Multiplicative Gaussian Particle Filter
This addresses filtering problems in robotics and related fields, but appears incremental as it builds on existing particle filter methods.
The paper tackles approximate inference in filtering problems by proposing a sampling-based approach that approximates distributions with weighted sums of continuous functions instead of discrete states, and demonstrates its potential through preliminary experiments on robot localization with comparisons to particle filters.
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the distribution with a weighted sum of functions from a set of continuous functions. Central to the approach is the use of sampling to approximate multiplications in the Bayes filter. We provide theoretical analysis, giving conditions for sampling to give good approximation. We next specialize to the case of weighted sums of Gaussians, and show how properties of Gaussians enable closed-form transition and efficient multiplication. Lastly, we conduct preliminary experiments on a robot localization problem and compare performance with the particle filter, to demonstrate the potential of the proposed method.