Modified Huber M-Estimate Function-Based Distributed Constrained Adaptive Filtering Algorithm Over Sensor Network

Most of the existing distributed adaptive filtering algorithms over wireless sensor networks (WSNs) are developed, aiming to solve unconstrained network optimization problems. However, in practice, the weight coefficients of the filter may need to satisfy a set of linear equations. Thus, a distributed adaptive algorithm that can solve the sensor network optimization problem under constraints is needed. Considering the possible impulsive interference in the observed signals, a novel robust distributed constrained adaptive algorithm called diffusion constrained least mean M-estimate (D-CLMM) is proposed by using the modified Huber function (MHF), which endows the network robustness to impulsive noise. The transient, steady-state performances and stability of the proposed D-CLMM are studied with the aid of some commonly used assumptions and verified by computer simulations. Moreover, the effectiveness of D-CLMM is verified in distributed parameter estimation and beamforming applications in non-Gaussian noise environments.