Fixed-lag smoothing using sequential importance sampling

In this paper we present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) for state space models with unknown parameters. Sequential processing using Monte Carlo simulation is an area of growing interest for many engineering and statistical applications where data arrive point by point rather than in a batch. The methods presented here are related to the particle filtering ideas seen in Gordon dal. (1993), Liu and Chen (1995), Berzuini et al. (1997), Pitt and Shephard (1999) and Doucet (1998). Techniques for fixed-lag simulation using either the filtering density or the smoothing density are developed. In addition we describe methods for regenerating parameters of the state-space model by sampling. We are concerned in particular with problems in 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.