A method for eliminating underwater acoustic communication pulse noise based on Kalman filter
By using an underwater acoustic impulse noise cancellation algorithm based on the INM Kalman filter and adjusting the weights of the observations, the problems of signal structure destruction and high computational complexity in traditional methods are solved, thus achieving efficient noise cancellation and performance improvement of underwater acoustic communication systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING INST OF TECH
- Filing Date
- 2023-11-08
- Publication Date
- 2026-06-02
Smart Images
Figure CN117459355B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of underwater acoustic communication technology, specifically relating to a method for eliminating impulse noise in underwater acoustic communication based on a Kalman filter. Background Technology
[0002] Underwater acoustic channels are open channels, and their communication performance is affected by external interference. Impulse noise, a common external interference in marine environments, severely impacts the performance of underwater acoustic communication systems. Nonlinear noise cancellation algorithms are commonly used to suppress impulse noise. These methods eliminate noise by zeroing or limiting the impulse noise in the received signal. While simple to operate and relatively low in complexity, they can damage the original signal structure, resulting in the loss of a significant amount of useful information. In recent years, with the development of compressed sensing technology, sparse reconstruction methods have been widely applied to impulse noise cancellation. This method addresses the sparsity of impulse noise by estimating it through signal reconstruction and removing the reconstructed signal from the received signal to reduce its interference with useful signals. However, it has high computational complexity, and its estimation performance is affected by the sparsity of the signal itself, showing a significant decrease in performance for signals with high sparsity.
[0003] Both of the above-mentioned processing methods reduce the impact of impulse noise by performing local processing on the signal, and the processing effect depends on the structural characteristics of the noise. When impulse noise occurs continuously within the communication frequency band, nonlinear impulse noise cancellation methods will result in a large number of continuous 0 values or amplitude-limited values in the processed signal, which will destroy the original signal structure and affect information recovery. Summary of the Invention
[0004] In view of this, the purpose of this invention is to provide a method for eliminating underwater acoustic impulse noise based on a Kalman filter, which can effectively recover the original signal, reduce the bit error rate of underwater acoustic communication, and improve the reliability of the communication system. An underwater acoustic impulse noise elimination algorithm based on an INM Kalman filter includes:
[0005] Step 1: Input the baseband signal received by the receiver of the underwater acoustic communication system and use it as the observation vector y. k , and the set of locations of received signal pulse noise Ω;
[0006] Step 2: Initialize state variables And error covariance matrix P 0|0 ;
[0007] Step 3: Predict the state variables at time k:
[0008] in, N represents the length of the data block obtained after encoding and interleaving in the underwater acoustic communication system. k Indicates process noise; This represents the final estimated value of the state variable x at time k-1; This represents the predicted value at time k-1 for time k;
[0009] The error covariance matrix for predicting time k: P k|k-1 =AP k-1|k-1 A T +Q k ;
[0010] Among them, P k-1|k-1 Let represent the error covariance matrix at time k-1; Indicates variance;
[0011] Step 4: Determine if there is impulse noise at each filtered signal position p:
[0012] If p∈Ω, then:
[0013] Calculate observation weights:
[0014] Among them, H k Represents the observation matrix; R kI Represents the impulse noise covariance matrix;
[0015] Calculate the Kalman gain:
[0016] if but:
[0017] Calculate the Kalman gain:
[0018] Among them, R kB R represents the background noise covariance matrix. kB ;
[0019] Step 5: Estimate state variables:
[0020] Update the error covariance matrix: P k|k =(IK k (p)H k )P k|k-1 ;
[0021] Step 6: Output the estimated values of the state variables. The estimated value P of the error covariance matrix k|k Then, proceed to the state estimation for the next moment.
[0022] The present invention has the following beneficial effects:
[0023] This invention proposes an underwater acoustic impulse noise cancellation algorithm based on an INM Kalman filter. This algorithm considers the impact of impulse noise on the filtering result. Building upon the traditional Kalman filter algorithm, it introduces confidence weights into the observations. By adjusting the weights of the observations in the state estimation, impulse noise is eliminated, reducing its introduction and impact on system performance, thus improving the filtering performance of the Kalman filter in impulse noise environments. Simulation results show that, compared with existing impulse noise cancellation algorithms, the proposed method effectively recovers the original signal, reduces the bit error rate (BER) of underwater acoustic communication, and improves the reliability of the communication system. Attached Figure Description
[0024] Figure 1 This is a flowchart of the signal processing for an underwater acoustic communication system.
[0025] Figure 2 The bit error rate performance curves are shown under different signal-to-noise ratio conditions.
[0026] Figure 3 The graph shows the bit error rate performance under different signal-to-interference ratios. Detailed Implementation
[0027] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0028] I. System Model
[0029] This invention proposes an underwater acoustic communication impulse noise cancellation algorithm based on a Kalman filter and applies it to a single-carrier underwater acoustic communication system. Figure 1 This is a schematic diagram of an underwater acoustic communication system.
[0030] The block diagram of the underwater acoustic communication system is as follows: Figure 1 As shown. The transmitted data is information bits b. t After encoding and interleaving, it becomes a data block of length N [x1,x2,…,x] N ], where x n =[x n,1 ,x n,2 ,…,x n,m [] represents a bit sequence of length m at time n, x n,m ={0,1}. Then, map each bit sequence to a symbol s. k The value is S = {α1, α2, ..., α2m}, where S is the set of constellation diagrams, and each α in the set... i Each corresponds to a specific bit sequence. In this invention, considering a single-transmitter, single-receiver system, the baseband transmitted signal can be expressed as:
[0031]
[0032] In the formula, x[n] represents a length of N. s The symbol sequence, h(t) is the pulse shaping function, T = N s T s The total signal duration. The baseband signal is modulated to a center frequency of f. c On the carrier wave, the obtained passband signal is
[0033]
[0034] The passband signal travels through the channel to the receiver. Assume the underwater acoustic channel model is as follows:
[0035]
[0036] Where N p A represents the number of multipath paths in the underwater acoustic channel. p (t) and τ p (t) represent the attenuation and delay of the p-th path, respectively. Assume that during data communication, the channel amplitude and delay change relatively slowly, i.e., A... p (t)≈A p ,τ p (t)≈τ p Based on this, the channel model can be further expressed as:
[0037]
[0038] In an environment with added interference, the passband signal received by the hydrophone is represented as:
[0039]
[0040] Where I(t) represents impulse noise, and v(t) is a variable with a mean of 0 and a variance of . Gaussian noise.
[0041] At the receiving end, the demodulation module performs the conversion between the passband and baseband signals. The converted baseband signal is represented as follows:
[0042]
[0043] Where LPF[·] represents a low-pass filter. Substituting equation (2) into equation (5) yields...
[0044]
[0045] With baseband sampling rate f s If y(t) is sampled, the input-output relationship of the discrete signal can be expressed as follows:
[0046]
[0047] Where I(m) and v(m) represent the discrete sampling points of impulse noise and Gaussian white noise, respectively. The discrete demodulated signal is filtered to eliminate the influence of impulse noise. Then, the processed signal is equalized and decoded to recover the system's transmitted bits, thus realizing the communication process. The input-output relationship of the single-carrier underwater acoustic communication system can be represented as a matrix as follows:
[0048] Y = HX + I + V#(9)
[0049] Where X is the transmitted signal matrix, Y is the received signal matrix, H is the channel matrix, and I and V represent the impulse noise matrix and Gaussian noise matrix, respectively.
[0050] II. Traditional Kalman Filtering Algorithm
[0051] As a widely used adaptive filter, the Kalman filter can filter the received signal based on predicted and observed data, thereby eliminating the impact of impulse noise on the transmitted signal to a certain extent and improving the performance of the communication system.
[0052] Traditional Kalman filters can be represented using a linear model:
[0053] x k =A k x k-1 +n k #(10)
[0054] y k =H k x k +v k #(11)
[0055] in, Let the state variables of the system at time k be represented. For the observation vector, Indicates process noise. To observe noise. Represents the transition matrix. Represents the observation matrix. When the process noise n k and observation noise v k When both are Gaussian noise with a mean of 0, their covariance matrices are expressed as Q. k and R k .
