## Building Robust Simulation-based Filters for Evolving Data Sets (1999)

Citations: | 27 - 0 self |

### BibTeX

@TECHREPORT{Carpenter99buildingrobust,

author = {James Carpenter and Peter Clifford and Paul Fearnhead},

title = {Building Robust Simulation-based Filters for Evolving Data Sets},

institution = {},

year = {1999}

}

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### Abstract

this paper we will focus on an alternative class of filters in which theoretical distributions on the state space are approximated by simulated random measures. The first goal in filter design is to produce a compact description of the posterior distribution of the state given all the observations available so far. A basic requirement is that this description should be readily updated as new data become available. A mechanism has therefore to be devised which enables the approximating random measure to evolve and adapt. 3 SIMULATION BASED FILTERS Simulation based filters have a long history in the engineering literature, dating back to the work of Handschin and Mayne (1969); Handschin (1970); Akashi and Kumamoto (1977). Doucet (1998) provides a comprehensive review of the material. Since the Kalman filter is essentially a Bayesian update formula, the theory of Bayesian time series analysis is directly relevant (West and Harrison, 1997). We take as our starting point the filter developed by Gordon (1993); Gordon et al. (1993). The essence of the method is contained in a paper by Rubin (1988) who proposed the Sampling Importance Resampling (SIR) algorithm for obtaining samples from a complex posterior distribution without recourse to MCMC. In the simple non-dynamic case described by Rubin (1988), the method consists of sampling n observations from the prior distribution, attaching weights to the sampled points according to their likelihood, and then sampling with replacement from this weighted discrete distribution. As n ! 1, the resulting set of values then approximates a sample from the required posterior (Smith and Gelfand, 1992). In the dynamic version, proposed by Gordon et al. (1993), the SIR algorithm is applied repeatedly as new data are acquired. One can think of...