Stochastic sampling algorithms for state estimation of jump Markov linear systems

Jump Markov linear systems are linear systems whose parameters evolve with time according to a finite-state Markov chain. Given a set of observations, our aim is to estimate the states of the finite-state Markov chain and the continuous (in space) states of the linear system. The computational cost in computing conditional mean or maximum a posteriori (MAP) state computing conditional mean or maximum a posteriori (MAP) state estimates of the Mark ov chain or the state of the jump Markov linear system grows exponentially in the number of observations. In this paper, we present three globally convergent algorithms based on sto chastic sampling methods for state estimation of jump Markov linear systems . The cost per iteration is linear in the data length. The first proposed a lgorithm is a data augmentation (DA) scheme that yields conditional mean st ate estimates. The second proposed scheme is a stochastic annealing (SA) ve rsion of DA that computes the joint MAP sequence estimate of the finite and continuous states. Finally, a Metropolis-Hastings DA scheme based on SA is designed to yield the MAP estimate of the finite-state Markov chain is pro posed. Convergence results of the three above-mentioned stochastic algorith ms are obtained. Computer simulations are carried out to evaluate the performances of the pr oposed algorithms. The problem of estimating a sparse signal developing fro m a neutron sensor based on a set of noisy data from a neutron sensor and t he problem of narrow-band interference suppression in spread spectrum code- division multiple-access (CDMA) systems are considered.