An adaptive mixture view of particle filters

Nicola Branchini, Víctor Elvira

Abstract: Particle filters (PFs) are algorithms that approximate the so-called filtering distributions in complex state-space models. We present a unified view on PFs as importance sampling with adaptive mixture proposals. Existing PFs can be derived as special cases by making specific choices for the components of the mixture proposals and for the importance weights. Our perspective clarifies that the existing PFs implicitly construct particular mixture proposals where the components are chosen independently of each other. We exploit the introduced flexibility of our perspective to propose a class of algorithms, adaptive mixture particle filters (AM-PF). Following IS arguments, the aim is to optimize the mixture proposal to match (an approximation of) the filtering posterior. We discuss two particular cases of the framework, the improved APF (IAPF) and the optimized APF (OAPF). In both linear and nonlinear dynamical systems models, our mixture particle filters consistently show improved performance compared to widely used algorithms such as the bootstrap particle filter (BPF) and the auxiliary particle filter (APF). We conclude by outlining promising future directions opened by our framework.