A dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals

Abstract

This invention relates to the field of marine acoustic detection technology and discloses a dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals. The method collects sonar signal sequences and tidal motion parameter sequences for the current sea area and divides the sonar signal into multiple time windows. Within each window, the phase offset is calculated based on the tidal parameters and converted into time-domain compensation coefficients through an established dynamic coupling model, performing preliminary phase correction on the sonar signal. Spectral analysis is performed on the initially suppressed signal to extract residual interference features, and the parameter weights of the dynamic coupling model are adjusted accordingly to generate an optimized model. This optimized model is applied to the processing of the next time window, forming an iterative suppression closed-loop process. This method can adaptively track the dynamic changes of tidal motion, effectively weakening its periodic modulation interference on sonar signals and improving the accuracy of sonar detection data in strong tidal areas such as nearshore and estuaries.

Description

Technical Field

[0001] This invention relates to the field of marine acoustic detection technology, specifically a dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals. Background Technology

[0002] Sonar technology, as a crucial tool for underwater detection, navigation, and communication, is significantly constrained by the complex marine environment. Among these factors, tidal motion, a large-scale, periodic hydrological phenomenon, is a key source of interference affecting the effectiveness of sonar in nearshore and estuarine areas. The periodic rise and fall of seawater caused by tides not only alters seawater depth but also triggers large-scale horizontal and vertical movements of water bodies. These movements directly modulate the propagation path and speed of sound waves in the seawater, as well as the reflection boundary conditions between the sea surface and the seabed, ultimately resulting in complex phase fluctuations, amplitude variations, and waveform distortions in the received sonar signals. In applications such as marine mapping, underwater target detection, and geological exploration, these tidal interference signals often mix with target echoes or useful signals, severely reducing the resolution of sonar images, the accuracy of target localization, and the precision of signal identification.

[0003] In existing technologies, various static or quasi-static compensation methods are commonly used to mitigate the impact of environmental interference on sonar. One common method is environmental parameter modeling, which involves establishing a fixed tidal correction model based on historical tidal data. This model then performs post-hoc corrections on sonar observations based on average or predicted tidal parameters. This method is effective for sea areas with stable and slow-changing tidal patterns, but it is inherently static and cannot respond in real time to short-term abnormal fluctuations or nonlinear changes caused by meteorological and ocean current factors during the tidal process. This results in poor compensation performance in practical application scenarios with severe weather or complex hydrological conditions, and may even introduce new errors.

[0004] Another approach is based on signal processing filtering techniques, such as using high-pass filters or adaptive filters to suppress low-frequency tidal interference components. However, the spectral characteristics of tidal interference are not constant and may overlap with the spectrum of the useful signal. Simple filtering often damages the useful low-frequency signal components while removing interference. Especially for long-duration integration detection tasks, the dynamic characteristics of tidal interference make it difficult for fixed-parameter filters to achieve ideal results. Although adaptive filtering has a certain tracking capability, its convergence speed, stability, and high dependence on the accuracy of the reference signal limit its practical application in sonar systems with high real-time requirements and difficult reference signal acquisition.

[0005] In addition, some studies have attempted to estimate and eliminate the tidal effect as a whole systematic error, but such methods usually rely on accurate synchronous hydrological observation data or have extremely high requirements on the motion attitude of the sonar system platform. They are costly to implement, complex in process, and difficult to be widely applied to various small and medium-sized sonar platforms or large-scale long-term observation networks.

[0006] Existing technologies for dealing with tidal interference on sonar signals generally suffer from drawbacks such as insufficient adaptability, poor real-time performance, susceptibility to damage to useful signals, or high implementation complexity. There is a lack of a dedicated algorithm capable of tracking tidal changes in real-time, dynamically, and adaptively, and precisely suppressing their impact on sonar signals. Therefore, there is an urgent need to develop a new technical solution that can effectively overcome these shortcomings and improve the performance of sonar in strong tidal environments. Summary of the Invention

[0007] The purpose of this invention is to provide a dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, this invention provides a dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals, the algorithm comprising: Collect sonar signal sequences and tidal motion parameter sequences for the current sea area, and divide the sonar signal sequences into multiple time windows; Within each time window, the phase offset of the sonar signal due to tidal motion is calculated based on the tidal motion parameter sequence; A dynamic coupling model between sonar signals and tidal motion is established, and the phase offset is converted into a time-domain compensation coefficient through the dynamic coupling model. Phase correction is performed on the sonar signal sequence based on the time-domain compensation coefficient to generate a sonar signal after preliminary suppression. Spectral analysis was performed on the sonar signal after initial suppression to extract residual tidal interference characteristics; The parameter weights of the dynamic coupling model are adjusted based on the residual tidal disturbance characteristics to generate an optimized dynamic coupling model. The optimized dynamic coupling model is applied to the sonar signal processing in the next time window to form an iterative suppression process.

[0009] Preferably, the step of calculating the phase shift of the sonar signal due to tidal motion based on the tidal motion parameter sequence includes: Obtain the rate of water level change and the amplitude of periodic fluctuations in the tidal motion parameter sequence within the current time window; Establish a function for the change in the propagation path length of the sonar signal based on the rate of water level change; The periodic fluctuation amplitude is input into the sound wave propagation speed correction function to calculate the change in the propagation speed of the sonar signal. By combining the propagation path length variation function and the propagation speed variation, the phase accumulation error at the time of sonar signal reception is derived; The phase accumulation error is normalized to obtain a standardized phase offset.

[0010] Preferably, establishing the dynamic coupling model between the sonar signal and the tidal motion includes: Construct a multi-layer neural network structure with tidal motion parameters as the input layer and phase correction coefficients as the output layer; The historically collected tidal motion parameter sequence and the corresponding sonar signal phase error are used as the training dataset; The time backpropagation algorithm is used to train a multi-layer neural network structure until the prediction error of the output layer phase correction coefficient is lower than a set threshold. Save the network parameters and connection weights after training to form a dynamically coupled model.

[0011] Preferably, the step of converting the phase offset into time-domain compensation coefficients through a dynamic coupling model includes: The phase offset calculated in the current time window is input into the input layer of the dynamic coupling model; Intermediate feature representations are generated through nonlinear transformation of the hidden layer of the dynamic coupling model; Based on the intermediate feature representation and the connection weights of the output layer, the temporal compensation coefficient vector is calculated; The time-domain compensation coefficient vector is time-aligned to match its length with the time window of the sonar signal sequence.

[0012] Preferably, the phase correction of the sonar signal sequence based on the time-domain compensation coefficient includes: Perform point-by-point multiplication of the time-domain compensation coefficient vector with the sonar signal sequence; Perform a Fourier transform on the multiplication result to convert it to the frequency domain representation; In the frequency domain, a phase rotation operation is applied to each frequency component, and the rotation angle is determined by the corresponding time-domain compensation coefficient; An inverse Fourier transform is performed on the frequency domain representation after phase rotation to obtain the time-domain sonar signal after preliminary suppression.

[0013] Preferably, the extraction of residual tidal interference features includes: Calculate the difference between the sonar signal after initial suppression and the original sonar signal; Wavelet packet decomposition is performed on the differential signal to obtain multi-scale sub-band signals; Statistical analysis of the energy distribution and zero-crossing rate characteristics of each sub-band signal; The energy distribution and zero-crossing rate characteristics are combined to form the residual tidal disturbance feature vector.

[0014] Preferably, adjusting the parameter weights of the dynamic coupling model based on residual tidal disturbance characteristics includes: Map the residual tidal disturbance feature vectors to the hidden layer space of the dynamic coupling model; Calculate the correlation coefficient between the activation values ​​of hidden layer nodes and the residual tidal disturbance feature vector; Adjust the connection weights from the hidden layer to the output layer based on the correlation coefficient; The connection weights from the input layer to the hidden layer are fine-tuned using gradient descent.

[0015] Preferably, the formation of the iterative suppression process includes: Before the next time window begins, load the optimized dynamic coupling model parameters; The newly acquired sonar signal sequence is processed using the updated dynamic coupling model; Record the evaluation indicators of the inhibition effect in the current time window; When the evaluation index exceeds the preset threshold, the model parameter saving operation is triggered.

