Marginalized particle filters for mixed linear/nonlinear state-space models

TLDR

The particle filter approximates posterior densities in nonlinear, non‑Gaussian problems but becomes computationally expensive as state dimension grows, so marginalizing linearly evolving states yields a Kalman filter per particle to reduce complexity. The paper derives the detailed formulation of a marginalized particle filter for general nonlinear state‑space models and discusses key special cases relevant to signal processing. The authors formulate the marginalized particle filter by integrating a Kalman filter for the linear sub‑states with a particle filter for the nonlinear sub‑states, and apply this hybrid scheme to an aircraft integrated navigation system. The hybrid filter reduces the dimensionality to three non‑marginalized states and achieves excellent performance on real flight data.

Abstract

The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non-Gaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state-space model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete high-dimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported.