A method for screening feedback channel of underwater acoustic sensor network based on variational bayesian inference

Abstract

This invention relates to a method for selecting feedback channels in underwater acoustic sensor networks based on variational Bayesian inference, comprising: receiving pilot signals and constructing an observation matrix; establishing Gaussian-Gamma, Bernoulli-Gaussian, and Gaussian prior models for multipath channels, impulse interference, and background noise; iteratively updating channel and interference parameters based on mean-field variational Bayesian inference; calculating the effective signal-to-noise ratio after interference suppression and introducing estimation uncertainty correction, dynamically adjusting the threshold, and adaptively selecting the optimal feedback channel. This invention can improve the robustness, real-time performance, and spectrum utilization efficiency of feedback channel selection.

Description

Technical Field

[0001] This invention relates to a method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference, belonging to the field of underwater acoustic communication and signal processing technology. Background Technology

[0002] In multi-hop communication within underwater acoustic sensor networks, real-time optimization of the feedback channel is crucial for ensuring the system's dynamic adaptability and spectral efficiency. Underwater acoustic channels exhibit significant time-varying, multipath, and strong frequency selectivity characteristics, and are susceptible to sudden impulse interference and complex background noise. This makes traditional channel selection methods based on fixed thresholds or instantaneous statistics difficult to make accurate judgments in dynamic environments. Especially in large-scale distributed network applications, channel selection needs to be completed within milliseconds to ensure timely and reliable transmission of feedback information such as routing updates and power control. Therefore, designing a method that can quickly and accurately separate channel response from anomalous interference and, based on this, achieve intelligent channel optimization is of great significance for improving the overall performance of underwater acoustic communication systems.

[0003] Currently, the methods for optimizing feedback channels in underwater acoustic sensor networks mainly follow three technical paths: static screening methods based on threshold decision, dynamic screening methods based on classical statistical estimation, and data-driven screening methods based on machine learning. Static screening methods based on threshold decisions perform binary selection of channels according to pre-set signal-to-noise ratio or bit error rate thresholds. While simple to implement and computationally inexpensive, their fixed thresholds cannot adapt to dynamic changes and sudden interference in marine channels. They are prone to misselection or omission when interference fluctuations are large, exhibiting poor robustness. Dynamic screening methods based on classical statistical estimation, such as minimum mean square error estimation or maximum likelihood estimation, estimate channel parameters in real time and then screen based on the estimation results. While they can track channel changes to some extent, most methods do not explicitly model the statistical characteristics of impulse interference and noise. Estimation accuracy drops significantly under strong interference environments, and they typically require high computational resources, making real-time deployment at edge nodes difficult. Data-driven screening methods based on machine learning use historical data to train classification or regression models to predict channel quality. They can learn nonlinear characteristics in complex environments, but their performance heavily depends on the completeness and representativeness of the training data. They lack generalization ability when data is scarce or the environment changes abruptly, and model inference still requires considerable computational power, making it difficult to meet real-time feedback requirements under strict resource constraints.

[0004] To improve the accuracy and efficiency of channel selection in underwater acoustic networks, researchers have proposed various improvement mechanisms in recent years, and the relevant literature is as follows:

[0005] 1. In 2023, S. Mu et al. proposed an adaptive matched-pursuit channel estimation algorithm based on compressed sensing in their paper "An Adaptive MP Algorithm for Underwater Acoustic Channel Estimation Based on Compressed Sensing" to address inter-carrier interference caused by the Doppler effect. This method significantly reduces computational complexity while maintaining estimation accuracy by introducing an adaptive sparse decision threshold. However, this method is primarily designed for additive Gaussian noise environments and does not explicitly model impulse interference. Its estimation performance may degrade in the presence of sudden, strong interference, and its sparse recovery process still requires multiple iterations, making it difficult to meet strict real-time requirements.

[0006] 2. In 2024, W. Li et al. proposed a channel estimation algorithm based on variational Bayesian inference for impulse noise environments in their paper "Robust Underwater Acoustic Channel Estimation in Impulsive Noise Environment". This method effectively suppresses impulse interference by introducing a binary indicator variable to automatically identify outliers and alternately inferring the posterior distribution of the channel and impulse noise. However, this algorithm requires multiple rounds of iterative updates during the inference process, resulting in long computation time. Furthermore, it does not extend its estimation results to a multi-channel quality assessment and optimization decision framework, making it difficult to directly apply to real-time feedback channel selection scenarios.