[0016] Preferably, the algorithm further includes: Establish a tidal motion parameter prediction model to predict tidal motion parameters for future time windows based on historical tidal data; The predicted tidal motion parameters are input into the dynamic coupling model in advance to generate pre-compensation coefficients; Pre-compensation is applied before the sonar signal actually arrives.

[0017] Preferably, the tidal motion parameter prediction model includes: Construct a temporal prediction structure based on a long short-term memory network; Historical tidal motion parameter training data were organized using a sliding window approach. Learn the long-term periodicity and short-term fluctuation patterns of tidal motion through gating mechanisms; Output the predicted sequence of tidal motion parameters for multiple future time points.

[0018] Compared with the prior art, the beneficial effects of the present invention are: The dynamic suppression algorithm proposed in this invention, through its unique process design, demonstrates significant advantages in addressing the interference of tidal motion on sonar signals. The algorithm divides the continuous sonar signal stream into easily processed segments using a time-window processing approach, making the calculation and compensation of tidal effects for each segment more timely and accurate, avoiding the cumulative errors and response lag problems caused by long-term data processing. Within each window, the phase offset is calculated based on real-time acquired tidal motion parameters. This step directly links the tidal motion in the physical world with the phase changes in the signal domain, laying the physical foundation for subsequent accurate compensation. This transforms the compensation operation from a blind mathematical transformation into a correction with clear physical meaning.

[0019] The core innovation of this algorithm lies in establishing a dynamic coupling model between sonar signals and tidal motion. This model transforms the calculated phase shift into operable time-domain compensation coefficients, bridging the gap between tidal physical parameters and signal processing parameters. This conversion allows compensation to be performed directly in the time domain, resulting in high computational efficiency and facilitating engineering implementation and real-time processing. Spectral analysis of the initially suppressed sonar signal to extract residual interference features constitutes the algorithm's feedback loop. It acknowledges potential shortcomings in the initial model or new situations arising from dynamic environmental changes, and by actively detecting residual tidal interference patterns, it provides a data-driven basis for the model's self-optimization.

[0020] By adjusting the parameter weights of the dynamically coupled model based on residual features, the algorithm acquires self-learning and adaptive capabilities. The model is no longer fixed but dynamically adjusts its internal parameters according to the processing effect of the previous window, thus better adapting to potentially changing tidal conditions in the next time window. This online optimization mechanism significantly enhances the algorithm's ability to track and suppress non-stationary and nonlinear tidal disturbances. Finally, the optimized model is applied to subsequent time windows, forming a continuous, closed-loop iterative suppression process. This iterative mechanism ensures that the algorithm can continuously and gradually improve its suppression effect throughout the entire sonar operation, effectively addressing both long-term changes and short-term fluctuations in tidal motion.

[0021] The entire algorithm constitutes a complete closed-loop system of "perception-compensation-evaluation-optimization". It not only effectively reduces signal phase distortion and amplitude fluctuations caused by tidal motion, improving the fidelity of sonar signals, but more importantly, its adaptive characteristics reduce over-reliance on the accuracy of prior tidal models, enhancing the robustness of the sonar system in various complex, time-varying tidal environments. By improving signal quality, this algorithm indirectly improves the accuracy and reliability of subsequent applications based on sonar data, such as target detection, identification, localization, and seabed mapping. The algorithm design balances theoretical rigor and engineering feasibility, providing a practical solution for integrating efficient tidal interference suppression functions into actual sonar systems. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the workflow of the dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals as described in this invention. Figure 2 This is a structural framework diagram of the dynamic coupling model; Figure 3 A flowchart for converting phase offset into time-domain compensation coefficients; Figure 4 A flowchart for phase correction; Figure 5 A flowchart for adjusting the parameter weights of a dynamic coupling model. Detailed Implementation

[0023] Please see Figure 1 This invention provides a dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals. This algorithm integrates sonar signal processing with tidal motion modeling to achieve dynamic compensation and iterative optimization. The overall implementation scheme is as follows: The system collects sonar signal sequences and tidal motion parameter sequences for the current sea area. The sonar signal sequences are divided into multiple time windows to process real-time data streams. Within each time window, the phase shift of the sonar signal caused by tidal motion is calculated based on the tidal motion parameter sequence. A dynamic coupling model between the sonar signal and tidal motion is established, converting the phase shift into time-domain compensation coefficients. These time-domain compensation coefficients are applied to the sonar signal sequence for phase correction, generating a pre-suppressed sonar signal. The pre-suppressed sonar signal undergoes spectral analysis to extract residual tidal interference features. These residual tidal interference features are used to adjust the parameter weights of the dynamic coupling model, generating an optimized dynamic coupling model. The optimized dynamic coupling model is applied to the sonar signal processing in the next time window, forming a continuous iterative suppression process to ensure the algorithm adapts to tidal changes.

[0024] Example 1: After acquiring the sonar signal sequence and tidal motion parameter sequence of the current sea area, the sonar signal sequence is divided into multiple consecutive time windows for real-time processing. The length of each time window is set according to the sampling frequency of the sonar signal and the typical period of tidal change. Within each time window, the system extracts two key physical quantities from the tidal motion parameter sequence: the rate of water level change and the amplitude of periodic fluctuations. The rate of water level change describes the speed at which the tidal level rises and falls per unit time, while the amplitude of periodic fluctuations reflects the oscillation intensity of the tide within a specific period. The rate of water level change is directly used to construct the sonar signal propagation path length variation function. This function establishes a mathematical relationship between water level change and the actual propagation distance of the sound wave from the transmitter to the receiver. This relationship is usually expressed as a linear or nonlinear mapping, and its specific form depends on the deployment geometry of the sonar system and the tidal dynamics characteristics. When the sonar transmitter and receiver are deployed vertically (such as a fixed seabed sonar), the tidal water level change and the propagation path length change are linearly related, as shown in the following formula: When sonar transmitters and receivers are deployed at an angle (such as shipboard and underwater sonar), the geometric projection relationship needs to be considered, and the function formula is as follows:

[0025] Where: ΔL(t) is the change in propagation path length at time t (unit: meters), k is the path length coefficient (unit: s / m), v(t) is the rate of change of tidal water level at time t (unit: m / s), and θ is the angle between the sonar beam and the vertical direction (unit: radians).

[0026] The periodic fluctuation amplitude is fed into the sound wave propagation speed correction function for processing. Based on fluid mechanics and acoustic principles, this function converts the changes in seawater density, temperature, and salinity caused by tides into changes in the sound wave propagation speed in the medium. The outputs of the sonar signal propagation path length variation function and the sound wave propagation speed correction function are simultaneously fed into the phase error derivation module. This module combines the propagation path length variation and propagation speed variation, calculating the phase accumulation error of the sonar signal at the receiving moment through integration or accumulation. The phase accumulation error characterizes the total amount of sound wave phase lead or lag caused by tidal motion. The phase accumulation error is standardized by the normalization module. This module uses a minimum-maximum scaling method to map the phase accumulation error to the [0,1] interval or uses the Z-score method to convert it into a distribution with a mean of zero and a standard deviation of one, thus obtaining the standardized phase offset. When tidal parameters are continuously acquired, the phase accumulation error is calculated through integration: When tidal parameters are sampled discretely, the phase accumulation error is calculated by summing the samples:

[0027] in: It is the phase accumulation error. It is the carrier frequency of the sonar signal. It is a time variable. It is the reference propagation path length. It is the reference speed of sound. It is the change in the speed of sound. It is the sampling period.

[0028] The standardized phase offset is used as input to the dynamic coupling model, which generates accurate time-domain compensation coefficients using the standardized phase offset. The rate of water level change is obtained from real-time data streams from tidal monitoring sensors or tidal forecast databases. Tidal monitoring sensors collect water level data at a fixed frequency, and the instantaneous rate of change is calculated using differential methods. The amplitude of periodic fluctuations is obtained by analyzing the spectral characteristics of the tidal water level sequence within a time window. The amplitude values ​​of the principal periodic components are extracted using Fast Fourier Transform or Wavelet Transform. The construction of the sonar signal propagation path length variation function considers the relative positions of the sonar transmitter and receiver, as well as the geometric influence of tidal water level changes on the sound wave propagation path. The path length variation function is typically expressed as a linear function of the water level change rate or a higher-order polynomial obtained by fitting experimental data.

