Iterative algorithms for optimal state estimation of jump Markov linear systems

Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. We present three original deterministic and stochastic iterative algorithms for optimal state estimation of JMLS whose computational complexity at each iteration is linear in the data length. The first algorithm yields conditional mean estimates. The second algorithm is an algorithm that yields the marginal maximum a posteriori (MMAP) sequence estimate of the finite state Markov chain. The third algorithm is an algorithm that yields the MMAP sequence estimate of the continuous state of the JMLS. Convergence results for these three algorithms are obtained. Computer simulations are carried out to evaluate their performance.