationary noise, solving the problem that the traditional fixed window method cannot track instantaneous changes in noise; the three parallel frequency domain convolution branches target low-frequency tide signals, mid-frequency sea wave interference, and high-frequency equipment noise, respectively. Feature extraction is performed, and the weights of each frequency domain convolution branch are dynamically adjusted through an attention mechanism. Even in severe sea conditions where sea clutter energy far exceeds that of the useful signal, the frequency domain adaptive denoising model still maintains its sensitivity to tidal signals, avoiding the loss of effective information caused by simple frequency domain filtering. Frequency domain processing is naturally sensitive to the periodicity and frequency structure of signals. When the nonlinear devices of the radar system generate harmonic components and intermodulation products, the frequency domain adaptive denoising model identifies the extended frequency components through frequency domain feature analysis, accurately separates nonlinear distortion noise in the noise estimation branch, and achieves effective suppression of broadband non-stationary noise by dynamically adjusting the subsequent adaptive filter coefficients.

[0043] The residual threshold is set as follows: during the training phase, the residual signal energy distribution between the denoised tide level data and the manually labeled real tide level change curves on the validation set is statistically analyzed, and the 95th percentile of the residual signal energy is calculated as the initial value of the residual threshold. In practical applications, the residual threshold is dynamically adjusted based on the statistical characteristics of the residual signal energy over 100 consecutive time windows. When the mean of the residual signal energy shows a significant upward trend, the residual threshold is increased by 15% to prevent over-filtering from causing distortion of the tide level signal. When the mean of the residual signal energy shows a significant downward trend, the residual threshold is decreased by 10% to improve the noise suppression effect.

[0044] The distance threshold is determined as follows: statistical analysis is performed on the time-varying noise feature vectors in the training dataset, the Euclidean distance between the time-varying noise feature vectors corresponding to all adjacent time windows is calculated, and the median of the Euclidean distance is multiplied by 1.5 to obtain the distance threshold. The distance threshold is used to control the sparsity of the undirected weighted graph. A larger distance threshold makes the undirected weighted graph sparser and the clustering results more discrete, which is suitable for scenarios with drastic noise changes. A smaller distance threshold makes the undirected weighted graph denser and the clustering results more compact, which is suitable for scenarios with relatively stable noise.

[0045] The adaptive filter coefficients are calculated as follows: The power spectral density of the noise is calculated based on the noise estimation result output by the frequency domain adaptive denoising model; the power spectral density of the noise is divided by the power spectral density of the preprocessed radar tide signal to obtain the power ratio of the noise to the signal; the optimal filter frequency response is calculated based on the power ratio of the noise to the signal using the Wiener filtering principle; the optimal filter frequency response is subjected to an inverse Fourier transform to obtain the time-domain adaptive filter coefficients; the length of the adaptive filter coefficients is set to 64, and truncation using a window function ensures the causality and stability of the filter.

[0046] The method for calculating the noise energy change rate is as follows: record the noise estimation results energy values ​​for three consecutive time windows, denoted as the noise energy of the previous window, the noise energy of the current window, and the noise energy of the next window, respectively; calculate the difference between the noise energy of the current window and the noise energy of the previous window, divide it by the noise energy of the previous window, and obtain the noise energy change rate; when the absolute value of the noise energy change rate is greater than 0.3, it is determined that the noise is in a rapidly changing state, and the update step size of the adaptive filter coefficients is set to 0.05; when the absolute value of the noise energy change rate is less than 0.1, it is determined that the noise is in a relatively stable state, and the update step size of the adaptive filter coefficients is set to 0.01; when the noise energy change rate is between 0.1 and 0.3, the update step size of the adaptive filter coefficients is set to 0.03.

[0047] The principle for setting the length of the time window is as follows: the sampling frequency of radar tide data is 10Hz, the time window length is set to 2 seconds, containing 20 sampling points; the overlap length between adjacent time windows is 1 second, containing 10 sampling points, and the overlap length ensures continuous tracking of noise characteristic changes; when sea conditions are severe, the time window length is shortened to 1 second according to the variance change of the preprocessed radar tide signal to improve the response speed to rapidly changing noise; when sea conditions are calm, the time window length is extended to 4 seconds to improve the accuracy and stability of noise estimation.

[0048] The Laplacian matrix is ​​calculated as follows: a degree matrix is ​​constructed, which is a diagonal matrix, and the diagonal elements are the sum of the weights of all edges connecting each graph node; the Laplacian matrix is ​​equal to the degree matrix minus the edge weight matrix; the Laplacian matrix is ​​normalized using a symmetric normalization method, dividing each element of the Laplacian matrix by the product of the square roots of the degree values ​​of the corresponding row and column; the normalized Laplacian matrix has better numerical stability and the eigenvalue decomposition results are more reliable.

[0049] The method for determining the number of clusters in the K-means clustering algorithm is as follows: the preset number of clusters is 2, and the graph structure nodes are divided into normal noise clusters and abnormal noise clusters; when the number of graph structure nodes in the abnormal noise clusters exceeds 30% of the total number of graph structure nodes, the number of clusters is increased to 3, and the abnormal noise clusters are further subdivided into strong abnormal noise clusters and weak abnormal noise clusters. Abnormal data points corresponding to strong abnormal noise clusters are removed, and abnormal data points corresponding to weak abnormal noise clusters are repaired by interpolation. The dynamic adjustment mechanism of the number of clusters improves the accuracy of abnormal data identification and avoids the erroneous removal of effective signal mutation points.

[0050] The implementation steps of the cubic spline interpolation method are as follows: For each removed outlier data point, select three normal data points before and after the outlier data point as interpolation reference points; construct a cubic spline function, the function value of the cubic spline function at each interpolation reference point is equal to the data value at the interpolation reference point, and the first and second derivatives at the interpolation reference points are continuous; determine the coefficients of the cubic spline function by solving a system of tridiagonal matrix equations; substitute the time of the outlier data point into the cubic spline function, calculate the interpolation result as the repaired data value; the cubic spline interpolation method ensures a smooth connection between the repaired data value and the surrounding normal data points, avoiding the introduction of new noise from abrupt interpolation changes.