[0029] The sound wave propagation speed correction function is based on an empirical formula for the speed of sound, which includes parameters such as seawater temperature, salinity, and depth. The periodic fluctuations caused by tides indirectly affect the speed of sound by altering these parameters. The specific formula for the empirical speed of sound is as follows:

[0030] in: It is the speed of sound wave propagation. It's the seawater temperature. It's the salinity of seawater. It refers to the depth of the seawater.

[0031] The derivation of the phase accumulation error is based on the acoustic wave propagation time difference model. This model calculates the time difference between sound wave transmission and reception in the presence and absence of tides. Multiplying this time difference by the acoustic wave angular frequency yields the phase error. Normalization ensures that the phase offset has a uniform dimension and range under different time windows and sea area conditions, eliminating the influence of data scale differences on subsequent models. Standardized phase offsets facilitate the identification and processing of dynamically coupled models, and their use improves convergence speed and compensation accuracy.

[0032] The entire computation process is completed within a single time window, involving multiple steps such as data reading, parameter calculation, function mapping, and normalization. These steps are processed in real time through pipelined or parallel computing architectures. Assume that the sound wave propagation time is [time value missing] when tides are present. When tides do not exist (baseline state), the sound wave propagation time is Then the propagation time difference The calculation formula is:

[0033] in: It is the time difference of sound wave propagation. It is the actual propagation time of sound waves from transmission to reception when tides are present. It is the reference time for sound wave propagation when tides do not exist.

[0034] Based on the time difference of propagation With the angular frequency of sound waves Phase cumulative error The calculation formula is:

[0035] in: It is the phase accumulation error. It is the angular frequency of the sound wave. It's the time difference in transmission.

[0036] The phase accumulation error is calculated using the minimum-maximum scaling method. Mapped to The interval is used to obtain the standardized phase offset. The formula is:

[0037] in: It is the standardized phase offset. It is the phase cumulative error at a certain sampling point within the current time window. It is the minimum value of the phase cumulative error of all sampling points within the current time window. It is the maximum value of the cumulative phase error of all sampling points within the current time window.

[0038] The time window is aligned with the data block size of the sonar signal, which is optimized based on the processor's computing power and memory capacity (typically 256-1024 sampling points). The rate of water level change is calculated using the central difference method (e.g., v(t) = [h(t+Δt) - h(t-Δt)] / (2Δt), where h is the water level value) or least squares fitting of the instantaneous derivative to reduce the impact of measurement noise. Extraction of the periodic fluctuation amplitude may require preprocessing with moving averages (window length 0.5-2 tidal cycles) or bandpass filtering (passband 1-24 hours) to enhance the significance of the tidal periodic component.

[0039] The path length variation function of sonar signals may take different forms in water depths <200 meters and deep-sea environments (water depth >1000 meters): in shallow-sea environments, the influence of tides on path length is more significant (because the proportion of paths reflected from the seabed is high, the path length variation caused by tides is 1.5-2 times that of water depth variation; in deep-sea environments, the proportion of direct waves is high, and the path length variation is approximately equal to the water depth variation). The sound wave propagation speed correction function needs to be calibrated periodically. The calibration process involves comparing the measured sound velocity (provided by a temperature, salinity, and depth gauge) with the model predictions to adjust the parameters (adjustment step size 0.01 m / s). The derivation of phase accumulation error needs to consider the refraction effect of the sound wave propagation path. The refraction effect introduces additional phase error in horizontally non-uniform water bodies (the error amount is usually <5%). The parameters of the normalization module can be adaptively adjusted based on historical data (the sliding window size is 5-10 tidal cycles) to adapt to the environmental characteristics of different sea areas. The standardized phase offset output interface is fully compatible with the input layer of the dynamic coupling model (data format is a 32-bit floating-point array), ensuring seamless data transfer between the two modules.

[0040] In the real-time processing flow, the tidal motion parameter sequence for each time window is cached in a circular buffer. The capacity of the circular buffer is set to twice the length of the time window (allowing redundant storage for one window). New data overwrites old data to achieve continuous processing. The sonar signal sequence is sampled by an analog-to-digital converter (16-24 bit sampling precision) and stored in a temporary memory area. This temporary memory area is connected to the computing unit via a high-speed bus (such as PCIe 4.0). The phase offset calculation module is implemented by a digital signal processor (DSP) or application-specific integrated circuit (ASIC). The DSP performs floating-point operations and function evaluation (operation latency requirement <10ms). The standardized phase offset is transmitted to the input port of the dynamic coupling model via the data bus. The data transmission process has CRC check and retransmission mechanisms to ensure reliability (bit error rate <10%). -6 ).

[0041] The real-time nature of water level change rates requires tidal monitoring data to have low latency (end-to-end latency <500ms), which is achieved through local sensor networks (such as LoRaWAN) or high-speed data links (such as fiber optics). Calculating the periodic fluctuation amplitude may involve frame overlap processing in spectral analysis (overlap rate 50%). Frame overlap processing improves frequency resolution but increases computational load (CPU utilization increases by approximately 30%). The parameters of the sonar signal propagation path length variation function can be determined through field experiments using GPS positioning (accuracy ±0.5m) and depth measurement equipment (accuracy ±0.1m) to calibrate geometric relationships. In addition to tidal data, the input parameters of the acoustic propagation velocity correction function may also integrate real-time measurements from a temperature, salinity, and depth profiler (sampling frequency 0.1-1Hz). The phase accumulation error derivation module requires high-precision clock synchronization (synchronization error <1μs), which ensures accurate measurement of the acoustic wave transmission and reception times. The scaling factor of the normalization processing module can be updated online (update cycle of 1 hour). The online update mechanism dynamically adjusts the normalization range based on the recent data distribution.

[0042] The standardized phase offset calculation process is embedded in the task scheduling of the real-time operating system (RTOS). The task scheduling assigns a high priority (priority level 2-3) to the phase offset calculation task to meet real-time constraints (deadline <20ms). The data integrity of the tidal motion parameter sequence is guaranteed by a checksum mechanism (such as MD5), which detects errors or loss during data transmission (100% detection rate). The split point of the sonar signal sequence is selected to avoid the moment of signal transients. The split point is usually located in the signal interval or the plateau phase (determined by energy detection method: signal energy is below 10% of the average energy) to reduce the truncation effect. The length of the time window is designed considering the typical time scale of tidal motion. The duration of the window is determined by the period of semi-diurnal tide (period 12.42 hours) or diurnal tide (period 24.84 hours) (usually 1 / 4-1 / 8 of the period). The implementation of the entire Example 1 relies on multi-level collaboration of multi-source data fusion, physical model calculation, and standardization processing. Multi-level collaboration ensures the accuracy (error <3%) and robustness of the phase offset estimation (stable operation even at sea state 3).

[0043] Example 2: See Figure 2 and Figure 3The dynamic coupling model is based on a multi-layer neural network structure. This structure uses tidal motion parameters as input layer nodes (number of nodes = 2 × feature dimension, where the feature dimension includes 5-8 parameters such as water level change rate and fluctuation amplitude), and phase correction coefficients as output layer nodes (number of nodes = number of sonar signal sampling points / time window). The input layer receives the standardized phase offset calculated in Example 1, which includes phase information derived from the water level change rate and periodic fluctuation amplitude. The hidden layer contains 3-5 nonlinear transformation layers, which introduce the model's expressive power through activation functions (such as ReLU or LeakyReLU). Historically collected tidal motion parameter sequences and corresponding sonar signal phase errors constitute the training dataset, covering tidal patterns under different seasons (spring / summer / autumn / winter) and different meteorological conditions (sunny / rainy / typhoon) (sample size ≥ 10). 5 (Group). The time-backpropagation algorithm is used to train multi-layer neural network structures. It calculates the gradient between the predicted error and the actual error of the output layer phase correction coefficients, and propagates this gradient back from the output layer to the input layer to adjust the network weights (initial learning rate of 0.001, using an exponential decay strategy). The training process iterates until the predicted error of the output layer phase correction coefficients falls below a set threshold (mean squared error < 10). -4 The threshold is set based on the phase tolerance of the sonar system (typically ±5°). The trained network parameters and connection weights are stored in non-volatile memory (such as EEPROM), which forms a loadable, dynamically coupled model.

