Normalized unscented Kalman filter and normalized unscented RTS smoother for nonlinear state-space model identification

A Kalman filter (KF) and Rauch-Tung-Striebel smoother (RTSS) provide the minimum mean square estimates of states for linear state-space models with additive Gaussian system and observation noises given a series of the past, current, and future observations. When the noise statistics such as the variances are unknown, initially normalizing the KF and RTSS algorithms by the total of the unknown variances provides new state estimation algorithms. We call these algorithms the normalized KF and normalized RTSS and on the basis of the log-likelihoods scored by the multiple trials with varied parameters, we can effectively identify the unknown system and observation noise variances. In this paper, we present the same normalization technique for nonlinear KF and RTSS algorithms named the unscented KF and unscented RTSS. In the same way as the normalized KF and normalized RTSS, these new normalized unscented KF and normalized unscented RTSS algorithms make it possible to estimate the unknown noise variances of nonlinear state-space models. Because it often happens that the noise variances are unknown in actual analysis cases, these algorithms are considerably effective from the aspect of the application viewpoints. The performance was confirmed by experiments using artificially generated data.