[0007] 3. In 2024, X. Li et al. proposed a channel estimation scheme based on vector approximate message passing for orthogonal time-frequency-space systems in their paper "Channel Estimation for OTFS Underwater Acoustic Communications via Vector Approximate Message Passing". This scheme utilizes the channel sparsity in the time-delay-Doppler domain and employs a Bernoulli-Gaussian prior distribution, achieving performance superior to traditional least squares or linear minimum mean square error methods. However, the approximate message passing algorithm itself involves complex matrix operations and iterative updates, resulting in a significant computational burden and difficulty in meeting low-latency requirements when processing multiple channels in parallel.

[0008] 4. In 2024, Liu Jin et al. proposed using deep neural networks or convolutional networks to enhance least squares channel estimation in their paper "Deep Learning Enhanced Least Squares Channel Estimation Algorithm for Underwater Acoustic Communication," correcting the channel frequency response by learning the estimation error through model learning. This method significantly improves performance at low signal-to-noise ratios, but it is a data-driven method that relies on a large amount of training data, and network inference still introduces additional computational overhead. It also faces challenges in latency and generalization ability when deployed on resource-constrained nodes.

[0009] 5. In 2025, Tan Gang et al. proposed a joint estimation algorithm for channel and impulse noise based on generalized approximate message-passing sparse Bayesian learning in their paper "Joint Estimation of Channel and Impulse Noise in Sparse Bayesian Acoustic OFDM Systems." This algorithm utilizes all subcarriers to construct a compressed sensing model, achieving joint recovery of the channel, interference, and data symbols. While improving estimation performance and reducing computational complexity, the iterative process may still converge slowly, and it does not effectively convert the joint estimation results into real-time channel optimization metrics, making it difficult to meet the millisecond-level decision-making requirements for feedback channels.

[0010] 6. In 2025, Yao Junhui et al. proposed a low-complexity carrier frequency offset estimation algorithm in their paper "Carrier Frequency Offset Estimation in Orthogonal Frequency Division Multiplexing Using Conjugate Phase Difference Information." This algorithm achieves time-varying Doppler estimation by utilizing the conjugate phase difference information of adjacent subcarriers, without the need to insert additional pilots. While this algorithm exhibits good performance in time-varying Doppler environments, it focuses on frequency offset estimation and does not address the joint processing of channel impulse response and impulse interference, making it difficult to directly apply to channel quality assessment requiring interference suppression. Summary of the Invention

[0011] The technical problem to be solved by this invention is: after completing the construction of the variational Bayesian inference joint estimation framework for pilot subcarrier constraints in multi-hop links, efficient parameter estimation and dynamic threshold screening are achieved by separating and modeling the channel impulse response and impulse interference, thereby ensuring the robustness and real-time performance of the feedback channel optimization process and significantly improving the environmental adaptability and spectrum resource utilization efficiency of the underwater acoustic communication system.

[0012] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0013] A method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference includes the following steps:

[0014] Step 1: Pilot signal reception and observation data construction

[0015] In multi-hop communication scenarios of underwater acoustic sensor networks, the receiving node receives pilot signals transmitted from the previous hop node within a predetermined pilot time slot. These pilot signals are pre-mapped to multiple subcarriers or subchannels. After receiving the pilot signals, bandpass filtering and DC component removal are performed for data preprocessing. Finally, a channel observation data matrix is ​​established based on the preprocessed pilot signals.

[0016] Step 2: Joint Prior Modeling

[0017] To avoid confusion between valid channel components and anomalous interference components during the estimation process, prior modeling is required, including channel prior modeling, impulse interference prior modeling, and noise statistical prior modeling.

[0018] Step 3: Variational Bayesian Inference

[0019] Under the assumption of a mean field, the joint posterior probability distribution is decomposed into multiple independent variational distributions, corresponding to the variational distributions of channel coefficients, impulse interference parameters, and noise statistical parameters, respectively. This transforms the difficult-to-calculate real channel distribution into multiple computable variational distributions. The parameters of each variational distribution are then initialized based on the statistical mean and variance of historical observation data. The channel and interference parameters are then updated iteratively, alternating between iterations, until the parameter change between two consecutive iterations is less than a preset threshold.

