Weighted diffusion continuous mixed p-norm algorithm for distributed estimation in non-uniform noise environment

Abstract This paper presents weighted diffusion least mean p-power (LMP) algorithm for distributed estimation of an unknown sparse vector in a sensor network. We consider a network, in which the variances of the noise for sensors are different, i.e., non-uniform noise condition. We replace the sum of mean square errors with a weighted sum of LMP for global and local cost functions of a sensor network. The weights are adaptive and are updated by a simple steepest-descent recursion to minimize the global and local cost functions of the adaptive algorithm. Further, we propose the adaptive weighted diffusion continuous mixed p-norm (CMPN) algorithm, which further improves the performance of the proposed weighted diffusion LMP algorithm. In the proposed weighted diffusion CMPN algorithm, p-power is considered adaptive and continuous in the range 1 ≤ p ≤ 2. Unlike the CMPN algorithm in the literature with uniform weights, the weighted diffusion CMPN algorithm uses adaptive weights, which are updated by a simple steepest descent recursion. We also extend the proposed algorithm to one-bit distributed estimation scenario. Performance analysis and simulation results show the efficacy of the proposed weighted diffusion LMP and CMPN algorithms. Further, the proposed one-bit weighted diffusion algorithms exhibit robustness against the different noise distributions.