[0051] The attention mechanism is calculated as follows: the outputs of the three frequency domain convolutional branches of the frequency domain fusion layer are mapped to query vector, key vector, and value vector respectively through a fully connected layer; the dot product of the query vector and the key vector is calculated and normalized to obtain the attention weights; the attention weights are multiplied by the value vectors and summed to obtain the weighted fusion features; the attention mechanism enables the frequency domain adaptive denoising model to dynamically adjust the contribution ratios of low-frequency component features, mid-frequency component features, and high-frequency component features according to the frequency characteristics of the current signal, and adaptively optimize the feature extraction strategy under different sea conditions and noise conditions.

[0052] The time-varying noise feature vector is a multi-dimensional vector containing the frequency value of the instantaneous high-energy frequency point, the amplitude value of the instantaneous high-energy frequency point, and the instantaneous frequency drift rate, which is used to describe the instantaneous characteristic change law of non-stationary noise in the time-frequency domain.

[0053] The frequency domain complex number representation is the complex number form obtained after converting the time domain signal to the frequency domain through a fast Fourier transform. The real part of the frequency domain complex number representation corresponds to the cosine coefficient of the frequency component, and the imaginary part of the frequency domain complex number representation corresponds to the sine coefficient of the frequency component.

[0054] The fusion feature is a comprehensive feature representation obtained by weighting and summing the low-frequency component features, mid-frequency component features, and high-frequency component features extracted from the three frequency domain convolution branches through attention weights. The fusion feature simultaneously contains noise and signal information from different frequency bands.

[0055] The embedding representation is a vector representation obtained by mapping the eigenvectors of the graph structure nodes to a low-dimensional space through the Laplacian matrix. The embedding representation preserves the similarity relationship between the graph structure nodes, which is convenient for subsequent clustering operations.

[0056] Optionally, the present invention also provides a computer-based method for forming an adaptive filtering system for non-stationary noise of radar tide data, wherein the computer is provided with a readable storage medium storing program instructions, and the program instructions execute the above-described method when running in the computer.

[0057] The specific implementation methods of the above steps are described in detail below.

[0058] The specific implementation of step S01 is as follows: First, electromagnetic wave echo signals reflected from the sea surface are collected by a radar sensor. These echo signals contain tidal level change information and various types of interference noise. The sampling frequency is set to 10Hz to meet the frequency characteristics requirements of tidal level changes. Then, the collected continuous time series is segmented and processed. The entire observation period is divided into multiple time windows with a length of 2 seconds. Each time window contains 20 sampling points. A 1-second overlap area is set between adjacent time windows to ensure continuous tracking of noise characteristic changes. When sea conditions are severe, the window length is shortened to 1 second according to the signal variance change to improve the response speed to rapidly changing noise. When sea conditions are calm, the window length is extended to 4 seconds to improve the accuracy of noise estimation. At the same time, the start and end times of each time window are recorded as the time reference for subsequent processing.

[0059] The specific implementation of step S02 is as follows: a short-time Fourier transform is performed on the original radar tide level echo signal within each time window to obtain the time-frequency distribution characteristics of the signal. The transformed time-frequency matrix contains information in both the time and frequency dimensions. The instantaneous amplitude value of each frequency point within the entire time window is calculated along the time axis. Frequency points with amplitude values ​​exceeding 1.5 times the average amplitude value are marked as instantaneous high-energy frequency points. These frequency points correspond to the frequency components where noise energy is concentrated. The frequency values ​​and corresponding amplitude values ​​of these instantaneous high-energy frequency points are recorded. Then, the frequency centroid at each moment is calculated along the frequency axis. The frequency centroid reflects the center position of the signal energy distribution in the frequency domain. The instantaneous frequency drift rate is obtained by calculating the rate of change of the frequency centroid with time. This parameter reflects the time-varying frequency characteristics of non-stationary noise. Finally, the frequency values, amplitude values, and instantaneous frequency drift rates of the instantaneous high-energy frequency points are combined to form a multi-dimensional time-varying noise feature vector. This vector completely describes the instantaneous characteristic change law of non-stationary noise in the time-frequency domain.

[0060] The specific implementation of step S03 is as follows: The time-varying noise feature vector corresponding to each time window is used as a node in the graph structure. The similarity between nodes is measured by calculating the Euclidean distance between the time-varying noise feature vectors of any two nodes. The reciprocal of the Euclidean distance is used as the edge weight connecting the two nodes to characterize the association strength between them. When the Euclidean distance between two nodes exceeds a distance threshold, the corresponding edge weight is set to zero, indicating that the nodes are not connected. The distance threshold is determined by multiplying the median of the Euclidean distance between the feature vectors of adjacent time windows in the training dataset by 1.5. The constructed undirected weighted graph contains all node and edge weight information. Then, the degree matrix and Laplacian matrix are calculated based on the edge weight matrix. The degree matrix is ​​a diagonal matrix, and the diagonal elements connect each node. The sum of all edge weights, the Laplacian matrix is ​​equal to the degree matrix minus the edge weight matrix, and symmetric normalization is performed to improve numerical stability. Eigenvalue decomposition is performed on the normalized Laplacian matrix, and the eigenvectors corresponding to the first few smallest eigenvalues ​​are extracted. These eigenvectors are used as the embedding representation of the nodes. The embedding representation maps the high-dimensional eigenvectors to the low-dimensional space and preserves the similarity relationship between nodes. In the embedding space, the K-means clustering algorithm is used to divide the nodes into normal noise clusters and abnormal noise clusters. The number of clusters is preset to 2. When the number of abnormal noise cluster nodes exceeds 30% of the total number of nodes, the number of clusters is increased to 3 to further subdivide the degree of abnormality. The distance between each node and the center of its cluster is calculated, and nodes whose distance exceeds the mean distance plus twice the standard deviation within the cluster are marked as abnormal noise nodes.

[0061] The specific implementation of step S04 is as follows: abnormal data points corresponding to the marked abnormal noise nodes are removed. For each removed abnormal data point, three normal data points before and after it are selected as interpolation reference points. A cubic spline function is constructed for data repair. The function value of the cubic spline function at each interpolation reference point is equal to the reference point data value, and the first and second derivatives are continuous. The coefficients of the cubic spline function are determined by solving a tridiagonal matrix equation system. The time of the abnormal data point is substituted into the cubic spline function to calculate the interpolation result as the repaired data value. The cubic spline interpolation method ensures a smooth connection between the repaired data and the surrounding normal data and avoids the introduction of new noise by abrupt interpolation changes. After the repair of all abnormal data points is completed, the preprocessed radar tide level signal is obtained.

