Designing 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-meansquares (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, so that the steady-state value of mean-square deviation (MSD) at each individual node become smaller that 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 are also provided that demonstrate the performance advantages of the proposed algorithm