[0056] When a Kalman filter is applied to a communication system, the observed quantity is the underwater acoustic signal received by the system, and the state variable is the estimated value of the transmitted signal. Combined with the communication processing, the transition of the state variable from time k-1 to time k can be expressed as:
[0057]
[0058] in
[0059]
[0060] n k =[x k ,0,…,0] T #(14)
[0061] in, This represents the final estimated value of the state variable x at time k-1; This represents the predicted value at time k-1 for time k;
[0062] During communication, because the transmitter interleaves and encodes the bit sequence of the transmitted symbols, the correlation between symbols at adjacent moments is extremely low, allowing x to be... k Assuming the mean is zero and the variance is... Gaussian noise. Clearly, the process noise is uncorrelated with the observation noise, therefore E[ν(k)n] H [(k)] = 0.
[0063] The estimation error covariance matrix corresponding to the predicted values of the state variables is:
[0064] P k|k-1 =AP k-1|k-1 A T +Q k #(15)
[0065] Where: P k-1|k-1 Let represent the error covariance matrix at time k-1;
[0066]
[0067] Kalman gain represents the weight of the influence of the predicted and observed values on the state variable, and can be expressed as:
[0068]
[0069] Among them, R k H represents the measurement noise covariance matrix. k Let be the channel impulse response matrix. Therefore, the state variables at time k can be expressed as:
[0070]
[0071] The corresponding updated covariance matrix is
[0072] P k|k =(IK k H k )P k|k-1 #(19)
[0073] According to the prediction and estimation model, the estimation of the current state is a linear process of the previous state estimate, while the verification process requires updating the data based on the observations and obtaining accurate state variable estimates after iteration, which are used for the equilibrium and decoding processes.
[0074] Using the matrix inversion lemma for equation (19), it can be expressed as:
[0075]
[0076] The state variables in equation (18) can be written as:
[0077]
[0078] in
[0079]
[0080] As can be seen from equation (21), the state variables It is a prediction and signal observation value y k A linear combination of weights α P and α R The prediction error covariance matrix P k|k-1 and the observation noise covariance matrix R k Determined. Therefore, during the Kalman filtering process, R... k The magnitude of the value will directly affect the reliability of the observation.
[0081] When the noise level is low, the corresponding observed value is close to the true signal value. In the state estimation process, the weight α... R A larger value should be assigned. On the other hand, when the noise value increases, the corresponding measured value will differ significantly from the true signal value, and the weight α of the observed value should be adjusted accordingly. R The value should be reduced. In underwater acoustic communication, impulse noise is a high-amplitude signal, therefore, signals interfered with by impulse noise will experience a deterioration in signal-to-noise ratio, reducing the reliability of observations. Therefore, the influence weight of observations should be reduced during the estimation process to minimize the introduction of impulse noise. However, in traditional Kalman filters, R... k The observation weight α remains constant throughout the filtering process. R It remains unchanged. However, in an impulse noise environment, the invariant α... R This will introduce more noise into the estimated values, affecting the filtering effect of the Kalman filter and failing to effectively improve the system's communication performance in impulse noise environments. To solve the above problems, this invention proposes the INM Kalman filter algorithm to achieve effective filtering in impulse noise environments.
[0082] III. INM Kalman Filter Algorithm
[0083] The INM Kalman filter fully considers the impact of impulse noise on the observations and achieves better filtering results by adjusting the weights of the observations. Unlike traditional Kalman filtering algorithms, the INM filter considers weight allocation during the Kalman gain update process, which can be expressed as:
[0084]
[0085] Where p is the current position of the filtered signal, and R k (p) From the impulse noise covariance matrix R kI and background noise covariance matrix R kB Composition. Weighting function α R (·) is defined as shown in equation (24) to prevent the Kalman gain from being destroyed by pulse noise with abnormally large amplitude.