[0062] The specific implementation of step S05 is as follows: the preprocessed radar tide level signal is input into a frequency domain adaptive denoising model. This model first converts the time-domain signal into a frequency-domain complex representation using a fast Fourier transform. The real part of the frequency-domain complex number corresponds to the cosine coefficient of the frequency component, and the imaginary part corresponds to the sine coefficient. Then, it enters three parallel frequency-domain convolution branches to extract low-frequency, mid-frequency, and high-frequency component features respectively. The convolution kernel parameters of each branch are directly defined and optimized in the frequency domain. According to the convolution theorem, time-domain convolution is equivalent to frequency-domain pointwise multiplication. By performing pointwise complex multiplication between the frequency-domain representation of the convolution kernel parameters and the frequency-domain complex representation of the signal, a frequency-domain convolution acceleration mechanism is achieved. This mechanism will calculate... The complexity is significantly reduced to less than one-tenth of that of traditional temporal convolution methods. The outputs of the three branches are weighted and fused through a frequency domain fusion layer. The fusion weights are dynamically calculated through an attention mechanism, which maps the outputs of the three branches to query vectors, key vectors, and value vectors, respectively. The dot product of the query vector and the key vector is calculated and normalized to obtain the attention weights. The attention weights are multiplied by the value vectors and summed to obtain the fusion features. The fusion features contain noise and signal information from different frequency bands. The noise estimation branch and the signal estimation branch extract the noise spectrum and signal spectrum from the fusion features, respectively. Finally, the frequency domain results are converted back to the time domain output noise estimation results and denoised signal estimation results through inverse fast Fourier transform.

[0063] The specific implementation of step S06 is as follows: The power spectral density of the noise is calculated based on the noise estimation result output by the frequency domain adaptive denoising model. The power spectral density of the noise is divided by the power spectral density of the preprocessed radar tide signal to obtain the power ratio of the noise to the signal. The optimal filter frequency response is calculated based on the power ratio using the Wiener filtering principle. The Wiener filter achieves optimal separation of signal and noise under the minimum mean square error criterion. An inverse Fourier transform is performed on the optimal filter frequency response to obtain time-domain adaptive filter coefficients of length 64. Window function truncation is used to ensure the causality and stability of the filter. The update step size of the filter coefficients is based on the noise energy. The rate of change is dynamically adjusted. The energy values ​​of the noise estimation results for three consecutive time windows are recorded. The difference between the noise energy of the current window and the noise energy of the previous window is calculated and divided by the noise energy of the previous window to obtain the noise energy change rate. When the absolute value of the rate of change is greater than 0.3, the noise is determined to be in a rapid change state and the update step size is set to 0.05. When the absolute value of the rate of change is less than 0.1, the noise is determined to be relatively stable and the update step size is set to 0.01. When the rate of change is between 0.1 and 0.3, the update step size is set to 0.03. The calculated adaptive filter coefficients are used to filter the preprocessed radar tide signal to obtain the denoised tide data.

[0064] The specific implementation of step S07 is as follows: Calculate the residual signal energy between the denoised tide level data and the preprocessed radar tide level signal. The residual signal energy reflects the sufficiency of the filtering process. Compare the residual signal energy with a set residual threshold. The residual threshold is initially determined during the training phase by the 95th percentile of the residual signal energy distribution on the statistical validation set. In practical applications, it is dynamically adjusted based on the statistical characteristics of the residual signal energy over 100 consecutive time windows. When the mean residual signal energy shows a significant upward trend, the residual threshold is increased by 15% to prevent over-filtering from distorting the tide level signal. When the mean shows a significant downward trend, the residual threshold is decreased by 10% to improve noise suppression. If the residual signal energy is greater than the residual threshold, it indicates insufficient noise suppression and the filtering intensity needs to be increased. In this case, the update step size of the adaptive filter coefficients is increased by 20%, and step S06 is repeated for further filtering. If the residual signal energy is less than the residual threshold, it indicates that the filtering effect meets the requirements. Output the denoised tide level data as the final result for subsequent tide level analysis and forecasting.

[0065] It should be noted that the first key technical idea of ​​this invention is to construct a time-varying noise feature vector by joint analysis in the time and frequency domains and identify abnormal noise nodes by graph-structured spectral clustering. Traditional methods usually use fixed thresholds or sliding window statistical methods to detect outliers, which are difficult to adapt to the instantaneous variation characteristics of non-stationary noise. This method extracts time-varying feature parameters such as instantaneous high-energy frequency points and frequency drift rate through short-time Fourier transform, maps the multidimensional feature vectors to graph-structured nodes, and uses spectral clustering algorithms to divide normal and abnormal clusters in the embedding space. This method makes full use of the local similarity and global difference of noise in the time and frequency domains, and has a strong ability to identify both abrupt and gradual noise. Compared with traditional methods, it can more accurately distinguish between abnormal noise and effective signal abrupt changes and avoids the mistaken rejection of real tidal level jumps.

[0066] The second key technical approach is to construct a frequency-domain adaptive denoising model and use a frequency-domain convolution acceleration mechanism to achieve efficient feature extraction. Traditional time-domain convolutional neural networks have high computational complexity and difficulty in capturing the frequency structure characteristics of long-term sequence signals. This method transforms time-domain convolution operations into frequency-domain pointwise multiplication operations based on the convolution theorem. The convolution kernel parameters are directly defined and optimized in the frequency domain, eliminating the frequency domain conversion step. The computational efficiency is increased to more than ten times that of traditional methods, meeting the requirements of real-time processing. At the same time, three parallel frequency-domain convolution branches extract features for low-frequency tide signals, mid-frequency sea wave interference, and high-frequency equipment noise, respectively. The weights of each frequency band are dynamically adjusted through an attention mechanism, so that the model can still maintain the sensitivity of tide signals in severe sea conditions where the energy of sea clutter far exceeds that of useful signals, avoiding the loss of effective information caused by simple frequency-domain filtering.

[0067] The third key technical approach is to dynamically adjust the adaptive filter coefficient update step size based on the noise energy change rate and iteratively optimize the filtering effect by combining it with a residual energy feedback mechanism. Traditional adaptive filtering methods typically use a fixed step size to update the filter coefficients, which results in slow convergence speed and tracking lag when the noise changes rapidly, and low convergence accuracy and steady-state error when the noise is stable. This method determines the noise change state by continuously monitoring the noise energy change rate. In the rapidly changing state, the update step size is increased to speed up the convergence speed, and in the stable state, the update step size is decreased to improve the convergence accuracy. At the same time, a residual energy feedback mechanism is introduced. When the residual energy exceeds the dynamically adjusted residual threshold, the filtering intensity is automatically increased and the filtering process is repeated until the requirements are met. This mechanism realizes adaptive tracking and effective suppression of broadband non-stationary noise.

[0068] The synergistic effect of the three key technical approaches mentioned above forms a complete denoising chain, from anomaly detection preprocessing to frequency domain feature modeling and adaptive filtering optimization. Time-frequency joint analysis and graph structure spectrum clustering effectively remove strong anomalous noise in the data preprocessing stage, reducing interference burden for subsequent processing. The frequency domain adaptive denoising model accurately separates noise and signal spectral components through efficient frequency domain convolution mechanism and attention fusion strategy, providing accurate noise estimation for filter design. Dynamic step size adjustment and residual feedback mechanism ensure that the filter can quickly converge to optimal performance under different noise conditions. The synergistic effect of the three makes the whole system highly robust to non-stationary noise and has high-precision processing capabilities. Compared with traditional single-stage optimization methods, it can stably output high-quality tidal data under a wider range of sea state conditions.

[0069] It should be noted that this invention also solves the following technical problems: traditional frequency domain filtering methods suffer from low computational efficiency when processing long-term radar tide data, and the complexity of time-domain convolution operations increases linearly with signal length and convolution kernel length, making it difficult to meet real-time processing requirements. This invention defines and optimizes the convolution kernel parameters directly in the frequency domain, using Fast Fourier Transform to convert time-domain convolution into pointwise complex multiplication in the frequency domain. Based on the convolution theorem, the computational complexity is significantly reduced. For long-sequence signals, an overlapping preservation method is used for segmented processing to avoid distortion at the boundaries of cyclic convolution, thus greatly shortening the computation time for processing long-sequence data and meeting the real-time requirements of marine tide monitoring systems. Simultaneously, the frequency domain parameterization design makes the features learned by the model more closely match the signal frequency characteristics, improving the ability to capture time-varying frequency components of non-stationary noise.

[0070] Furthermore, this invention addresses the technical problem of lost effective information due to simple frequency domain filtering caused by sea clutter energy far exceeding that of the tide level signal under severe sea conditions. This invention constructs three parallel frequency domain convolutional branches to independently extract features from low-frequency tide level signals, mid-frequency sea wave interference, and high-frequency equipment noise. An attention mechanism dynamically adjusts the fusion weights of each branch based on the current signal spectrum characteristics. Noise and signal spectra are modeled in the noise estimation and signal estimation branches, respectively. When sea clutter energy surges, the attention mechanism automatically increases the weight of the mid-frequency branch to enhance the identification of sea wave interference, while maintaining the sensitivity of the low-frequency branch to the tide level signal, preventing the tide level signal from being misjudged as noise and rejected in strong noise environments. Combined with dynamically adjusted filter coefficients and a residual energy feedback mechanism, robust extraction of the tide level signal is achieved under complex sea conditions.

[0071] Specifically, the principle of this invention is as follows: The invention solves the problem of non-stationary noise tracking by establishing a closed-loop feedback mechanism for real-time noise characteristic perception and dynamic adjustment of filter parameters. It simultaneously observes the signal in the time and frequency domains through short-time Fourier transform, capturing the drift rate of the instantaneous frequency centroid of the noise and the amplitude changes of high-energy frequency points. These time-varying features are mapped to a graph structure for spectral clustering analysis. From the perspective of time evolution, abnormal noise jump patterns are identified. After removing sudden anomalies in the preprocessing stage, the frequency-domain adaptive denoising model directly extracts features in the frequency domain using the convolution theorem, avoiding computational redundancy in time-domain convolution. (The last sentence appears to be incomplete and requires further context.) The row branches independently model noise types for different frequency bands. The attention mechanism dynamically allocates the weights of each branch according to the current signal spectrum characteristics. The noise estimation results are transformed into optimal filter coefficients through Wiener filtering principle. The update step size is adaptively set according to the noise energy change rate in the continuous time window. When the noise changes rapidly, the step size is increased to accelerate tracking. When the noise is stable, the step size is decreased to improve stability. Residual energy monitoring forms an outer iterative control to ensure that the filtering effect reaches the preset accuracy requirements. This series of links constitutes a complete adaptive tracking link, enabling the filtering system to continuously synchronize with the instantaneous characteristic changes of non-stationary noise.

[0072] The following provides a specific embodiment 1 of the present invention. The specific implementation of steps S01 and S05 in this embodiment 1 is the same as that described above, and will not be repeated in detail here. The specific implementation of other steps is described in detail below.

[0073] The specific implementation of step S02 is to perform a short-time Fourier transform on the original radar tide level echo signal within each time window to obtain the time-spectrum matrix. ,in For the first A time index, The value range is 1 to , For the first Frequency index, The value range is 1 to The instantaneous amplitude value at each frequency point is calculated along the time axis of the time-frequency spectrum matrix. The formula for the instantaneous amplitude value is as follows:

[0074] ;

[0075] In the formula, For frequency The instantaneous amplitude value at the specified point, in units of voltage. ; This represents the number of time sampling points within the time window. The time spectrum matrix at time t and frequency The amplitude value at the location, in units of ; For the first time window Each sampling time, in units of ; For the first Frequency points, in units of Frequency points where the instantaneous amplitude is greater than 1.5 times the average amplitude are defined as instantaneous high-energy frequency points. The formula for determining this criterion is as follows:

[0076] ;

[0077] In the formula, This represents the number of frequency sampling points. For the first Frequency points, in units of ; This is a frequency point index, with values ​​ranging from 1 to... The frequency centroid of the time-frequency spectrum matrix is ​​calculated along the frequency axis at each moment. The formula for the centroid of frequency is expressed as follows:

[0078] ;

[0079] In the formula, For a moment The frequency centroid, in units Instantaneous frequency drift rate The formula is expressed as follows:

[0080] ;

[0081] In the formula, Instantaneous frequency drift rate, in units of ; This is the time interval, with a default value of 0.1. ; For a moment The frequency centroid, in units ; For a moment The frequency centroid, in units Time-varying noise feature vector The formula is expressed as follows:

[0082] ;

[0083] In the formula, This is a time-varying noise feature vector, and all its components are dimensionless. For the first The frequency values ​​of each instantaneous high-energy frequency point, in units of , For indexes of instantaneous high-energy frequency points; For reference frequency, the default value is 100. ; For the first The amplitude value of each instantaneous high-energy frequency point, in units of ; For reference range, the default value is 1. ; The reference frequency drift rate is 10 by default. .

