Stochastic sampling algorithms for state estimation of jump Markov linear systems

TitleStochastic sampling algorithms for state estimation of jump Markov linear systems
Publication TypeJournal Article
Year of Publication2000
AuthorsDoucet, A., A. Logothetis, and V. Krishnamurthy
JournalAutomatic Control, IEEE Transactions on
Pagination188 -202
Date Publishedfeb.
Keywordscode division multiple access, convergence, data augmentation, discrete time systems, finite-state Markov chain, globally convergent algorithms, interference suppression, joint MAP sequence estimate, jump Markov linear systems, linear systems, Markov processes, maximum a posteriori state estimates, mean state estimates, Metropolis-Hastings scheme, narrow-band interference suppression, neutron sensor, sampling methods, simulated annealing, sparse signal, spread spectrum code-division multiple-access systems, spread spectrum communication, state estimation, stochastic annealing, stochastic sampling algorithms

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 estimates of the Markov chain or the state of the jump Markov linear system grows exponentially in the number of observations. We present three globally convergent algorithms based on stochastic sampling methods for state estimation of jump Markov linear systems. The cost per iteration is linear in the data length. The first proposed algorithm is a data augmentation (DA) scheme that yields conditional mean state estimates. The second proposed scheme is a stochastic annealing (SA) version 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. Convergence results of the three above-mentioned stochastic algorithms are obtained. Computer simulations are carried out to evaluate the performances of the proposed algorithms. The problem of estimating a sparse signal developing from a neutron sensor based on a set of noisy data from a neutron sensor and the problem of narrow-band interference suppression in spread spectrum code-division multiple-access (CDMA) systems are considered


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