An adaptive distributed parameter estimation approach in incremental cooperative wireless sensor networks

Abstract This paper studies the distributed estimation problem of in a wireless sensor network (WSN) where the collected observations are used to estimate a deterministic network-wide parameter. We propose an adaptive distributed parameter estimation approach for WSN, named as DI-NLMS, using the incremental least-mean squares (I-LMS) technique and exploiting the spatio-temporal diversity to achieve fast convergence rate and satisfactory steady state performance. In this algorithm, every individual node shares the changes in the surrounding environment with its immediate neighbors such that the information on such changes, that affect convergence rate and steady state performance, can fully characterize the features of the entire network. We deduce the optimal variable step size for I-LMS and give the distributed step size updating strategy. A guideline on how to exploit the spatio-temporal dimensions for LMS-type implementations is outlined and an algorithm is proposed. We derive theoretically the minimal mean-square derivation (MSD) for DI-NLMS in steady state. The simulations for derived theoretical results and target localization application confirm the effectiveness and efficiency of the proposed algorithm.