Robust auxiliary particle filters using multiple importance sampling

A poor choice of importance density can have detrimental effect on the efficiency of a particle filter. While a specific choice of proposal distribution might be close to optimal for certain models, it might fail miserably for other models, possibly even leading to infinite variance. In this paper we show how mixture sampling techniques can be used to derive robust and efficient particle filters, that in general performs on par with, or better than, the best of the standard importance densities. We derive several variants of the auxiliary particle filter using both random and deterministic mixture sampling via multiple importance sampling. The resulting robust particle filters are easy to implement and require little parameter tuning.