Distributed Widely Linear Multiple-Model Adaptive Estimation

The paper considers the problem of estimating the state of a complex-valued stochastic hybrid system observed distributively using an agent/sensor network (AN/SN) with complex-valued (possibly noncircular) observations. In several distributed estimation problems, a suitable model to describe the underlying system is unknown a priori, i.e., distributed state estimation with structural uncertainty. Motivated by application of widely linear processing techniques in such problems, the paper proposes a class of distributed multiple-model adaptive estimation algorithms, referred to as the CD/MMAE. By incorporating the particular structure of the complex-valued observations on the second moment, first we develop two hierarchical CD/MMAE implementations and then use them as the building blocks and develop a diffusion-based hybrid estimator for decentralized estimation without incorporation of a fusion centre. The paper derives a new form of the adaptation law and a new form of information fusion, which takes advantage of the full second-order statistical properties of the underlying observations. Convergence properties of the proposed diffusion-based CD/MMAE are then investigated. We show that the adaptive weight of all local nodes converges to the true mode with probability one. Simulation results indicate that the proposed hybrid estimators provide improved performance and convergence properties over their traditional counterparts.