[0020] Step 4: Channel Quality Assessment and Feedback Channel Selection

[0021] Based on the posterior mean and posterior variance of the channels, the effective signal-to-noise ratio (SNR) after interference suppression for each sub-channel is calculated to comprehensively reflect channel gain and estimation reliability. Simultaneously, a channel estimation uncertainty correction factor is introduced into the SNR calculation to reduce the probability of misselection of high-uncertainty channels. Then, based on the currently inferred noise statistics and interference intensity, the SNR screening threshold is dynamically adjusted, allowing the threshold to adaptively update with environmental changes. Sub-channels with SNR higher than the dynamic threshold are included in the candidate feedback channel set. Finally, the optimal feedback channel is selected from the candidate feedback channel set according to a preset optimization criterion.

[0022] In step one above, the channel observation data matrix is ​​defined as follows:

[0023] Construct a matrix Y, where row k corresponds to the sub-channel number, column n corresponds to the pilot symbol number, and elements... The amplitude of the received signal. ,in For channel coefficients, Pilot signal, For pulse interference components, This represents background noise. Thus, the row vectors reflect the spatial frequency characteristics of different sub-channels, while the column vectors reflect the time-domain variations of the pilot signal.

[0024] In step two above, the joint prior modeling is as follows:

[0025] Considering the multipath propagation characteristics of underwater acoustic channels, it is assumed that the channel impulse response exhibits a sparse distribution in the time delay domain or frequency domain, which can be represented by a Gaussian-gamma prior distribution. ,in This is a sparse hyperparameter; when it approaches infinity, the corresponding channel coefficient is 0, and when it approaches 0, it indicates that the signal coefficient has a value. To make... It can learn adaptively and can set gamma priors. . It is a preset small constant;

[0026] To address the non-Gaussian impulse interference characteristics present in underwater acoustic communication, a burst-type probability prior is set for the interference component, so that the interference remains zero most of the time and only shows significant amplitude at a few moments or in sub-channels. A Bernoulli-Gaussian prior distribution can be used. ,in It is an indicator variable; when it is 1, it indicates that there is interference, and when it is 0, it indicates that there is no interference. ,in This represents the probability of interference occurring. Because interference is sparse, it is usually set to less than 0.1. This represents the variance of the interference amplitude.

[0027] To address background environmental noise, a stationary noise statistical prior is introduced to describe unavoidable random disturbances in the system. This can be represented by Gaussian noise.

[0028] In step three above, the channel parameters and interference parameters are updated iteratively using the following method:

[0029] In the first stage, under the condition of fixed interference statistical parameters and noise parameters, the variational distribution parameters of the channel coefficients are updated based on the current observation data and prior constraints to obtain the posterior mean and posterior variance of the channel. In the second stage, under the condition of fixed channel parameters, the location and statistical parameters of the impulse interference are updated based on the observation residuals and the interference prior model to reconstruct the interference support set. The parameter update formula is as follows: , , , ,

[0030] .

[0031] in Indicates the updated N is the maximum value of n; The posterior mean of the channel. For the posterior variance of the channel, Let represent the posterior probability that the 𝑘-th subchannel has pulse interference at the 𝑛-th pilot time. Indicates the updated .

[0032] In step four above, the method for introducing a channel estimation uncertainty correction factor in the signal-to-noise ratio calculation is as follows:

[0033] For the k-th sub-channel, before uncertainty correction, the signal-to-noise ratio is... In variational Bayesian estimation, a large posterior variance indicates low reliability of the channel estimate, while a small posterior variance indicates higher reliability. Therefore, an uncertainty correction factor can be introduced. .

[0034] In step four above, the method for adaptively updating the threshold according to environmental changes is as follows:

[0035] Calculate the signal-to-noise ratio (SNR) of each channel, take the average value as the threshold SNR, and add a safety factor to adjust the system robustness. This can effectively cope with situations where no channel is available due to rapid increases or decreases in SNR caused by environmental changes. ,in , used to adjust the system robustness, where m is the number of sub-channels.

