A modern perspective on auxiliary particle filters

The auxiliary particle filter (APF) is a popular algorithm for the Monte Carlo approximation of the optimal filtering equations of state space models. This paper presents a summary of several recent developments which affect the practical implementation of this algorithm as well as simplifying its theoretical analysis. In particular, an interpretation of the APF, which makes use of an auxiliary sequence of distributions, allows the approach to be extended to more general Sequential Monte Carlo algorithms. The same interpretation allows existing theoretical results for standard particle filters to be applied directly. Several non-standard implementations and applications are also discussed