GP-SUM. Gaussian Process Filtering of non-Gaussian Beliefs

This work centers on the problem of stochastic filtering for systems that yield complex beliefs. The main contribution is GP-SUM, a filtering algorithm for dynamic systems expressed as Gaussian Processes (GP), that does not rely on linearizations or Gaussian approximations of the belief. The algorithm can be seen as a combination of a sampling-based filter and a probabilistic Bayes filter. GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. Both, the sampling of the state and its propagation, are made possible by relying on the GP form of the system. In practice, the belief has the form of a weighted sum of Gaussians. We evaluate the performance of the algorithm with favorable comparisons against multiple versions of GP-Bayes filters on a standard synthetic problem. We also illustrate its practical use in a pushing task, and demonstrate that GP-SUM can predict heteroscedasticity, i.e., different amounts of uncertainty, and multi-modality when naturally occurring in pushing.