[0036] The beneficial effects of this invention are as follows: Through the above-mentioned technical means, the beneficial effects of this invention are as follows: First, in steps one and two, by constructing an observation data matrix containing channel coefficients, impulse interference, and background noise, and applying Gaussian-gamma sparse priors to the channel impulse response and Bernoulli-Gaussian sparse priors to the impulse interference, a refined modeling of the sparse multipath structure and sudden impulse interference of the underwater acoustic channel is achieved, providing a reliable prior information foundation for subsequent high-precision estimation. Second, in step three, variational Bayesian inference is used to decompose the joint posterior distribution into multiple variational distributions under the mean-field assumption. By iteratively updating the channel coefficients and impulse interference parameters, adaptive separation of the channel response and anomalous impulses is achieved, effectively suppressing the contamination of channel estimation by impulse interference. Compared with traditional least squares or matching pursuit methods, it can still maintain high estimation accuracy and robustness under strong interference environments. Finally, step four calculates the effective signal-to-noise ratio based on the channel's posterior mean and variance, and introduces an estimation uncertainty correction factor to reduce the probability of misselection of high-uncertainty channels. Simultaneously, it dynamically adjusts the screening threshold using real-time inferred noise and interference parameters, allowing the threshold to adaptively update with the environment. This avoids the problem of fixed thresholds failing in dynamic underwater acoustic channels, ultimately achieving millisecond-level, highly reliable feedback channel selection. Through the above optimization strategies, this invention not only solves the technical challenges of poor adaptability of traditional threshold methods, weak anti-interference capabilities of classical statistical methods, and data-dependent and computationally demanding machine learning methods, but also ensures the real-time performance and accuracy of channel selection under limited computing resources at edge nodes. It significantly improves the spectral efficiency and environmental adaptability of underwater acoustic sensor networks, demonstrating outstanding technical advantages and broad engineering application prospects. (See attached figures.)

[0037] Figure 1 This is a schematic diagram of the flow of the pilot signal reception and observation data of the present invention;

[0038] Figure 2 This is a schematic diagram of the joint prior model of the present invention;

[0039] Figure 3 This is a schematic diagram of the variational Bayesian inference process of the present invention;

[0040] Figure 4 This is a schematic diagram illustrating the screening process for channel quality assessment and feedback channel selection in this invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0042] A method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference, comprising the following steps:

[0043] Step 1: As Figure 1As shown, pilot signal reception and observation data construction are performed. In the multi-hop communication scenario of underwater acoustic sensor networks, the receiving node receives the pilot signal sent by the previous hop node within a predetermined pilot time slot. This pilot signal is pre-mapped to multiple subcarriers or subchannels. In practice, the receiving node synchronizes with the network clock and activates the receiving circuit within the agreed pilot time slot window. After receiving the pilot signal, bandpass filtering is first performed to remove out-of-band noise. This step is achieved by configuring an analog bandpass filter or digital filter at the receiver front end, effectively filtering out environmental noise outside the passband and possible interference from other frequency bands. Subsequently, the filtered signal undergoes data preprocessing by removing the DC component. This can be achieved by calculating the mean of the signal segment using a sliding window mean subtraction method and subtracting it from the original sampled value, ensuring that the subsequently processed signal fluctuates around the zero mean. Finally, a channel observation data matrix is ​​constructed based on the preprocessed pilot signal. A matrix Y is constructed, where row k corresponds to the subchannel number, column n corresponds to the pilot symbol number, and elements... This represents the amplitude of the received signal. This amplitude is typically obtained by sampling, quantizing, and calculating the amplitude of the signal within each sub-channel and each pilot symbol period. Its physical model can be represented as follows: .in This represents the channel coefficient of the sub-channel at this moment, used to characterize the channel's attenuation and phase effects on the signal. For the known pilot signal, This includes potential pulse interference components, such as sudden human-induced disturbances or transient disturbances caused by marine biological activity. Background noise is typically modeled as additive white Gaussian noise. The matrix constructed in this way has row vectors that comprehensively reflect the fading characteristics of the sub-channel over time, and column vectors that reflect the frequency selectivity of the channel, together providing a complete observation dataset for subsequent variational Bayesian inference.

[0044] Step Two: As Figure 2 As shown, joint prior modeling is employed. This step, a crucial link in constructing the probabilistic inference framework from observational data, focuses on establishing a joint prior probabilistic model capable of effectively distinguishing between channel response and impulse interference. First, for sparse prior modeling of the channel impulse response, considering the sparse multipath characteristics of the underwater acoustic channel in the time delay domain, a hierarchical Gaussian-gamma prior is used. Each complex channel coefficient... Assigned a precision parameter The complex Gaussian prior with conditions, i.e. Precision parameters The value of directly affects the sparsity of the channel coefficients: the larger the value, the smaller the variance of the corresponding coefficient, thus being compressed close to zero; the smaller the value, the more energy the coefficient can carry, representing an effective multipath. To achieve adaptive learning of sparsity, further... Set the gamma distribution as the super-prior, that is... This conjugate prior structure not only guarantees computational closure, but its long-tail property also automatically drives most of the computation. The value tends to be larger, thus promoting the evolution of the channel towards a sparse structure as a whole.