[0084] The specific implementation of step S03 is to use the time-varying noise feature vector corresponding to each time window as a graph structure node. Calculate any two graph structure nodes... and Euclidean distance between The formula for Euclidean distance is as follows:

[0085] ;

[0086] In the formula, Graph structure nodes and The Euclidean distance between them is dimensionless because each component of the time-varying noise feature vector is dimensionless. is the dimension of the time-varying noise feature vector; Graph structure nodes The first time-varying noise eigenvector One component, dimensionless; Graph structure nodes The first time-varying noise eigenvector One component, dimensionless; For the first Graph structure node index; For the first Graph structure node index; The component index of the feature vector, with values ​​ranging from 1 to... Edge weight The formula is expressed as follows:

[0087] ;

[0088] In the formula, To connect the nodes of the graph structure and The edge weights are dimensionless. The distance threshold is dimensionless and is obtained by calculating the median of the Euclidean distance between the time-varying noise feature vectors corresponding to all adjacent time windows in the training dataset, and then multiplying it by 1.5. An undirected weighted graph containing all graph structure nodes and edge weights is constructed, with the edge weight matrix... for A symmetric matrix, where The total number of nodes in the graph structure is given by the matrix elements. .

[0089] The spectral clustering algorithm is used to cluster the nodes of the graph structure. First, the degree matrix is ​​calculated based on the edge weight matrix of the undirected weighted graph. The degree matrix is ​​a diagonal matrix, with diagonal elements The formula is expressed as follows:

[0090] ;

[0091] In the formula, Graph structure nodes The degree value is dimensionless. Laplace matrix. The formula is expressed as follows:

[0092] ;

[0093] In the formula, It is the Laplace matrix, a dimensionless matrix; It is a degree matrix, a dimensionless matrix; This is the edge weight matrix, a dimensionless matrix. The normalized Laplace matrix is ​​also shown. The formula is expressed as follows:

[0094] ;

[0095] In the formula, The normalized Laplace matrix is ​​a dimensionless matrix. The degree matrix is ​​a negative 1 / 2 power, and its diagonal elements are Dimensionless. Eigenvalue decomposition is performed on the normalized Laplacian matrix to extract the eigenvalues. The eigenvectors corresponding to the smallest eigenvalues ,in This represents the number of clusters, with a default value of 2. The feature vectors are used as the embedding representation of the graph structure nodes. The formula for embedding a matrix is ​​expressed as follows:

[0096] ;

[0097] In the formula, for The embedding representation matrix is ​​a dimensionless matrix. These are feature vectors, each with a dimension of . Dimensionless. In the embedding space, the K-means clustering algorithm is used to divide the graph structure nodes into normal noise clusters and abnormal noise clusters, and the value of each graph structure node is calculated. With its cluster center distance The formula for distance is expressed as follows:

[0098] ;

[0099] In the formula, Graph structure nodes With cluster center The distance is dimensionless; Graph structure nodes The embedding representation vector is The first of the matrix Rows, dimensions are Dimensionless; For clusters The center vector of , with dimension . Dimensionless; It is the Euclidean norm; This is the cluster index. Graph nodes whose distance is greater than the cluster mean plus twice the standard deviation are marked as anomalous noise nodes. The formula for the judgment condition is as follows:

[0100] ;

[0101] In the formula, For clusters The mean distance from all nodes in the graph structure to the cluster center, dimensionless; For clusters The standard deviation of the distances from all nodes in the graph structure to the cluster center, dimensionless. Mean distance within the cluster. The formula is expressed as follows:

[0102] ;

[0103] In the formula, For clusters The number of nodes in the internal diagram structure; Represents graph structure nodes Belongs to cluster ; For clusters A graph structure set of nodes. Standard deviation of intra-cluster distances. The formula is expressed as follows:

[0104] .

[0105] The specific implementation of step S04 involves removing the marked outlier data points and using cubic spline interpolation to repair the data at the removal locations. For each removed outlier data point, three normal data points before and after it are selected as interpolation reference points to construct a cubic spline function. The cubic spline function has the same function value at each interpolation reference point as the data value at that point, and its first and second derivatives are continuous at the interpolation reference points. The cubic spline function is valid in the interval... The formula is expressed as follows:

[0106] ;

[0107] In the formula, These are cubic spline function values, in units of... ; For time, the unit is ; For the first The time of each interpolation reference point, in units of ; For the first The time of each interpolation reference point, in units of ; The coefficient of the constant term is given in units of 1000 ppm. ; The coefficient of the linear term, in units of ; The coefficient of the quadratic term is given in units of 1000 ppm. ; The coefficient of the cubic term, in units of The timestamps of the outlier data points are substituted into a cubic spline function, and the interpolation result is used as the repaired data value.

[0108] The specific implementation of step S06 is to calculate the power spectral density of the noise based on the noise estimation results output by the frequency domain adaptive denoising model. The formula for power spectral density is as follows:

[0109] ;

[0110] In the formula, For frequency The power spectral density of the noise at that location, in units of ; For noise estimation results at frequency The frequency domain representation at this point is obtained by performing a Fast Fourier Transform on the time-domain signal of the noise estimation branch output by the frequency-domain adaptive denoising model, and the unit is 1200 ppm. ; Sampling frequency, in units of ; The number of points for the Fast Fourier Transform. The power spectral density of the preprocessed radar tide signal. The formula is expressed as follows:

[0111] ;

[0112] In the formula, For frequency The power spectral density of the preprocessed radar tide signal, in units of ; For the preprocessed radar tidal signal at frequency Frequency domain representation at, unit is The power ratio of noise to signal. The formula is expressed as follows:

[0113] ;

[0114] In the formula, For frequency The power ratio of noise to signal is dimensionless. Using the Wiener filtering principle, the optimal filter frequency response is determined. The formula is expressed as follows:

