Estimation and detection for systems with second order Markovian switching coefficients

The state estimation and mode detection of linear systems with second order Markovian switching coefficients are considered. Two approaches to this problem are given. The first approach is a generalized pseudo-Bayesian approach that utilizes r³ filter updates for each measurement and r models. The second approach utilizes mixing of the previous model-conditioned estimates similar to that of the interacting multiple model algorithm to estimate the state and the mode of the system with r² filter updates for r models.