[0044] When the phase offset is input into the input layer of the dynamic coupling model, the input layer nodes pass the values ​​to the hidden layers. The hidden layers of the dynamic coupling model perform nonlinear transformation processing, which maps the input data to a high-dimensional feature space (typically 4-8 times the dimension of the input layer) using either the Sigmoid function (suitable for scenarios with limited output range) or the ReLU function (to alleviate gradient vanishing in deep networks). The hidden layer output generates an intermediate feature representation, which captures the complex correlation patterns between tidal motion and phase error (such as nonlinear coupling and time-varying delay). Based on the intermediate feature representation and the connection weights of the output layer, the connection weights of the output layer are calculated into a temporal compensation coefficient vector through matrix multiplication. The temporal compensation coefficient vector contains compensation values ​​corresponding one-to-one with the sonar signal sampling points (accuracy ±0.001). The temporal compensation coefficient vector undergoes time alignment processing, which uses linear interpolation or spline interpolation methods to ensure that the vector length perfectly matches the time window of the sonar signal sequence (interpolation error <1%).

[0045] The construction of a multi-layer neural network requires determining the network depth and the number of nodes. The network depth is selected based on the complexity of tidal motion (3-5 layers in complex nearshore environments, 2-3 layers in open sea areas). The number of nodes in the input layer corresponds to the number of tidal motion parameters, including phase shift and related derived features (such as rate of change and second derivative). The number of nodes in the output layer is equal to the dimension of the phase correction coefficients to be generated (matching the sonar signal sampling rate). The weights of the hidden layers are initialized using the Xavier initialization method (to ensure consistent variance of activation values ​​across layers and avoid gradient vanishing), which maintains a stable distribution of activation values. The construction of the training dataset requires a large amount of historical measurement data, which is cleaned (removing outliers, such as using the 3σ criterion) and labeled (manually annotating the true phase error values). The forward propagation phase of the time backpropagation algorithm calculates the network output, involving a linear combination of weights and input data, and activation function transformation. Error calculation uses the mean squared error loss function (L2 loss), which measures the deviation between the predicted phase correction coefficients and the true values. Gradient descent optimization algorithms (such as Adam or RMSprop) update network weights. Gradient descent optimization algorithms use momentum terms (β=0.9) or adaptive learning rate strategies to accelerate convergence.

[0046] Training the dynamically coupled model requires high-performance computing resources, such as GPU clusters (≥16GB VRAM per node), which shorten training time (typical training cycle <72 hours). The trained dynamically coupled model is deployed on a sonar signal processing system, which uses an application programming interface (API) to call the model for inference (inference latency <5ms / window). Before inputting phase offsets into the dynamically coupled model, data format conversion is required, transforming floating-point numbers into tensor structures (dimensions [1, N], where N is the number of input features). Nonlinear transformations of hidden layers may include dropout regularization, which randomly disables some nodes during training (dropout rate 0.2-0.5) to prevent overfitting. The dimensionality of intermediate feature vectors is much higher than the original input; the dimensionality of intermediate feature vectors is reduced using principal component analysis (PCA) and then visualized (retaining 95% variance). The generation of the temporal compensation coefficient vectors needs to ensure numerical stability, which is maintained through gradient pruning (gradient norm ≤5) and weight normalization techniques.

[0047] Time alignment considers the synchronization issue between the sonar signal sampling clock and the tidal data acquisition clock. Clock synchronization is solved using timestamp alignment algorithms (such as linear interpolation to compensate for time differences). The update mechanism of the dynamically coupled model supports online learning, which uses newly acquired data in real time to fine-tune model parameters (learning rate decays to 1 / 100 of the initial value). The choice of activation function in the multi-layer neural network structure affects model performance; the selection of activation function is achieved by comparing the fitting effects of different functions through cross-validation (ReLU outperforms Sigmoid in deep networks). Data augmentation techniques are used to expand the training dataset by adding Gaussian white noise (signal-to-noise ratio 20-30dB) or a ±5% time offset to the original tidal sequence to generate new samples. The time backpropagation algorithm is implemented using a deep learning framework, such as TensorFlow or PyTorch, which provides automatic differentiation functionality. The dynamically coupled model is stored in a binary file format (such as HDF5), which contains the network topology (number of layers, number of nodes) and weight matrix (32-bit floating-point precision).

[0048] The determination of the number of hidden layer nodes involves balancing model complexity and overfitting. This balance is monitored through validation set performance (node ​​additions are stopped when the validation set error increases for five consecutive epochs). Input layer data is normalized to maintain consistency with the output standard of Example 1 (range [0,1]). Data normalization stabilizes the model training process numerically (leading to faster convergence of the loss function). The scale of the output layer phase correction coefficients is constrained to the range [0,1] using the Sigmoid function. This scale constraint prevents excessively large absolute values ​​in the compensation coefficients (preventing signal distortion). Labeling of historical training data requires accurate sonar phase error measurement, which is obtained through reference signal comparison (using a calibration signal with known phase). The batch size of the time backpropagation algorithm affects training stability. A larger batch size (32-128 samples / batch) is chosen based on memory capacity to improve parallel efficiency. The inference speed of the dynamically coupled model is optimized through layer fusion, which combines multiple consecutive linear operations (convolution + activation) into a single computational step (improving inference speed by 30-50%).

[0049] When inputting phase offsets into the dynamically coupled model, a sliding window averaging (window length typically 3-5 sampling points) may be required. This averaging smooths out instantaneous fluctuations using arithmetic or weighted averaging (weight coefficients [0.2, 0.6, 0.2]), improving model robustness (reducing noise interference by 15-20%). Feature representations in hidden layers can be enhanced through attention mechanisms. These mechanisms (e.g., multi-head self-attention, number of heads = 4-8) assign higher weights to features at important time points (weight values ​​range [0,1], normalized using softmax). Time alignment of the temporal compensation coefficient vector requires interpolation point calculation. The number of interpolation points is determined based on the ratio of the sonar signal sampling rate (e.g., 48kHz) to the tidal data sampling rate (e.g., 1Hz) (typically 48000:1, requiring 48000 coefficient points to be interpolated). Version management of the dynamically coupled model records each parameter update (version number format V1.YYMMDD.HHMM). Version management allows for rollback to previous stable versions in case of failure (retaining the 5 most recent versions). Visualization tools for multi-layer neural network structures aid in debugging. These tools (such as TensorBoard) display feature map heatmaps (darker colors indicate higher feature importance) to analyze the model's focus. An early stopping mechanism during training prevents overfitting; training is terminated when the validation set error increases for five consecutive epochs (patience=5, min_delta=1e-5).

[0050] The practical deployment of the dynamically coupled model needs to consider computational latency constraints. These constraints require that the inference time for a single iteration be less than 1 / 10 of the sonar signal time window length (e.g., if the window length is 1 second, the inference time must be <100ms). The input to the phase offset may contain sequences of multiple time steps (typically 5-10 time steps). These sequences are captured using recurrent neural network structures (such as LSTM or GRU) to capture temporal dependencies (the number of memory units is twice the number of input features). Residual connections in hidden layers improve gradient flow, and through identity mapping, they make deep network training more stable (gradient descent speed improved by 20-30%). Post-processing of the temporal compensation coefficient vector may include low-pass filtering (cutoff frequency 0.1-1Hz), which eliminates high-frequency noise in the coefficient sequence (noise suppression ratio >25dB). Porting the dynamically coupled model to heterogeneous computing platforms requires quantization, which converts 32-bit floating-point weights to 8-bit integers (precision loss <2%) to reduce model size (compression ratio 4:1). The class balance of the training data is adjusted by oversampling, which (SMOTE algorithm) increases the number of samples in the minority class tidal pattern (making the sample ratio of each class close to 1:1).

