Fast particle filters for multi-rate sensors

Computational complexity is a major concern for practical use of the versatile particle filter (PF) for nonlinear filtering applications. Previous work to mitigate the inherent complexity includes the marginalized particle filter (MPF), with the fastSLAM algorithm as one important case. MPF utilizes a linear Gaussian sub-structure in the problem, where the Kalman filter (KF) can be applied. While this reduces the state dimension in the PF, the present work aims at reducing the sampling rate of the PF. The algorithm is derived for a class of models with linear Gaussian dynamic model and two multi-rate sensors, with different sampling rates, one slow with a nonlinear and/or non-Gaussian measurement relation and one fast with a linear Gaussian measurement relation. For this case, the KF is used to process the information from the fast sensor and the information from the slow sensor is processed using the PF. The problem formulation covers the important special case of fast dynamics and one slow sensor, which appears in many navigation and tracking problems.