Recursive Bayesian estimation for Markov jump linear systems with unknown mode-dependent state delays

This study considers the minimum mean square error estimation problem for a class of jump Markov linear systems with unknown mode-dependent state delays. In order to show the difficulties caused by the unknown delays, the online Bayesian equation of the investigated system is firstly developed by incorporating the time-delay estimation into the recursion of system states. However, computing such optimal estimation causes an exponential increase in the requirement of computation and storage load. Therefore two different approximation techniques: interacting multiple-model approximation and detection-estimation method are utilised to obtain two suboptimal but executable filtering algorithms, respectively. Simulation results of the proposed methods for a system are presented to illustrate the effectiveness.