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

This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian processes (GP), that does not rely on linearizations or unimodal 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. Effective sampling and accurate probabilistic propagation are possible by relying on the GP form of the system, and a Gaussian mixture form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also illustrate its practical use in a pushing task, and demonstrate that it predicts heteroscedasticity, i.e., different amounts of uncertainty, and multi-modality when naturally occurring in pushing.