[0051] Interpretive methods for the dynamic coupling model analyze feature importance. Interpretive methods, such as SHAP (SHapley Additive exPlanations), display the contribution of each input parameter to the output (value range [-1, 1], positive values ​​indicate positive influence, negative values ​​indicate negative influence). An outlier detection mechanism is implemented before the phase offset is input into the dynamic coupling model. This outlier detection mechanism (based on the 3σ criterion or the isolated forest algorithm) eliminates erroneous data caused by sensor failures (detection accuracy > 95%). Grouped convolution operations in the hidden layers reduce the number of parameters. Grouped convolution operations (number of groups = number of input channels / 2) process multi-channel tidal parameters in parallel (reducing parameters by 50% and computation by 40%). The generation results of the temporal compensation coefficient vector are verified through simulation. The simulation verifies the rationality of the coefficients under typical tidal scenarios (such as spring tides / neap tides / storm surges) (compensation error must be < 5%). The long-term stability of the dynamic coupling model is maintained through regular retraining (period 1-3 months) to adapt to climate changes in the marine environment (seasonal changes in water temperature / salinity). Pruning optimization of multi-layer neural network structures reduces model size. Pruning optimization (based on L1 regularization or Taylor expansion importance evaluation) removes connection weights that have little impact on the output (pruning rate 30-50%, accuracy loss <1%).

[0052] Example 3: See Figure 4 The pointwise multiplication of the time-domain compensation coefficient vector with the sonar signal sequence is performed in the digital signal processor. The pointwise multiplication multiplies each sonar signal sample point with the corresponding time-domain compensation coefficient scalar. The multiplication result is fed into the Fast Fourier Transform (FFT) module, which converts the time-domain signal into a frequency-domain representation. The frequency-domain representation contains frequency components in complex form, each with amplitude and phase attributes. A phase rotation operation is applied to each frequency component in the frequency domain. The angle of the phase rotation operation is determined by the time-domain compensation coefficient vector through a linear mapping relationship. The phase rotation operation is implemented through complex multiplication, which multiplies the frequency component by a rotation phase factor. The calculation of the rotation phase factor requires converting the time-domain compensation coefficients into corresponding rotation angles; this conversion relationship is defined by the following formula:

[0053] in This represents the rotation angle (in radians) of the k-th frequency component. This represents the k-th coefficient value in the time-domain compensation coefficient vector. It is a proportionality factor (dimensionless). It is the length of the Fast Fourier Transform. The frequency domain representation after phase rotation is reconstructed into a time domain signal by the Inverse Fast Fourier Transform, and the output of the Inverse Fast Fourier Transform is the sonar signal after preliminary suppression.

[0054] The pre-suppressed sonar signal is compared with the original sonar signal using a differential operation. The differential operation generates a residual error signal. The differential operation formula is as follows:

[0055] in: It is a residual error signal. It is the original sonar signal. It is the compensated sonar signal.

[0056] The residual error signal is processed by wavelet packet decomposition. Wavelet packet decomposition uses the Daubechies wavelet basis function to decompose the signal into multiple sub-bands. The decomposition formula is as follows:

[0057] Among them, the Daubechies wavelet basis functions Satisfies the two-scale equation:

[0058] in: It is the first Layer Wavelet packet coefficients of each sub-band It is the number of decomposition levels. It is a sub-sequence number. These are Daubechies wavelet basis functions. It is a scaling function. These are wavelet / scale filter coefficients.

[0059] Each sub-band signal corresponds to a specific frequency range. The energy distribution of the sub-band signal is obtained by calculating the sum of squares, and the specific calculation formula is as follows:

[0060] in: It is the first Layer-band signal energy, It is the first Number of sub-bands.

[0061] The zero-crossing rate feature counts the number of times each sub-band signal crosses the zero point per unit time. The energy distribution and zero-crossing rate feature are combined to form a multi-dimensional feature vector. The residual tidal interference feature vector encapsulates the tidal interference patterns that were not completely suppressed.

[0062] The implementation of pointwise multiplication requires consideration of data alignment, which necessitates that the length of the time-domain compensation coefficient vector be exactly the same as the sonar signal sequence. The length of the Fast Fourier Transform (FFT) is chosen to be an integer power of 2, allowing for radix-2 optimization to improve computational efficiency. Storage of the frequency domain representation requires a complex memory buffer, which alternately stores the real and imaginary parts. The angular mapping for phase rotation operations must avoid phase aliasing, which occurs when the angle exceeds ±π radians. The rotation phase factor is generated using Euler's formula, which converts the angle into a complex exponential form. The output of the Inverse Fast Fourier Transform (IFT) requires amplitude normalization to maintain signal energy conservation.

[0063] The time alignment accuracy of differential operations affects the quality of the residual error signal; time alignment accuracy can be achieved at the subsampling level through interpolation methods. The number of layers in wavelet packet decomposition determines the frequency resolution; increasing the number of layers improves frequency resolution but decreases time resolution. The order of the Daubechies wavelet is chosen to balance time-frequency localization characteristics; higher-order wavelets have better frequency localization. Subband energy calculation uses a sliding window method, with the sliding window length related to the tidal period. Zero-crossing rate statistics use thresholding to avoid false zero-crossings caused by noise. The dimensionality of the eigenvectors is optimized through principal component analysis, which preserves the main variance components.

[0064] Each element of the time-domain compensation coefficient vector is multiplied and accumulated with the sonar sampling point. This multiplication and accumulation operation can be implemented in parallel at the hardware level using multiply-accumulators. The butterfly operation mode of the Fast Fourier Transform is suitable for a pipelined architecture, which processes multiple butterfly stages simultaneously. The complex multiplication for frequency-domain phase rotation requires four real multiplications and two additions, as shown in the following formula:

[0065] Among them, rotation angle Obtained by mapping from time-domain compensation coefficients:

[0066] in: These are time-domain compensation coefficients. It is a frequency domain signal (before / after compensation). It is the frequency point number. It is the number of decomposition levels. It is the frequency domain phase rotation angle. It is an angle scaling factor. It is the Fourier transform length.

[0067] Complex number multiplication can be converted into a coordinate rotation digital computer algorithm, the specific formula of which is:

[0068] in, , .

[0069] in: It is the real / imaginary part of the frequency domain signal. It is the real / imaginary part of the frequency domain signal after rotation.

[0070] Frequency domain filtering before the inverse fast Fourier transform can remove out-of-band noise, which may originate from electronic devices. The amplitude of the differential signal reflects the suppression effect; a large differential amplitude indicates strong residual interference. The tree structure of wavelet packet decomposition covers the entire frequency band, and the tree structure selects the most representative sub-band through the optimal basis algorithm.

[0071] The energy distribution calculation includes the energy proportion of each sub-band, which indicates the concentrated region of interference in the frequency domain. The time variation pattern of the zero-crossing rate reflects the non-stationary characteristics of the interference, which are analyzed through multi-time-window statistical analysis. Eigenvector normalization ensures uniformity of dimensions across all dimensions; the normalization process employs a max-min scaling method. The scaling factor α in the phase rotation angle formula requires calibration, which uses a test signal with a known phase shift. The transform length N in the formula determines the interval between frequency components, which affects the accuracy of the phase rotation.

[0072] The range of the time-domain compensation coefficient vector is constrained to the interval [0,1], and this range constraint is achieved using the Sigmoid function. The input to the Fast Fourier Transform (FFT) requires window function preprocessing to reduce spectral leakage. The conjugate symmetry of the frequency domain representation is used to verify data integrity; this conjugate symmetry exists in the spectrum of the real signal. Parallelization of the phase rotation operation allows simultaneous execution at multiple frequency points, utilizing a single-instruction multiple-data architecture. The output of the inverse FFT is truncated to remove artifacts introduced by circular convolution. Spectral analysis of the differential signal reveals the periodicity of residual interference, which may originate from unmodeled tidal harmonics.

[0073] Boundary effects of wavelet packet decomposition are mitigated by symmetric continuation, which maintains signal continuity. Logarithmic transformation of subband energy enhances the dynamic range and compresses large amplitude differences. Joint analysis of zero-crossing rate and energy distribution identifies interference types; clustering algorithms are used to classify interference patterns. Dimensionality reduction of eigenvectors preserves key discriminant information; this reduction is achieved through linear discriminant analysis. The coefficient index k in the phase rotation angle formula corresponds to the frequency index, which is linearly related to the physical frequency. The parameters α and N in the formula are stored in a configuration file, allowing for on-site adjustment without modifying the code.

