This paper studies the mean and mean-square behaviors of the M-estimate based normalized subband adaptive filter algorithm (M-NSAF) with robustness against impulsive noise. Based on the contaminated-Gaussian noise model, the stability condition, transient and steady-state results for the algorithm are formulated analytically. The analysis results help us to better understand the M-NSAF performance in impulsive noise. To further obtain fast convergence and low steady-state estimation error, we derive a variable step size (VSS) M-NSAF algorithm. This VSS scheme is also generalized to proportionate M-NSAF variants for sparse systems. Computer simulations on system identification in impulsive noise and acoustic echo cancellation with double-talk are performed to demonstrate our theoretical analysis and the effectiveness of the proposed algorithms.

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate update at each node. A recursive strategy for computing the constraint is proposed using side information from the neighboring nodes to further improve the robustness. We also analyze the mean-square convergence behavior of the proposed algorithm. The second proposed algorithm is a modification of the first one based on the dichotomous coordinate descent iterations. It has a performance similar to that of the former, however its complexity is significantly lower especially when input regressors of agents have a shift structure and it is well suited to practical implementation. Simulations show the superiority of the proposed algorithms over previously reported techniques in various impulsive noise scenarios.

This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to exploit the underlying sparsity of systems and to further improve the learning performance, a sparse variant is also developed by combining the $l_{0}$ -norm of the estimates into the update process. We then carry out an analysis of the transient, steady-state and stability behaviors of the algorithms in a unified framework. In particular, we employ an analytical method that is simpler than conventional approaches to deal with the score function since it removes the requirements of integrals and Price's theorem. Simulations in impulsive noise environments show that the proposed algorithms are superior to some existing diffusion algorithms and the theoretical results are verifiable.

This paper presents a family of robust set-membership normalized subband adaptive filtering (RSM-NSAF) algorithms for acoustic echo cancellation (AEC). By using a new robust set-membership error bound, the RSM-NSAF algorithm obtains improved robustness against impulsive noises and decreased steady-state misalignment relative to the conventional set-membership NSAF (SM-NSAF) algorithm. To exploit the sparsity of the impulse response, the L ₀ norm constraint robust set-membership NSAF (L ₀ -RSM-NSAF), robust set-membership improved proportionate NSAF (RSM-IPNSAF), and L ₀ norm constraint robust set-membership improved proportionate NSAF (L ₀ -RSM-IPNSAF) algorithms are derived by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the L ₀ norm of the weighted updated weight vector. Simulations in AEC application confirm the improvements of the proposed algorithms in performance.