[0115] ;

[0116] In the formula, For frequency The optimal filter frequency response is dimensionless. Performing an inverse Fourier transform on the optimal filter frequency response yields the time-domain adaptive filter coefficients. The adaptive filter coefficients are set to a length of 64, and truncation using a Hanning window function ensures the causality and stability of the filter. (Noise-reduced tide data) The formula is expressed as follows:

[0117] ;

[0118] In the formula, index for time The corresponding denoised tide level data, in units of ; For the first Each adaptive filter coefficient is dimensionless. For the preprocessed radar tide signal, index at time The corresponding value, in units of ; For time indexing; This represents the filter tap index, ranging from 0 to 63. The update step size for the adaptive filter coefficients. Based on the rate of change of noise energy The formula for the rate of change of noise energy under dynamic adjustment is as follows:

[0119] ;

[0120] In the formula, The noise energy change rate is dimensionless. The current window noise energy, in units of ; Front window noise energy, unit: Current window noise energy The formula is expressed as follows:

[0121] ;

[0122] In the formula, This represents the number of sampling points within the time window. The noise estimation results output by the frequency domain adaptive denoising model are indexed at time step. The corresponding value, in units of Front window noise energy The calculation method is the same as for the noise energy of the current window, only corresponding to the data of the previous time window. Update step size The formula is expressed as follows:

[0123] ;

[0124] In the formula, This is the dimensionless update step size for the adaptive filter coefficients.

[0125] The specific implementation of step S07 is to calculate the residual signal energy between the denoised tide level data and the preprocessed radar tide level signal. The formula for the residual signal energy is as follows:

[0126] ;

[0127] In the formula, The residual signal energy is expressed in units of 1. ; This represents the number of signal sampling points. Indexing the denoised tide level data by time. The corresponding value, in units of ; For the preprocessed radar tide signal, index at time The corresponding value, in units of When the residual signal energy is greater than the set residual threshold... Then, increase the update step size of the adaptive filter coefficients by 20% and repeat step S06. When the residual signal energy is less than the residual threshold, output the denoised tide level data as the final result. (Residual threshold) The method for setting the threshold is as follows: during the training phase, statistically analyze the residual signal energy distribution between the denoised tide data and the manually labeled true tide change curves on the validation set. The 95th percentile of the residual signal energy is then calculated as the initial value for the residual threshold, with units of [unit missing]. In practical applications, the residual threshold is dynamically adjusted based on the statistical characteristics of the residual signal energy over 100 consecutive time windows.

[0128] It should be explained that the time-varying noise feature vector construction formula unifies the instantaneous high-energy frequency values, instantaneous high-energy frequency amplitude values, and instantaneous frequency drift rates of different dimensions into a dimensionless space through normalization processing. This makes noise features of different frequency bands and energy levels comparable, avoids a single feature component dominating the entire feature vector, and improves the accuracy of graph structure node clustering. The Euclidean distance and edge weight formula converts distance into a similarity metric through reciprocal mapping. The introduction of a distance threshold achieves sparsity control of the undirected weighted graph, maintaining the robustness of clustering in scenarios with drastic noise changes. The normalization processing of the Laplacian matrix, through symmetric normalization of the degree matrix to the power of -2, solves the numerical instability problem caused by the difference in degree values ​​of graph structure nodes, making the eigenvalue decomposition results more reliable. The embedding representation preserves the similarity relationship between graph structure nodes, facilitating accurate partitioning in subsequent K-means clustering. The formulas for the mean and standard deviation of intra-cluster distances provide statistical criteria for identifying anomalous noise nodes. By using the statistical criterion of the mean plus twice the standard deviation, over 95% of normal noise nodes are retained under the assumption of normal distribution, while only significantly deviating anomalous noise nodes are removed, avoiding the erroneous removal of effective signal abrupt changes. The cubic spline interpolation function uses a high-order polynomial to ensure the continuity of the function value, first derivative, and second derivative of the interpolation result at the reference point. The dimensional design of each coefficient ensures overall dimensional balance as the time variable increases exponentially, and the repaired data values ​​are smoothly connected with surrounding normal data points without introducing new noise or distortion. The formulas for calculating noise power spectral density and signal power spectral density achieve the conversion from power to power spectral density by dividing the square of the frequency domain amplitude by the frequency resolution. The power ratio of noise to signal constitutes the core parameter of Wiener filtering, and the optimal filter frequency response formula achieves optimal separation of noise and signal in the frequency domain by minimizing the mean square error criterion.

[0129] ;

[0130] This formula achieves complete signal passage with a filter frequency response close to 1 when the noise power is much lower than the signal power, and complete noise suppression with a filter frequency response close to 0 when the noise power is much higher than the signal power, automatically adapting to different noise levels. The time-domain convolution operation formula applies the frequency-domain filter coefficients to the signal value at each time step, achieving adaptive tracking of non-stationary noise. The noise energy change rate formula quantifies the time-varying speed of noise by the difference in noise energy between adjacent time windows.

[0131] ;

[0132] This formula reflects the severity of noise non-stationarity by comparing the relative rate of change of noise energy between the current window and the previous window. The piecewise setting of the update step size allows the filter coefficients to adjust rapidly when noise changes quickly, and to adjust in small steps when noise is relatively stable to maintain stability. The residual signal energy formula evaluates the filtering effect by comparing the denoised signal with the original signal. The dynamic adjustment mechanism of the residual threshold adaptively optimizes the filtering depth based on the statistical characteristics of the residuals in practical applications, ensuring noise suppression while avoiding distortion of the tide signal due to over-filtering. The overall scheme achieves efficient and accurate filtering of non-stationary noise in radar tide data through the synergistic effect of joint time-frequency domain analysis, graph structure clustering anomaly detection, frequency domain adaptive denoising, and iterative optimization mechanisms, maintaining sensitivity and accuracy of the tide signal even under harsh sea conditions and strong noise interference.

[0133] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: To verify the effectiveness of the invention, technicians built a numerical simulation analysis environment and performed non-stationary noise adaptive filtering processing on radar tide level data collected continuously for 24 hours from a coastal observation station. The radar tide gauge equipped at the observation station operates at a frequency of 26 GHz, with a sampling frequency set to 10 Hz, continuously acquiring 864,000 raw echo signal data points. During the data acquisition period, sea conditions changed from calm to moderate and then to severe, providing an ideal test scenario for verifying the algorithm's adaptability under different noise environments.

