A Mixture Regularized Rao-Blackwellized Particle Filter for Terrain Positioning

This study is concerned with the development of a robust particle filtering algorithm tailored to the problem of terrain-aided positioning (TAP) via radar altimeter measurements. The Rao-Blackwellized particle filter (RBPF) is a popular particle filtering algorithm for TAP that takes advantage of the nature of the state-space model by sampling particles in a subspace of the state space, yielding more efficient estimators than the standard particle filter. Like most Monte Carlo filters, the standard RBPF uses the transition kernel as the proposal distribution during the particle update step. However, in contexts where the likelihood function is peaky, this may be highly inefficient since samples may fall in regions of low posterior probability. To address this issue, it is often advocated to use an importance sampling density that takes into account the latest observation. In a sequential importance sampling context, an optimal importance density is available but can be easily sampled only for specific state-space models, which raises the question of how to design a proposal density that is efficient yet easy to sample from. In this paper, we propose a particle filtering importance sampling method adapted to multimodal distributions. It hinges on the use of a robust proposal density as well as a cluster-based representation of the multimodal posterior. This leads to a novel marginalized particle filter, the regularized RBPF, that is evaluated on a challenging terrain positioning application.