Fixed-lag smoothing using sequential importance sampling

In this paper we present methods for fixed-lag smoothing using Sequent ial Importance sampling (SIS) for state space models with unknown parameters. Sequential processing usi ng Monte Carlo simulation is an area of growing interest for many engineering and statistical applicatio ns where data arrive point by point rather than in a batch. The methods presented here are related to the p articl filtering ideas seen in Gordonet al. (1993), Liu and Chen (1995), Berzuini et al. (1997), Pitt and Shephard (1998) and Doucetet al. (1998). Techniques for fixed-lag simulation using either the filteri ng density or the smoothing density are developed. In addition we describe methods for r egenerating parameters of the state-space model by sampling. We are concerned in particular with problems i n Digital Communication systems where off-line or batch-based methods, such as Markov chain Monte Carlo (MCMC), are not well suited. The new techniques are demonstrated by application to a standard digital communications model and the performance of the various methods is compared.

[1]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[2]  Alan E. Gelfand,et al.  Bayesian statistics without tears: A sampling-resampling perspective , 1992 .

[3]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[4]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[5]  Jun S. Liu,et al.  Blind Deconvolution via Sequential Imputations , 1995 .

[6]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[7]  S. Godsill,et al.  Bayesian blind deconvolution for mobile communications , 1997 .

[8]  J. Heller,et al.  Viterbi Decoding for Satellite and Space Communication , 1971 .

[9]  D. Mayne,et al.  Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering† , 1969 .

[10]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[11]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[12]  Patrick Duvaut,et al.  Fully Bayesian analysis of Hidden Markov models , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[13]  Neil J. Gordon,et al.  Bayesian State Estimation for Tracking and Guidance Using the Bootstrap Filter , 1993 .

[14]  N. G. Best,et al.  Dynamic conditional independence models and Markov chain Monte Carlo methods , 1997 .

[15]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.