[0074] Multiplication of the time-domain compensation coefficient vector with the sonar signal may introduce quantization errors, which can be reduced by increasing the word length. The floating-point precision of the Fast Fourier Transform (FFT) affects phase calculations; single-precision or double-precision floating-point numbers should be used. The numerical stability of frequency-domain phase rotation requires controlling the angle range, which is limited to [-π, π] to avoid large-angle rotations. The scaling factor of the Inverse Fast Fourier Transform compensates for the transform gain; a scaling factor of 1 / N maintains energy conservation. The time-domain integral of the differential signal may reveal phase drift, which can be tracked using Kalman filtering. The optimal basis selection for wavelet packet decomposition is based on the entropy criterion, which minimizes information redundancy. The time derivative of subband energy shows the energy variation trend, which is related to tidal rhythms. The frequency-domain distribution of the zero-crossing rate reflects the modulation characteristics of the interference, which can be extracted through envelope analysis. The time series of eigenvectors can be used for long-term pattern learning, which is achieved through recurrent neural networks.

[0075] Example 4: See Figure 5 The residual tidal disturbance feature vector *v* is mapped to the hidden layer space of the dynamically coupled model through a linear transformation. The linear transformation formula is *h = W·v + b*, where *W* is the weight matrix (dimension [number of hidden layer nodes, feature vector dimension]), and *b* is the bias vector (dimension [number of hidden layer nodes, 1]). The weight matrix is ​​determined by the input dimension of the hidden layer nodes. The correlation coefficient between the activation value *a* of the hidden layer nodes and the residual tidal disturbance feature vector *v* is calculated using the Pearson product-moment correlation coefficient, with the formula *r = Cov(a,v) / (σ*). a ·σ v The Pearson product-moment correlation coefficient r measures the degree of linear correlation between two variables (range [-1, 1]). The connection weights Δw = η·r·a·v from the hidden layer to the output layer are adjusted based on the correlation coefficient. T (T represents transpose), the weight adjustment is proportional to the magnitude of the correlation coefficient (η is the learning rate, typically 0.001-0.01). The connection weights from the input layer to the hidden layer are fine-tuned using stochastic gradient descent. The learning rate of stochastic gradient descent is dynamically adjusted according to the gradient magnitude of the loss function surface (the learning rate decreases when the gradient magnitude is >1 and increases when it is <0.1).

[0076] The optimized dynamic coupling model is loaded from non-volatile memory before the start of the next time window. Non-volatile memory stores the latest version of the model parameters. The updated dynamic coupling model processes newly acquired sonar signal sequences, including phase offset calculation, temporal compensation coefficient generation, and phase correction. The suppression effect evaluation index for the current time window is recorded in the operation log, which includes a timestamp, evaluation index value, and model version number. When the evaluation index exceeds a preset threshold, a model parameter save operation is triggered, writing the parameters currently in memory to persistent storage.

[0077] The process of mapping residual tidal disturbance feature vectors to the hidden layer space involves matrix multiplication, which projects the feature vectors from the original dimension (e.g., 64-dimensional) to the hidden layer dimension (e.g., 256-dimensional). The activation values ​​of hidden layer nodes are calculated using the Sigmoid activation function a = 1 / (1+e^(-1 / 2)). -x The Sigmoid activation function compresses the weighted input into the [0,1] interval. The correlation coefficient calculation requires standardization, which converts the activation values ​​and feature vectors to zero mean and unit variance (z = (x - μ) / σ, where μ is the mean and σ is the standard deviation). The direction of weight adjustment is determined by the sign of the correlation coefficient; positive correlation (r>0.3) strengthens connection weights (Δw>0), while negative correlation (r<-0.3) weakens connection weights (Δw<0). The number of iterations in stochastic gradient descent is controlled by an early stopping strategy, which terminates training when the validation set error increases for three consecutive epochs (patience=3).

[0078] The loading process of the dynamically coupled model includes parameter verification and memory allocation. Parameter verification checks file integrity and version compatibility. Newly acquired sonar signal sequences undergo preprocessing steps, including denoising and normalization. The suppression effect evaluation index uses the signal-to-noise ratio (SNR) improvement, which compares the change in signal quality before and after processing. The triggering conditions for saving model parameters are configurable, including threshold comparison and duration determination.

[0079] Dimension reduction in hidden layer spatial mapping may lose some information; however, it preserves most of the variance by retaining principal components. Significance testing of correlation coefficients excludes random correlations; the p-value is calculated using a t-distribution. The magnitude of weight adjustments is scaled by the learning rate, which is gradually reduced using a time decay strategy. The batch size in stochastic gradient descent affects the parameter update frequency; a larger batch size is chosen based on available memory. The loading time of dynamically coupled models affects system real-time performance; loading time is reduced using parameter compression techniques.

[0080] Evaluation metrics exceeding preset thresholds require smoothing, which uses moving averages to eliminate instantaneous fluctuations. Model parameter saving employs atomic writes to prevent data corruption. The update frequency of residual tidal interference feature vectors is synchronized with model adjustments, typically once per time window. Overfitting is monitored by analyzing the distribution of hidden layer node activation values, achieved through activation value histograms. The computational complexity of the correlation coefficient is O(n), linearly related to the number of nodes.

[0081] Network stability needs to be maintained during weight adjustment, which is achieved through weight constraint regularization. The momentum term of stochastic gradient descent accelerates convergence and retains historical update directions. The dynamically coupled model supports hot-swapping, allowing the new model to be loaded while the old model continues to serve. The sonar signal sequence cache management employs a first-in, first-out (FIFO) strategy to ensure data freshness. The evaluation metric recording system supports querying and visualization, which are used for performance analysis.

[0082] Version management for model parameter saving operations uses incremental numbering (e.g., V1.YYMMDD.HHMM), which facilitates backtracking and recovery (retaining the 10 most recent versions). The weights of the residual tidal interference feature vector mapping are trainable, and weight training is optimized using the Backpropagation-Time Trial (BPTT) algorithm (learning rate 0.001, 500 iterations). Sparsity reduction of hidden layer node activation values ​​reduces computation; sparsity is induced by L1 regularization (λ=0.001-0.01) (sparseness ratio 30-50%). Correlation coefficient calculation uses vectorization operations, which are accelerated using Single Instruction Multiple Data (SIMD) instructions (improving computational efficiency by 2-4 times). Gradient clipping for weight adjustments prevents explosion, and gradient clipping limits the maximum value of the gradient norm (usually set to 5.0).

[0083] The parallel implementation of stochastic gradient descent utilizes multi-core processors, enabling data parallelism (split by sample, batch size 64-128) or model parallelism (split by layer, suitable for ultra-deep networks). The loading progress display of the dynamically coupled model provides user feedback, indicated by progress bars or percentages. Timestamp synchronization of the sonar signal sequences is crucial, and this synchronization is calibrated using a network time protocol. Historical data for evaluation metrics can be exported for analysis in CSV and JSON formats. The backup strategy for model parameter saving includes multiple copies stored in different physical locations.

[0084] The table below shows the main parameters used in the parameter tuning process of the dynamic coupling model and their value ranges:

[0085] The choice of the number of hidden layer nodes needs to balance expressive power and computational cost. A higher number of nodes (e.g., 200) increases model complexity (parameters increase by 50%) but improves fitting ability (error decreases by 15%). The initial learning rate affects convergence speed; an excessively large learning rate (>0.1) causes loss function oscillations (fluctuation amplitude >20%), while an excessively small learning rate (<0.001) results in slow convergence (increases the number of iterations by 3 times). Setting the correlation coefficient threshold excludes weakly correlated connections and avoids over-responding to random fluctuations (set the weight adjustment to 0 for connections with |r|<0.3). The determination of the evaluation metric window size considers temporal continuity; an excessively large window (>20) delays the response (lags by 10-20 minutes), while an excessively small window (<5) is sensitive to noise (fluctuations increase by 25%). The parameter retention threshold configuration controls the model update frequency; a higher threshold (e.g., 0.95) requires stricter performance standards (only retaining the top 5% of models).

