Research On Robust Sparsity-Induced Adaptive Filters

Adaptive filters are widely used in system identification,channel equalization,echo cancellation,active noise control,and so on.The estimation of sparse systems by adaptive filter is widely employed in the above applications.For sparse system estimation,constraint of lower-order norm of weight vector and proportional adaptation are the two most commonly used optimization methods to accelerate the convergence rate of adaptive filters.This thesis systematically studies the design and performance optimization of robust sparse adaptive filters in three different scenarios.For the scenario where the system output signal is interfered by impulsive noise,a family of sparse affine projection least lncosh(S-AP-Llncosh)filters are proposed.When the input signals of the adaptive filter are highly correlated,the affine projection method whitens the input signals by reusing past data to ensure that the filter is able to achieve a fast convergence rate.When there is heavy tail impulsive interference in the environment,the least lncosh method can effectively suppress the influence of impulsive noise on filtering accuracy.Moreover,the step-size of the filter is optimized by using the model-driven method,which addresses the problem of trade-off between the convergence rate and steady-state misalignment.For the scenario where the input signal of the filter is interfered by noise,a general optimization model is proposed to derive proportional total adaptive filters.Then,based on this model a proportional total normalized least mean square(PTNLMS)filter and a proportional maximum total correntropy(PMTC)filter are proposed.The proportional total normalized least mean square filter has a low computational cost and a fast convergence in Gaussian noise environment.The proportional maximum total correntropy filter converges quickly and is robust in non-Gaussian noise environment.In addition,the steady-state performance of the filters is analyzed.For the scenario where the input signal of the system is missing at random times,an imputation based missing data normalized least mean square(Imd-NLMS)filter is proposed.In this scenario,the normalized least mean square filter will produce a large estimation bias.The imputation based missing data normalized least mean square filter can effectively reduce the bias and is less sensitive to the changes in eigenvalue spread of the input-correlation matrix than the LMS filter.In addition,based on the proportional adaptive strategy,an imputation based missing data proportional normalized least mean square(Imd-PNLMS)filter and its convex combination optimization filter are proposed,which can effectively improve the accuracy of sparse system identification.The superiority of the proposed sparse adaptive filters in their own scenarios and the accuracy of theoretical analysis results are verified by several groups of experiments,which provide theoretical basis and method guidance for engineers to design sparse adaptive filters.