Research On Non-standard Adaptive Filter

The standard adaptive filter has the stationary input signal without noise and the flawless desired signal without the impulsive noise.Recently,the standard adaptive filters have attracted extensive research attention.However,in the practical applications,the aforementioned conditions for the standard adaptive filter may not be met.For example,the input may be noisy or non-stationary,and the desired signal may be censored or disturbed by the impulsive noise.When the input signal and desired signal are under any of the aforementioned harsh environments,the adaptive filter is referred to as a non-standard adaptive filter.Using the traditional adaptive algorithms to deal with the non-standard adaptive filter problems under harsh environments,the performance of the filtering algorithms will suffer from deterioration.In order to solve the above problems,this dissertation studies a series of non-standard adaptive filtering algorithms.The work can be summarized as follows:1)This dissertation first states the basic elements of the adaptive filter structure.In addition,this dissertation introduces the conditions that the basic elements of the standard adaptive filter need to meet.Then,the basic concepts of standard adaptive filters are summarized.In the sequel,the non-standard adaptive filters under various harsh environments are introduced.Finally,the existing non-standard adaptive filtering algorithms under the harsh environment are reviewed.Besides,the shortcomings of the current algorithms are analyzed.2)This dissertation studies the non-standard adaptive filter with noisy input.In order to improve the performance of the constrained LMS and sparse normalized LMS algorithms under noisy input environment,two bias-compensated adaptive filtering algorithms are proposed in this dissertation.? A bias-compensated constrained least mean square(BC-CLMS)adaptive filtering algorithm for noisy input is proposed.In order to derive the proposed algorithm,a new cost function is introduced,whose gradient vector is unbiased.Therefore,the proposed algorithm can mitigate the effects of input noise and obtain an unbiased estimate.Then,the detailed performance analysis of the proposed algorithm is provided.Finally,simulations are conducted to demonstrate the advantages of the proposed algorithm.In addition,the correctness of the performance analysis is verified by the simulation.? A new normalized least mean square(NLMS)algorithm is proposed to identify the sparse systems where the input signal is corrupted by the white noise.This algorithm is called the bias-compensated zero-attracting NLMS(BC-ZA-NLMS)algorithm.The BC-ZA-NLMS algorithm introduces a bias-compensated vector to eliminate the bias caused by the input noise.The l1 norm is also introduced in the the cost function to derive the BC-ZA-NLMS algorithm.In addition,in order to solve the problem of time-varying sparseness,a bias-compensated reweighted ZA-NLMS(BC-RZA-NLMS)algorithm is also proposed.Two proposed algorithms are superior to the traditional NLMS and bias-compensated NLMS(BC-NLMS)algorithms in identifying sparse systems.Finally,the Monte Carlo simulations are performed to demonstrate the advantages of the proposed BC-ZA-NLMS and BC-RZA-NLMS algorithms.3)This dissertation studies the performance of distributed adaptive filters under cyclostationary input.The performance of the diffusion least mean square(DLMS)algorithm under cyclostationary input is analyzed.In this dissertation,the cyclostationary white Gaussian signal is adopted,which is a typical non-stationary signal and widely used in many practical applications.4)This dissertation studies the non-standard adaptive filter where the desired signal is under the harsh environments.In many practical applications of adaptive signal processing,the desired signal may be censored and corrupted by the impulsive noise.In this case,the performance of the traditional adaptive filtering algorithm may suffer from large performance degradation and even are not converged.In order to solve this problem,this dissertation proposes a new LMS algorithm with error nonlinearities by using the maximum correntropy criterion(MCC)and the censored regression algorithm.The algorithm can achieve good performance in the environment where the desired signal is censored and corrupted by the impulsive noise.Then,the performance analysis of the censored regression MCC adaptive algorithm is provided.5)This dissertation applies a novel LMS adaptive algorithm with error nonlinearities to the adaptive estimation of signals defined over graphs in the presence of the impulsive noise.The LMS adaptive algorithm with error nonlinearities is derived by minimizing the cost function based on the hyperbolic tangent.Therefore,the proposed algorithm is also called the adaptive hyperbolic tangent(AHT)algorithm on the graph.If the signal on the graph is band-limited,the algorithm can effectively reconstruct the signal from the partial observation signal under the impulsive noise environment.In addition,the theoretical analysis of the AHT algorithm on the graph is used to design an effective sampling strategy on the graph.6)This dissertation investigates non-standard adaptive filters where the input and desired signals are simultaneously corrputted by the harsh environments,i.e.,the input is noisy and the desired signal is censored and disturbed by the impulsive noise.When the existing adaptive filtering algorithm is in the above environment,the performance will deteriorate.In this dissertation,the bias correction estimator and the bias compensated algorithm are combined to propose the bias compensated robust set membership algorithm for censored regression(N-CR-BC-RSM).The algorithm can not only compensate the bias caused by the censored measurement and input noise but also be robust against the impulsive noise.