Study On Echo Cancellation Algorithm Based On Kalman Filtering

Kalman adaptive echo cancellation method is the main method in the field of acoustic echo cancellation,with good robustness and real-time performance,and is widely used in systems such as cell phones,video conferencing and hearing aids.However,traditional algorithms assume the background noise to conform to Gaussian distribution for the sake of analysis on the one hand,and do not make full use of the sparse characteristics of the system on the other hand,thus limiting the adaptability of the algorithm to different environments and the effect of echo cancellation.To this end,this thesis presents an in-depth study of Kalman adaptive echo cancellation algorithms under non-Gaussian noise conditions,including:Firstly,based on the long and sparse impulse response of the echo path,this thesis decomposes the echo path into shorter impulse responses by using the Kronecker integral solution and uses two shorter adaptive filters for system identification,which can not only improve the computational efficiency but also improve the accuracy of the solution.After an in-depth study of the entropy theory to suppress the effect of non-Gaussian noise,the Kalman filter algorithm based on the maximum correntropy Kalman filter algorithm(MCKF-NKP,Maximum Correntropy Kalman filter Nearest Kronecker product),which not only improves the computational efficiency but also suppresses the effect of non-Gaussian noise.Secondly,considering that each weight factor of the impulse response to be identified has independent volatility and uncertainty,this thesis,based on the proposed MCKF-NKP algorithm,derives a recursive formula for the process noise variance of the impulse response to be identified described by a first-order Markov model in the state equation using the difference of adjacent moment filters,and proposes a maximum correlation entropy Kronecker integral solution based on the Kalman filtering algorithm(MCKF-NKP-ICF,MCKF-NKPIndividual Control factors)based on the Kronecker integral solution of the maximum correlation entropy is proposed,thus avoiding the problem of pre-determining the process noise variance in advance by traditional algorithms and making the algorithm more robust.Finally,the theoretical analysis of the convergence of the proposed algorithm is presented,and the sufficient conditions for the convergence of the algorithm are given,and the simulation experiments of echo cancellation of Gaussian white noise signals,speech-like spectral noise signals and real speech signals are carried out under the conditions of non-Gaussian noise with different pulse levels.