[0045] Secondly, for the suddenness prior modeling of impulse interference, to characterize its sudden occurrence and potentially large amplitude in the time or frequency domain, a Bernoulli-Gaussian mixture prior is adopted, which is a typical sparse signal representation model. This is achieved by introducing binary latent variables. As an indicator of the existence of interference, the prior probability Set to a small value (e.g., 0.1) to reflect the sparsity of interference. Based on this, the interference amplitude... The conditional distribution is defined as: when When =1, ;when When =0, =0. Here Set to a relatively large value to accommodate potentially significant pulse amplitudes. This model can simultaneously infer the location of interference during the estimation process (via...). ) and amplitude (through This enables joint detection and estimation of impulse interference. Finally, prior modeling of the stationarity of background noise is performed; for additive Gaussian background noise, its variance... It is given a conjugate inverse gamma a priori, namely This choice not only satisfies the physical constraint that the noise variance is positive, but also, due to its conjugate nature, maintains the posterior distribution form in subsequent variational updates, thus obtaining an analytical update formula. Hyperparameters can be set based on prior knowledge of the system noise basis, providing a stable random perturbation benchmark for the model. In summary, this step formally characterizes the statistical properties of channel impulse response, impulse interference, and noise by introducing Gaussian-Gamma priors, Bernoulli-Gaussian mixed priors, and inverse gamma priors, respectively. These three are then observed through the model. (in, These elements are coupled together to form a complete hierarchical probabilistic graphical model.

[0046] Step 3: As Figure 3The variational Bayesian inference process begins with the following steps: First, under the mean-field assumption, the joint posterior probability distribution of the channel, impulse interference, and noise is decomposed into three independent variational distributions, corresponding to the channel coefficients, interference parameters, and noise statistics, respectively. Then, the parameters of each variational distribution are initialized based on the statistical characteristics of historical observation data, including the channel posterior mean and variance, the probability of interference presence, and the noise variance. Next, an alternating iterative update phase begins: In the first phase, the interference and noise parameters are fixed, and the parameters of the channel variational distribution are updated using the current observation data and the channel prior, resulting in the updated channel posterior mean and variance. In the second phase, the channel parameters are fixed, and the probability of impulse interference presence and amplitude statistics are updated based on the observation residuals and the interference prior model, reconstructing the interference support set. These two phases are iterated until the changes in all parameters in two adjacent iterations are less than a preset threshold. At this point, the variational distribution converges, the inference process ends, and the final estimation results of the channel, interference, and noise are output.

[0047] Step Four: Channel Quality Assessment and Feedback Channel Selection. This step, based on the posterior mean and posterior variance of the channel obtained through variational Bayesian inference, completes sub-channel quality assessment, correction calculation, adaptive threshold screening, and optimal feedback channel selection. For example... Figure 4 As shown, firstly, the posterior mean and posterior variance of the channel gain for each sub-channel are extracted at the underwater acoustic network layer. Secondly, a channel estimation uncertainty correction factor is introduced at the computation layer to calculate the effective signal-to-noise ratio (SNR) after interference suppression. This factor comprehensively reflects the channel gain and estimation reliability, effectively reducing the probability of misselecting sub-channels with low estimation reliability, making the evaluation results more consistent with actual transmission performance. Next, at the screening layer, the screening threshold is dynamically and adaptively updated based on the current noise statistics and interference intensity. A dynamic threshold is generated by weighting the global SNR mean, and it is adjusted in real time according to environmental changes to avoid the problem of no usable channels due to sudden changes in channel quality. Finally, sub-channels with a corrected SNR higher than the dynamic threshold are included in the candidate feedback channel set, while low-quality channels are removed. In the candidate set, the optimal channel is selected as the dedicated feedback channel for the underwater acoustic sensor network based on preset optimization criteria such as maximum SNR and minimum estimation uncertainty, completing the entire screening process. This step is illustrated in the appendix. Figure 4 The three-layer structure completes channel quality calculation, adaptive decision-making, and optimal channel output. Combined with variational Bayesian posterior statistical features, it improves the accuracy and robustness of feedback channel selection in complex underwater acoustic environments.