[0086] The projection matrix of the residual tidal interference feature vector mapping requires orthogonality constraints. These constraints are achieved through Gram-Schmidt orthogonalization, ensuring that the column vectors of the projection matrix are pairwise orthogonal (inner product < 1e-6), preserving the relative relationships between vectors. Batch normalization of hidden layer node activation values ​​improves training stability. Batch normalization adjusts the activation value distribution (mean μ=0, standard deviation σ=1, scaling parameter γ=1, offset parameter β=0). Rolling calculation of correlation coefficients updates the historical window, using a sliding window (window size 5-10 cycles) to maintain the latest data. The magnitude decay of weight adjustments increases with the number of iterations, employing a simulated annealing strategy (decay factor 0.99 / iteration). Stochastic gradient descent gradient accumulation supports mini-batch training; parameters are updated after gradient accumulation (accumulating for 4-8 forward propagations), reducing memory usage.

[0087] The loading failure handling of the dynamically coupled model includes a retry mechanism, which automatically retryes (up to 3 times, 100ms interval) in case of temporary errors (such as I / O timeouts). Sonar signal sequence loss detection is implemented via heartbeat packets, which periodically (every 100ms) check the continuity of the data stream (a timeout of 200ms is considered a loss). Systematic drift of evaluation metrics requires baseline correction, which deducts the impact of environmental changes (such as seasonal water temperature variations) (baseline values ​​are updated monthly). Integrity verification of model parameter storage operations uses checksums, which (CRC32 algorithm) detect bit errors during storage (error rate <1e-9). Outlier pruning of residual tidal interference feature vectors avoids interference; outlier pruning removes data exceeding three standard deviations (μ±3σ) (pruning rate <5%).

[0088] Visualization of hidden layer node activation values ​​helps understand model behavior. Visualization is achieved by reducing the dimensionality to 2D using t-SNE or UMAP to display activation patterns (color-coded node importance). Time series analysis of correlation coefficients reveals pattern changes. Time series analysis uses an autoregressive model (AR(3)) to predict trends (prediction error <10%). Momentum coefficients for weight adjustment maintain consistency in the update direction. Momentum coefficients are typically set to 0.9 (to accelerate convergence and suppress oscillations). Adaptive learning rate algorithms for stochastic gradient descent adapt to different parameters. Adaptive learning rate algorithms such as Adam (β1=0.9, β2=0.999, ε=1e-8) adjust the learning rate for each parameter. Loading priority of dynamically coupled models is configurable. Priority settings (levels 0-10) ensure that critical models (such as the primary model) are loaded first (loading delay <100ms).

[0089] The time alignment of the sonar signal sequence uses Dynamic Time Warping (DTW), which processes variable-length sequences (window size set to 10% of sequence length, distance metric using Euclidean distance). Outlier detection for evaluation metrics marks anomalies using the Isolation Forest algorithm (contamination=0.05, 100 trees). Model parameters store metadata recordings of operation information, including timestamps, operator identifiers, and hardware environment (CPU / GPU model). Dimensional expansion of the residual tidal interference feature vector includes interactive features, constructed through feature cross-referencing (e.g., water level change rate × fluctuation amplitude, temperature × salinity). Attention weights on hidden layer node activation values ​​highlight important nodes, and these weights (normalized via softmax) learn node contributions (weight sum equal to 1). Correlation coefficient filtering smooths random fluctuations using a low-pass filter (cutoff frequency 0.1Hz, order 4). Sparse constraints on weight adjustment induce feature selection, implemented using Lasso regularization (λ=0.005) (non-zero weight percentage <40%). In the warm-up phase of stochastic gradient descent, the learning rate is gradually increased. During the warm-up phase (the first 1000 steps), the learning rate is linearly increased from 1 / 10 of the initial value to the target value to avoid initial instability. The loading and validation of the dynamically coupled model includes an integrity check, which verifies the parameter structure (matching the number of layers and nodes) and the range of values ​​(weights within [-5,5]).

[0090] Example 5: Tidal Motion Parameter Prediction Model Construction Based on Long Short-Term Memory (LSTM) Network Architecture. The LTM network architecture includes an input gate, a forget gate, an output gate, and a cell state mechanism. Historical tidal motion parameter training data is organized using a sliding window, which continuously covers the time series data at fixed time steps. The gating mechanism learns the long-term periodicity and short-term fluctuation patterns of tidal motion, controlling information flow through sigmoid and tanh functions. The LTM network architecture outputs a predicted sequence of tidal motion parameters for multiple future time points, including parameters such as the rate of water level change and the amplitude of periodic fluctuations. The predicted tidal motion parameters are pre-input into a dynamic coupling model, which generates a pre-compensation coefficient vector. The pre-compensation coefficients are applied before the actual arrival of the sonar signal, and this pre-compensation operation uses a digital filter to achieve phase lead compensation.

[0091] The training of the Long Short-Term Memory (LSTM) network architecture uses the temporal backpropagation algorithm, which calculates gradients through temporal expansion. The sliding window size covers at least two tidal cycles, with the tidal cycle determined to be 12 or 24 hours depending on the sea area characteristics. The forgetting gate in the gating mechanism determines the proportion of historical information retained, calculating a forgetting factor based on the current input and the previous state. The input gate controls the amount of new information added, adjusting the update rate of candidate cell states. The output gate controls the output proportion of hidden states, filtering the information to be transmitted at the current moment. Cell states act as carriers of long-term memory, and information is linearly transferred through the gating mechanism.

[0092] The length of the prediction sequence is aligned with the time window of the sonar signal processing, and the prediction sequence contains tidal parameters for the next 5-10 time points. After receiving the prediction parameters, the dynamically coupled model performs forward inference, which generates pre-compensation coefficients through matrix operations. The pre-compensation operation completes coefficient loading before sonar signal acquisition, and the coefficients are loaded into the registers of the digital signal processor. The input dimension of the Long Short-Term Memory (LSTM) network architecture corresponds to the number of tidal parameters, including features such as water level height and trends. The output dimension is proportional to the number of prediction time points and is mapped to the target dimension through a fully connected layer.

[0093] The step size of the sliding window determines the data update frequency; the step size setting needs to balance computational load and prediction timeliness. The parameters of the gating mechanism are learned through training, using mean squared error as the loss function. Cell state updates include candidate value computation, generated from the current input and the previous hidden state. The accuracy of the predicted sequence is improved through residual connections, which alleviate the gradient vanishing problem. The inference latency of the dynamically coupled model needs optimization, accelerated by layer fusion and quantization. The application of pre-compensation coefficients needs to consider propagation latency, which is compensated for through timestamp synchronization.

[0094] The number of layers in the Long Short-Term Memory (LSTM) network architecture is chosen based on complexity; increasing the number of layers improves expressive power but increases computational cost. Data preprocessing in the sliding window includes normalization, which scales parameters from different scales to a uniform range. The gating mechanism utilizes vectorized operations, leveraging the parallel computing advantages of GPUs. Post-processing of the predicted sequence includes smoothing filtering, which eliminates abrupt changes in the prediction results. The input interface of the dynamically coupled model requires data format conversion, which encapsulates the predicted sequence into a tensor structure. The timing control of the pre-compensation operation is triggered by a timer synchronized with the sonar sampling clock. The training data for the LSM network architecture requires sufficient samples, covering tidal patterns across different seasons. Symmetrical padding is used for sliding window boundary processing to maintain the continuity of data at the window edges. Orthogonal initialization is used for the gating mechanism, ensuring the stability of gradient propagation. Uncertainty in the predicted sequence is estimated using Monte Carlo dropout, which randomly closes nodes during the inference phase. The weights of the dynamically coupled model remain fixed, ensuring determinism in the prediction phase. The pre-compensation coefficients are stored using a circular buffer, which supports a smooth transition between old and new coefficients.