[0134] Technicians first segmented the raw echo signal, dividing the continuous time series into 86,400 time windows based on a time window length of 2 seconds and an overlap length of 1 second. For example... Figure 2As shown, the original radar tide signal exhibits significant non-stationary characteristics in the time domain, with the signal amplitude fluctuating drastically over time and showing abrupt amplitude changes in some periods. For each time window's 20 sampling points, technicians performed a short-time Fourier transform to obtain a time-spectrum matrix. This matrix has dimensions of 20×11, with the frequency axis containing 11 frequency points from 0Hz to 5Hz. By calculating the instantaneous amplitude value of each frequency point along the time axis, a total of 2847 instantaneous high-energy frequency points were identified, all of which had amplitude values ​​exceeding 1.5 times the average amplitude value. The time-varying rate of change of the frequency centroid along the frequency axis yielded an instantaneous frequency drift rate sequence, with typical values ​​ranging from 0.08. Up to 0.35 Between. The identified instantaneous high-energy frequency points, frequency values, amplitude values, and instantaneous frequency drift rates are combined to form a time-varying noise feature vector, and each feature vector contains three dimensions of feature parameters.

[0135] Technicians mapped 86,400 time-varying noise feature vectors to graph structure nodes and calculated the Euclidean distance between any two nodes. Statistical analysis of the Euclidean distances between feature vectors from adjacent time windows in the training dataset yielded a median of 0.42, and a distance threshold of 0.63 was set. When the Euclidean distance between two nodes exceeded 0.63, the corresponding edge weight was set to zero. The resulting undirected weighted graph contained 86,400 nodes and approximately 258,000 valid edges. Figure 3 As shown, a spectral clustering algorithm is used to cluster the nodes of the graph structure. First, the Laplacian matrix is ​​calculated and eigenvalue decomposition is performed. The eigenvectors corresponding to the two smallest eigenvalues ​​are extracted as the embedding representations of the nodes. In the two-dimensional embedding space, the K-means clustering algorithm is used to divide the nodes into normal noise clusters and abnormal noise clusters. The normal noise cluster contains 81,536 nodes, and the abnormal noise cluster contains 4,864 nodes. The distance between each node and the center of its cluster is calculated. Nodes whose distance is greater than the mean distance within the cluster plus twice the standard deviation are marked as abnormal noise nodes. A total of 1,872 abnormal noise nodes were identified, corresponding to abnormal data points accounting for 2.17% of the total data volume.

[0136] After removing the marked outlier data points, technicians used cubic spline interpolation to repair the data. For each removed outlier data point, three normal data points before and after it were selected as interpolation reference points. A cubic spline function was constructed, and the coefficients of the tridiagonal matrix equations were determined. The preprocessed radar tide level signal was obtained after interpolation repair. As shown in Table 1, the distribution characteristics of outlier data points differ significantly under different sea state conditions.

[0137] Table 1. Distribution characteristics of outlier data points under different sea states

[0138]

[0139] Technicians input the preprocessed radar tide signal into a frequency-domain adaptive denoising model for processing. The model's frequency-domain convolutional feature extraction layer contains three parallel branches: the low-frequency branch's convolution kernel parameters cover the 0Hz to 0.5Hz frequency band, the mid-frequency branch covers the 0.5Hz to 2Hz frequency band, and the high-frequency branch covers the 2Hz to 5Hz frequency band. The time-domain signal is converted to a frequency-domain complex representation using a Fast Fourier Transform (FFT), and point-by-point complex multiplication is performed in the frequency domain to complete the convolution operation. The frequency-domain fusion layer dynamically calculates the fusion weights of the three branches using an attention mechanism. In calm sea conditions, the weights are 0.65 for the low-frequency branch, 0.28 for the mid-frequency branch, and 0.07 for the high-frequency branch, while in severe sea conditions, the weights are adjusted to 0.42, 0.39, and 0.19, respectively. The noise estimation branch extracts the noise spectrum from the fusion features and calculates the noise power spectral density, with its peak frequency appearing at 1.2Hz, corresponding to the dominant frequency of wave interference. The signal estimation branch extracts the signal spectral components and obtains the denoised signal estimation result through an inverse Fast Fourier Transform (IFFT).

[0140] The adaptive filter coefficients were calculated based on the noise estimation results. The optimal filter frequency response was obtained using the Wiener filtering principle, and a time-domain filter coefficient of length 64 was obtained through inverse Fourier transform. Technicians recorded the noise energy values ​​for three consecutive time windows as 18.3, 23.7, and 31.5, respectively. The noise energy change rate for the current window was calculated to be 0.295, indicating that the noise was in a rapidly changing state. The filter coefficient update step size was set to 0.03. The preprocessed radar tide signal was then filtered to obtain preliminary denoising results. Figure 4 As shown, the residual signal energy between the denoised tide level data and the preprocessed signal was calculated to be 4.82, while the set residual threshold was 3.65. The residual energy exceeding the threshold indicates that the denoising effect did not meet expectations. The technicians increased the filter coefficient update step size by 20% to 0.06 and re-processed the filter. After the second iteration, the residual signal energy decreased to 3.18, satisfying the convergence condition, and the final denoised tide level data was output.

[0141] As shown in Table 2, after the complete processing flow, the noise suppression effect of different frequency bands shows obvious differences.

[0142] Table 2. Statistics on noise suppression effects in different frequency bands

[0143]

[0144] like Figure 5As shown, the final output denoised tide level data curve exhibits a smooth and continuous characteristic, preserving the slow trend of the actual tide level change while effectively suppressing high-frequency fluctuations introduced by wave interference and equipment noise. Compared with the manually labeled actual tide level curve, the mean square error of the denoised data is 0.043m, a 77.0% reduction compared to the mean square error of 0.187m in the preprocessed signal. The signal-to-noise ratio improves from 8.3dB in the original signal to 24.6dB, an improvement of 16.3dB.

