Sampling strategies for Monte Carlo filters of non-linear systems

We illustrate the potential pitfalls in the choice of sampling strategies for simulating the posterior distribution in a linear system with a non-linear observation process. We focus on the example of bearings only tracking, and use simulation to compare the convergence rate of various Metropolis-Hastings strategies, in the context of a simple model. The results indicate that the inclusion of a global `scale move´ in the Metropolis-Hastings sampler dramatically increases the convergence rate. Using such a Metropolis-Hastings sampler as a benchmark, we are able to explore the efficacy of other sampling strategies, such as the Gibbs sampler, and the effect of the prior distribution on the posterior distribution. We are further able to evaluate various recursive filtering algorithms, such as the Kalman filter and the SIR filter. Finally, we discuss ways in which the `global´ Metropolis-Hastings approach could be modified to take account of the computational advantages of recursive filtering techniques. In the context of bearings only tracking, these advantages accrue from assuming that all our prior knowledge about the target position at time t is accurately encapsulated in our current estimate of the target distribution at time t, and can therefore be discarded