Locally Adaptive Cooperative Kalman Smoothing and Its Application to Identification of Nonstationary Stochastic Systems

One of the central problems of the stochastic approximation theory is the proper adjustment of the smoothing algorithm to the unknown, and possibly time-varying, rate and mode of variation of the estimated signals/parameters. In this paper we propose a novel locally adaptive parallel estimation scheme which can be used to solve the problem of fixed-interval Kalman smoothing in the presence of model uncertainty. The proposed solution is based on the idea of cooperative smoothing-the Bayesian extension of the leave-one-out cross-validation approach to model selection. Within this approach the smoothed estimates are evaluated as a convex combination of the estimates provided by several competing smoothers. We derive computationally attractive algorithms allowing for cooperative Kalman smoothing and show how the proposed approach can be applied to identification of nonstationary stochastic systems.