[0145] This invention represents a significant improvement over traditional fixed-window filtering methods. Traditional methods employ low-pass or band-pass filters with fixed parameters, which cannot adapt to the instantaneous changes in non-stationary noise. When noise frequency components drift over time, fixed filter parameters lead to noise residue or loss of effective signal. This invention extracts time-varying noise feature vectors through joint time-frequency domain analysis and identifies abnormal noise patterns using graph-structured node clustering, achieving accurate tracking of the time-varying characteristics of noise. The frequency-domain adaptive denoising model uses a frequency-domain convolution acceleration mechanism, transforming time-domain convolution operations into point-by-point frequency-domain multiplication. This reduces computational complexity from a linear relationship with the convolution kernel length to a logarithmic relationship, enabling real-time processing of long-term series data. Three parallel frequency-domain convolution branches optimize feature extraction strategies for low-frequency tide signals, mid-frequency wave interference, and high-frequency equipment noise, respectively. An attention mechanism dynamically adjusts the weights of each branch, resolving the contradiction between noise suppression and signal preservation that traditional methods cannot balance under severe sea conditions. The adaptive filter coefficients dynamically adjust the step size based on the rate of change of noise energy. Increasing the step size accelerates convergence when noise changes rapidly, and decreasing it improves filtering accuracy when noise is stable. This adaptive mechanism overcomes the trade-off between convergence speed and steady-state error inherent in traditional fixed-step methods. The residual energy feedback iteration mechanism ensures that the filtering results meet preset accuracy requirements, avoiding under-filtering or filtered waveform problems that may occur with single-pass filtering in traditional methods. In summary, this invention constructs a complete non-stationary noise filtering system from noise feature identification, frequency domain acceleration processing, multi-scale feature fusion to adaptive parameter adjustment, providing an effective technical means for high-precision processing of radar tidal data.

[0146] It should be noted that the variables involved in this invention are explained in detail in Tables 3 and 4.

[0147] Table 3. Variable Explanation Table (Part 1)

[0148]

[0149] Table 4. Variable Explanation Table (Part Two)

[0150]

[0151] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for adaptive filtering of non-stationary noise in radar tide level data, characterized by, The radar tide level original echo signal is collected and segmented, time-frequency domain joint analysis is performed on the radar tide level original echo signal in each time window, a time-varying noise feature vector is extracted, the time-varying noise feature vector is mapped into a graph structure node, a spectral clustering division algorithm is used for clustering grouping to identify abnormal noise nodes, the abnormal data points are removed, and a cubic spline interpolation method is used for repair to obtain a pretreated radar tide level signal, the pretreated radar tide level signal is input into a frequency domain adaptive denoising model, noise mode features are extracted through a frequency domain convolution acceleration mechanism, noise estimation results are output, adaptive filter coefficients are calculated according to the noise estimation results, the update step of the adaptive filter coefficients is dynamically adjusted according to the noise energy change rate, the pretreated radar tide level signal is filtered to obtain denoised tide level data, and the residual signal energy between the denoised tide level data and the pretreated radar tide level signal is calculated; when the residual signal energy is greater than a residual threshold, the update step is increased and the filtering is repeated; when the residual signal energy is less than the residual threshold, the denoised tide level data is output. The frequency domain adaptive denoising model comprises a fast Fourier transform layer, a frequency domain convolution feature extraction layer, a frequency domain point-by-point multiplication layer, a frequency domain fusion layer, a noise estimation branch, a signal estimation branch and an inverse fast Fourier transform layer; the frequency domain convolution feature extraction layer comprises three parallel frequency domain convolution branches for extracting low-frequency component features, medium-frequency component features and high-frequency component features.

2. The method of claim 1, wherein, The time-frequency domain joint analysis comprises the following steps: performing short-time Fourier transform on the radar tide level original echo signal in the time window to obtain a time-frequency spectrum matrix, calculating an instantaneous high-energy frequency point along a time axis direction, calculating an instantaneous frequency drift rate along a frequency axis direction, and combining the frequency value of the instantaneous high-energy frequency point, the amplitude value of the instantaneous high-energy frequency point and the instantaneous frequency drift rate to form a time-varying noise feature vector.

3. The method of claim 2, wherein, The instantaneous high-energy frequency point refers to a frequency point with an instantaneous amplitude value greater than 1.5 times an average amplitude value, and the instantaneous frequency drift rate refers to a rate of change of a frequency gravity center with time.

4. The method of claim 3, wherein, The mapping into a graph structure node comprises the following steps: taking the time-varying noise feature vector corresponding to each time window as a graph structure node, calculating the Euclidean distance between any two graph structure nodes, taking the reciprocal of the Euclidean distance as an edge weight, setting the edge weight to zero when the Euclidean distance is greater than a distance threshold, and constructing an undirected weighted graph.

5. The method of claim 4, wherein, The spectral clustering division algorithm comprises the following steps: calculating a Laplacian matrix according to the edge weight matrix of the undirected weighted graph, performing eigenvalue decomposition on the Laplacian matrix to extract an eigenvector, taking the eigenvector as an embedding representation of the graph structure node and dividing it into a normal noise cluster and an abnormal noise cluster by using a K-means clustering algorithm, and marking the graph structure nodes with a distance greater than the average intra-cluster distance plus two times the standard deviation as abnormal noise nodes.

6. The method of claim 5, wherein, The Laplacian matrix is calculated by subtracting the edge weight matrix from a degree matrix and performing symmetric normalization.

7. The method of claim 6, wherein, The steps of the cubic spline interpolation method are as follows: three normal data points before and after the abnormal data point are selected as the interpolation reference points to construct a cubic spline function; the coefficients of the cubic spline function are determined by solving a three-diagonal matrix equation set; and the time of the abnormal data point is substituted into the cubic spline function to calculate the interpolation result as the repaired data value.

8. The method of claim 7, wherein, The fusion weights of the frequency domain fusion layer are dynamically calculated through the attention mechanism, the attention mechanism maps the outputs of the three frequency domain convolution branches into query vectors, key vectors and value vectors respectively, the dot product of the query vectors and the key vectors is normalized to obtain attention weights, the attention weights are multiplied with the value vectors and summed to obtain weighted fusion features.

9. The method of claim 8, wherein, The implementation principle of the frequency domain convolution acceleration mechanism is that the convolution kernel parameters are directly defined and optimized in the frequency domain, the time domain signal is converted to the frequency domain through fast Fourier transform, complex point-by-point multiplication is performed in the frequency domain, the signal is converted back to the time domain through inverse fast Fourier transform, and the overlapping save method is used for segmented processing for long sequence signals.

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