Robust Smoothing for State-Space Models with Unknown Noise Statistics

摘要

The Kalman smoother provides optimal smoothing for fully-known state-space models. However, model uncertainty degrades the performance of the smoother dramatically. In this paper, we are concerned with state-space models, in which noise statistics are unknown and propose an optimal Bayesian Kalman smoother (OBKS), which is optimal relative to the posterior distribution of the unknown noise parameters. The Bayesian innovation process and Bayesian orthogonality principle lie at the heart of the proposed smoothing framework. Through introducing the effective Kalman smoothing gain, we develop a recursive forward-backward structure, which is analogous to that of the classical Kalman smoother. We demonstrate the effectiveness of the proposed smoother by applying it to a target tracking example.