Design of an incremental LMS adaptive network with desired mean-square deviation

The distributed estimation problem arises in many sensor network-based applications. Recently, adaptive networks have been proposed in the literature to solve the problem of linear estimation in a cooperative fashion. Among the adaptive networks, the incremental-based algorithms (networks) offer excellent estimation performance, specially in small size networks. The goal of this paper is to design an incremental least-mean-squares (LMS) adaptive network with predefined performance. Specifically, under small step-sizes and some conditions on the data, we assign the step size parameter at any node in an incremental LMS adaptive network, in a way that that the steady-state value of mean-square deviation (MSD) at each individual node becomes smaller than a desired value. In the proposed algorithm, the step-size is adjusted for each node according to its measurement quality which is stated in terms of observation noise variance. Simulation results demonstrate the performance advantages of the proposed algorithm.