A Particle Fusion Approach for Distributed Filtering and Smoothing

Abstract

Distributed state estimation is an important tool for coordinated team decision-making and typically involves sharing information between robots in order to outperform individual state estimation. The shared information typically takes the form of relative measurements which allow team members to act as virtual sensors for other robots where the virtual sensor uncertainty is corrupted also by the team member’s state uncertainty. However, incorporating relative measurements commonly depends on a pointwise product operation in most distributed estimation techniques which is well defined for continuously-valued distributions but ill-defined for particle-based distributions. We propose a drop-in replacement for the pointwise product based on using the generalized Hölder’s inequality to upper-bound the product over a series of grid cell sets that discretize the state space. This upper-bound is well defined for particle-based distributions and allows for tighter approximations by decreasing the volume of the sets. We leverage the approach to realize two distributed estimation strategies that use a pointwise product, the Kullback–Leibler Average and Belief Propagation and use these methods in simulations and experiments with a pair of miniature autonomous blimps. We found that after distributed smoothing, we were able to achieve an average improvement of ∼25.1% and ∼35.2% in the position tracking error, indicating our distributed smoothing strategy is able to improve the tracking performance of our initial filtering estimates.