[0095] The attention mechanism in the Long Short-Term Memory (LSTM) network architecture enhances features at important time points, calculating the weight distribution across different time steps. Multi-scale feature extraction using sliding windows employs different window sizes to capture both short- and long-term tidal variations. Variant structures of the gating mechanism, such as gated recurrent units (ROUs), simplify computation by merging the number of gates. Evaluation metrics for the predicted sequence include mean absolute error (MAO), which measures the deviation between predicted and actual values. Post-processing of the dynamically coupled model's output includes amplitude limiting to prevent pre-compensation coefficients from exceeding reasonable limits. Calibration of the pre-compensation operation uses a reference signal, providing a phase reference for system correction.

[0096] Hyperparameter tuning for the Long Short-Term Memory (LSTM) network architecture utilizes grid search, which evaluates different parameter combinations on a validation set. The sliding window is dynamically adjusted based on tidal activity variations, determined using variance metrics from historical data. Gating mechanisms prevent gradient explosion by limiting the maximum value of the gradient norm. Multi-step prediction of the predicted sequence employs a sequence-to-sequence structure, which includes encoder and decoder components. Version compatibility of the dynamically coupled model needs to be maintained, allowing for the alternation of old and new prediction models. The pre-compensation operation achieves microsecond-level time precision, guaranteed by a high-resolution clock.

[0097] Distributed training in the Long Short-Term Memory (LSTM) network architecture accelerates the learning process by partitioning data across multiple computing nodes. Sliding window data augmentation adds random noise, which enhances the model's robustness. The choice of activation function in the gating mechanism affects nonlinear expressiveness; a combination of tanh and sigmoid is used. Confidence intervals for predicted sequences provide reliability assessments, estimated using the Bootstrap method. The caching mechanism of the dynamically coupled model stores frequently used prediction patterns, quickly retrieving pre-compensation coefficients via a lookup table. Adaptive adjustments to the pre-compensation operation are based on real-time feedback, derived from residual tidal disturbance features from Example 4.

[0098] Lightweight deployment of the Long Short-Term Memory (LSTM) network architecture utilizes knowledge distillation, compressing complex models into small networks. Anomaly detection using a sliding window identifies sensor faults; anomaly detection is based on the Isolation Forest algorithm to label anomalous data. Interpretability analysis of the gating mechanism reveals important time points; this analysis is achieved through gradient-weighted class activation mapping. The fusion processing of predicted sequences combines results from multiple models; weighted averaging improves prediction stability. The input feature expansion of the dynamically coupled model incorporates meteorological data, such as air pressure and wind speed, which influence tidal behavior. Delay compensation in the pre-compensation operation estimates signal propagation time; this delay compensation is calculated using an underwater sound speed model.

[0099] The Long Short-Term Memory (LSTM) network architecture continuously learns to adapt to environmental changes, periodically updating model parameters with new data. Sliding window spectral analysis identifies periodic components, extracting dominant frequencies through Fourier transform. Sparsity reduction in the gating mechanism reduces the number of parameters, achieving feature selection through L1 regularization. Spatiotemporal expansion of the predicted sequence introduces multi-location data, using graph neural networks to model marine correlations. The redundant design of the dynamically coupled model includes a backup model, which takes over when the primary model fails. The verification process for pre-compensation operations uses simulated signals, synthesizing various tidal interference scenarios to test the system.

[0100] The Long Short-Term Memory (LSTM) network architecture will not be elaborated upon here.

[0101] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0102] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals, characterized in that, Includes the following steps: Collect sonar signal sequences and tidal motion parameter sequences for the current sea area, and divide the sonar signal sequences into multiple time windows; Within each time window, the phase offset of the sonar signal due to tidal motion is calculated based on the tidal motion parameter sequence; A dynamic coupling model between sonar signals and tidal motion is established, and the phase offset is converted into a time-domain compensation coefficient through the dynamic coupling model. Phase correction is performed on the sonar signal sequence based on the time-domain compensation coefficient to generate a sonar signal after preliminary suppression. Spectral analysis was performed on the sonar signal after initial suppression to extract residual tidal interference characteristics; The parameter weights of the dynamic coupling model are adjusted based on the residual tidal disturbance characteristics to generate an optimized dynamic coupling model. The optimized dynamic coupling model is applied to the sonar signal processing in the next time window to form an iterative suppression process.

2. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 1, characterized in that, The calculation of the phase shift of the sonar signal due to tidal motion based on the tidal motion parameter sequence includes: Obtain the rate of water level change and the amplitude of periodic fluctuations in the tidal motion parameter sequence within the current time window; Establish a function for the change in the propagation path length of the sonar signal based on the rate of water level change; The periodic fluctuation amplitude is input into the sound wave propagation speed correction function to calculate the change in the propagation speed of the sonar signal. By combining the propagation path length variation function and the propagation speed variation, the phase accumulation error at the time of sonar signal reception is derived; The phase accumulation error is normalized to obtain a standardized phase offset.

3. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 2, characterized in that, The establishment of the dynamic coupling model between sonar signals and tidal motion includes: Construct a multi-layer neural network structure with tidal motion parameters as the input layer and phase correction coefficients as the output layer; The historically collected tidal motion parameter sequence and the corresponding sonar signal phase error are used as the training dataset; The time backpropagation algorithm is used to train a multi-layer neural network structure until the prediction error of the output layer phase correction coefficient is lower than a set threshold. Save the network parameters and connection weights after training to form a dynamically coupled model.

4. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 3, characterized in that, The process of converting the phase offset into time-domain compensation coefficients through a dynamic coupling model includes: The phase offset calculated in the current time window is input into the input layer of the dynamic coupling model; Intermediate feature representations are generated through nonlinear transformation of the hidden layer of the dynamic coupling model; Based on the intermediate feature representation and the connection weights of the output layer, the temporal compensation coefficient vector is calculated; The time-domain compensation coefficient vector is time-aligned to match its length with the time window of the sonar signal sequence.

5. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 4, characterized in that, The phase correction of the sonar signal sequence based on the time-domain compensation coefficient includes: Perform point-by-point multiplication of the time-domain compensation coefficient vector with the sonar signal sequence; Perform a Fourier transform on the multiplication result to convert it to the frequency domain representation; In the frequency domain, a phase rotation operation is applied to each frequency component, and the rotation angle is determined by the corresponding time-domain compensation coefficient; An inverse Fourier transform is performed on the frequency domain representation after phase rotation to obtain the time-domain sonar signal after preliminary suppression.

6. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 5, characterized in that, The extraction of residual tidal interference features includes: Calculate the difference between the sonar signal after initial suppression and the original sonar signal; Wavelet packet decomposition is performed on the differential signal to obtain multi-scale sub-band signals; Statistical analysis of the energy distribution and zero-crossing rate characteristics of each sub-band signal; The energy distribution and zero-crossing rate characteristics are combined to form the residual tidal disturbance feature vector.

7. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 6, characterized in that, The adjustment of parameter weights in the dynamic coupling model based on residual tidal disturbance characteristics includes: Map the residual tidal disturbance feature vectors to the hidden layer space of the dynamic coupling model; Calculate the correlation coefficient between the activation values ​​of hidden layer nodes and the residual tidal disturbance feature vector; Adjust the connection weights from the hidden layer to the output layer based on the correlation coefficient; The connection weights from the input layer to the hidden layer are fine-tuned using gradient descent.

8. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 7, characterized in that, The iterative suppression process includes: Before the next time window begins, load the optimized dynamic coupling model parameters; The newly acquired sonar signal sequence is processed using the updated dynamic coupling model; Record the evaluation indicators of the inhibition effect in the current time window; When the evaluation index exceeds the preset threshold, the model parameter saving operation is triggered.

9. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 8, characterized in that, Also includes: Establish a tidal motion parameter prediction model to predict tidal motion parameters for future time windows based on historical tidal data; The predicted tidal motion parameters are input into the dynamic coupling model in advance to generate pre-compensation coefficients; Pre-compensation is applied before the sonar signal actually arrives.

10. The dynamic suppression algorithm for real-time elimination of the influence of tidal motion on sonar signals according to claim 9, characterized in that, The tidal motion parameter prediction model includes: Construct a temporal prediction structure based on a long short-term memory network; Historical tidal motion parameter training data were organized using a sliding window approach. Learn the long-term periodicity and short-term fluctuation patterns of tidal motion through gating mechanisms; Output the predicted sequence of tidal motion parameters for multiple future time points.

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