An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: it may be applied to any state transition or measurement model. A simulation example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.

Stoch~stic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative samphng-(or Monte Ca~lo-) bas.ed approaches to the calculation of numerical estimates of marginal probability distributions. The three ap~roache.s w~1l be reviewed, compared, and contrasted in relation to various joint probability structures frequently enc.ountered in applications, In particular, the relevance of the approaches to calculating Bayesian posterior densities for a vanety of structured models will be discussed and illustrated.

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