On marginal particle filters with linear complexity

The choice of proposal distribution affects critically the efficiency of a particle filter (PF). When it is not feasible to increase the number of particles, then more advanced proposals may avoid particle depletion. One further option is to compute the marginal posterior distribution. However, exact marginalization has quadratic complexity in the number of particles. This contribution discusses and compares some ideas for implementing a marginal PF with linear complexity, leading to an accept-reject algorithm. However, it turns out that the proposed solution can be interpreted as a way to implement the optimal proposal. Different proposals with and without marginalization are compared on a simple example.