Distributed estimation based on covariances under network-induced phenomena described by random measurement matrices

Recursive distributed filtering and fixed-point smoothing algorithms are proposed from measurements through sensor networks perturbed by random parameter matrices and additive noises. The proposed observation model provides a unified framework to consider some network-induced random phenomena. Using an innovation approach, intermediate distributed optimal least-squares (LS) linear estimators are firstly obtained at each sensor node, processing the available output measurements, not only from the own sensor but also from its neighbouring sensors according to the network topology. After that, the proposed distributed estimators are designed at each node as the LS matrix-weighted linear combination of the intermediate estimators within its neighbourhood. The proposed algorithms use only covariance information and do not require the state-space model of the signal. To compare the accuracy of the estimators, recursive expressions for the estimation error covariance matrices are also derived. A simulation example shows the effectiveness of the proposed estimation algorithms and some of the network-induced uncertainties covered by the observation model with random parameter matrices considered in this paper.