Claims

1. A method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference, characterized in that: Includes the following steps: Step 1: Pilot signal reception and observation data construction In the multi-hop communication scenario of underwater acoustic sensor network, the receiving node receives the pilot signal sent by the previous hop node within a predetermined pilot time slot, wherein the pilot signal is pre-mapped to multiple subcarriers or subchannels; after receiving the pilot signal, bandpass filtering and DC component removal are performed for data preprocessing. Finally, a channel observation data matrix is ​​established based on the preprocessed pilot signals; Step 2: Joint Prior Modeling Prior modeling is performed in advance, including channel prior modeling, impulse interference prior modeling, and noise statistics prior modeling; Step 3: Variational Bayesian Inference Under the assumption of mean field, the joint posterior probability distribution is decomposed into multiple independent variational distributions, corresponding to the variational distributions of channel coefficients, impulse interference parameters, and noise statistics parameters, respectively. The real channel distribution is transformed into multiple computable variational distributions. Then, the parameters of each variational distribution are initialized based on the statistical mean and variance of historical observation data. The channel parameters and interference parameters are then updated iteratively alternately until the parameter change in two adjacent iterations is less than a preset threshold. Step 4: Channel Quality Assessment and Feedback Channel Selection Based on the posterior mean and posterior variance of the channel, the effective signal-to-noise ratio (SNR) after interference suppression for each sub-channel is calculated. A channel estimation uncertainty correction factor is introduced into the SNR calculation. The SNR screening threshold is dynamically adjusted according to the currently inferred noise statistics and interference intensity, so that the threshold is adaptively updated with changes in the environment. Sub-channels with an SNR higher than the dynamic threshold are included in the candidate feedback channel set. Finally, the optimal feedback channel is selected from the candidate feedback channel set according to the preset optimization criteria.

2. The method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference as described in claim 1, characterized in that: In step one, the channel observation data matrix is ​​defined as follows: Construct a matrix Y, where row k corresponds to the sub-channel number, column n corresponds to the pilot symbol number, and elements... The amplitude of the received signal. ,in For channel coefficients, Pilot signal, For pulse interference components, This is background noise.

3. The method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference according to claim 1, characterized in that: In step two, the joint prior modeling method is as follows: Considering the multipath propagation characteristics of underwater acoustic channels, it is assumed that the channel impulse response exhibits a sparse distribution in the time delay domain or frequency domain, which is represented by a Gaussian-gamma prior distribution. ,in For sparse hyperparameters, when they approach infinity, the corresponding channel coefficient is 0; when they approach 0, it indicates that the signal coefficient has a value. To make... It can learn adaptively and can set gamma priors. ; It is a preset small constant; To address the non-Gaussian impulse interference characteristics in underwater acoustic communication, a burst-type probabilistic prior is set for the interference component, ensuring that the interference remains zero most of the time and only exhibits significant amplitude at a few moments or in sub-channels. A Bernoulli-Gaussian prior distribution is used. ,in This is an indicator variable; a value of 1 indicates interference, and a value of 0 indicates no interference. ,in This indicates the probability of interference occurring; it should be set to less than 0.

1. Indicates the variance of the interference amplitude; To address background environmental noise, a stationary noise statistical prior is introduced to describe unavoidable random disturbances in the system, represented by Gaussian noise.

4. The method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference according to claim 3, characterized in that: In step three, the method for updating and iterating the channel parameters and interference parameters is as follows: In the first stage, under the condition of fixed interference statistics parameters and noise parameters, the variational distribution parameters of the channel coefficients are updated according to the current observation data and prior constraints to obtain the posterior mean and posterior variance of the channel. In the second stage, under the condition of fixed channel parameters, the location and statistical parameters of the impulse interference are updated based on the observation residuals and the interference prior model, and the interference support set is reconstructed. The parameter update formula is as follows: , , , , ;in Indicates the updated N is the maximum value of n; The posterior mean of the channel. For the posterior variance of the channel, Let represent the posterior probability that the 𝑘-th subchannel has pulse interference at the 𝑛-th pilot time. Indicates the updated .

5. The method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference according to claim 4, characterized in that: In step four, the method for introducing a channel estimation uncertainty correction factor in the signal-to-noise ratio calculation is as follows: For the k-th sub-channel, before uncertainty correction, the signal-to-noise ratio is... An uncertainty correction factor is introduced into variational Bayesian estimation. ; This represents the variance of noise interference.

6. The method for filtering feedback channels in underwater acoustic sensor networks based on variational Bayesian inference according to claim 5, characterized in that: In step four, the method for adaptively updating the threshold according to environmental changes is as follows: Calculate the signal-to-noise ratio (SNR) of each channel, take the average value as the threshold SNR, and add a safety factor to adjust the system robustness. ,in , used to adjust the system robustness, where m is the number of sub-channels.

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