16.5 The SIS Auxiliary Particle Filter

The use of a well chosen SIS proposal distribution, img, should ensure that the current observation zn is incorporated into the proposal procedure so that particles are not moved blindly into regions of the state space that are unlikely given that observation. Obviously, the BPF fails to achieve this objective since the current observation is not considered when img. As we discussed previously, the OPF chooses img, but it is difficult to implement except in special cases. The SIS auxiliary particle filter (APF) is a particle filter that incorporates the current observations into the proposal distribution in a suboptimal way.

In the standard resampling SIS particle filter, including the BPF, the particles are resampled after the particles are drawn from the importance density and the weights have been updated by the current observation. In the OPF, on the other hand, resampling takes place before the particles are sampled from the importance density. This can be verified by comparing Table 16.5 with either Table 16.2 or Table 16.4. In Ref. [16] and Chapter 13 of Ref. [17], Pitt and Shephard proposed the APF as a variant of the standard SIS where the resampling ...

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