[0086]
[0087] Where Ω represents the set of locations of impulse noise in the received signal, and if the current filtered signal is interfered with by impulse noise, the Kalman gain K... k Assigned lower weights, R is considered during the calculation. kI To mitigate the impact of background noise and reduce the introduction of outliers, when the filtered signal is not affected by impulse noise, the weight function is 1, and the Kalman gain calculation only considers the background noise covariance matrix R. kB Therefore, the state estimate can be expressed as:
[0088]
[0089] The updated covariance matrix is:
[0090] P k|k =(IK k (p)H k )P k|k-1 #(26)
[0091] The recursive process of INM Kalman filtering is as follows:
[0092] Step 1: Input the baseband signal received by the receiver of the underwater acoustic communication system and use it as the observation vector y. k , and the set of locations of received signal pulse noise Ω;
[0093] Step 2: Initialize state variables And error covariance matrix P 0|0 ;
[0094] Step 3: Predict the state variables at time k:
[0095] in, N represents the length of the data block obtained after encoding and interleaving in the underwater acoustic communication system. k Indicates process noise; This represents the final estimated value of the state variable x at time k-1; This represents the predicted value at time k-1 for time k;
[0096] The error covariance matrix for predicting time k: P k|k-1 =AP k-1|k-1 A T +Q k ;
[0097] Among them, P k-1|k-1 Let represent the error covariance matrix at time k-1; Indicates variance;
[0098] Step 4: Determine if there is impulse noise at each filtered signal position p:
[0099] If p∈Ω, then:
[0100] Calculate observation weights:
[0101] Among them, H k Represents the observation matrix; R kI Represents the impulse noise covariance matrix;
[0102] Calculate the Kalman gain:
[0103] if but:
[0104] Calculate the Kalman gain:
[0105] Among them, R kB R represents the background noise covariance matrix. kB ;
[0106] Step 5: Estimate state variables:
[0107] Update the error covariance matrix: P k|k =(IK k (p)H k )P k|k-1 ;
[0108] Step 6: Output the estimated values of the state variables. The estimated value P of the error covariance matrix k|k Then, proceed to the state estimation for the next moment.
[0109] Example:
[0110] This invention primarily studies the suppression and elimination of impulse noise in underwater acoustic communication systems, and proposes an underwater acoustic impulse noise cancellation algorithm based on an INM Kalman filter. This algorithm, building upon traditional Kalman filtering, considers the impact of impulse noise on the system. By adjusting the weights of observations in the estimates through a weighting function, it reduces the introduction of impulse noise during the filtering process and improves system performance. Simulation results show that, under impulse noise conditions, compared to existing impulse noise cancellation methods, the proposed algorithm effectively eliminates noise and improves the robustness of the system during the filtering process.
[0111] Simulation experiments were conducted under four processing methods: no pulse processing, pulse blanking, traditional Kalman filtering, and INM Kalman filtering. First, under a signal-to-interference ratio (SNR) of -6 dB pulse noise, the system performance of each processing method was compared under different SNR conditions. The bit error rate results are as follows: Figure 2 As shown.
[0112] Then, under a signal-to-noise ratio (SNR) of 5 dB, the system performance of each processing method was compared under different SNR conditions. The bit error rate results are as follows: Figure 3 As shown.
[0113] Compared to traditional Kalman filtering methods, INM Kalman filtering effectively suppresses the introduction of impulse noise during the iteration process, reducing the impact of impulse noise on the filtering results and significantly improving communication performance. This demonstrates that the INM algorithm has a good suppression effect on impulse noise.
[0114] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for eliminating underwater acoustic impulse noise based on an INM Kalman filter, characterized in that, include: Step 1: Input the baseband signal received by the receiver of the underwater acoustic communication system and use it as the observation vector. and the set of locations of received signal impulse noise ; Step 2: Initialize state variables And error covariance matrix ; Step 3: Predict the state variables at time k: ; in, N represents the length of the data block obtained after encoding and interleaving in the underwater acoustic communication system. Indicates process noise; This represents the final estimated value of the state variable x at time k-1; This represents the predicted value at time k-1 for time k; The error covariance matrix for predicting time k: ; in, Let represent the error covariance matrix at time k-1; , Indicates variance; Step 4: Determine the position of each filtered signal Is there impulse noise? if ,but: Calculate observation weights: ; in, Represents the observation matrix; Represents the impulse noise covariance matrix; Calculate the Kalman gain: ; if ,but: Calculate the Kalman gain: ; in, Represents the background noise covariance matrix ; Step 5: Estimate state variables: ; Update the error covariance matrix: ; Step 6: Output the estimated values of the state variables. The estimated value of the error covariance matrix Then, proceed to the state estimation for the next moment.