Augmented Particle Filters

ABSTRACT

Particle filters have been widely used for online filtering problems in state–space models (SSMs). The current available proposal distributions depend either only on the state dynamics, or only on the observation, or on both sources of information but are not available for general SSMs. In this article, we develop a new particle filtering algorithm, called the augmented particle filter (APF), for online filtering problems in SSMs. The APF combines two sets of particles from the observation equation and the state equation, and the state space is augmented to facilitate the weight computation. Theoretical justification of the APF is provided, and the connection between the APF and the optimal particle filter (OPF) in some special SSMs is investigated. The APF shares similar properties as the OPF, but the APF can be applied to a much wider range of models than the OPF. Simulation studies show that the APF performs similarly to or better than the OPF when the OPF is available, and the APF can perform better than other filtering algorithms in the literature when the OPF is not available.

KEYWORDS:

• Nonlinear filtering
• Particle filter
• Sequential Monte Carlo
• State–space model

Acknowledgments

The authors thank the editor, the associate editor, and three referees for valuable suggestions.

Funding

This work was partially supported by the National Science Foundation grant ATM-0620550.