Efficient Sequential Monte Carlo With Multiple Proposals and Control Variates

Sequential Monte Carlo is a useful simulation-based method for online filtering of state-space models. For certain complex state-space models, a single proposal distribution is usually not satisfactory and using multiple proposal distributions is a general approach to address various aspects of the filtering problem. This article proposes an efficient method of using multiple proposals in combination with control variates. The likelihood approach of Tan (2004) is used in both resampling and estimation. The new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates. The guidance for selecting multiple proposals and control variates is also given. Numerical examples are used to demonstrate that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter.