GP-SUM. Gaussian Processes Filtering of non-Gaussian Beliefs
This work addresses filtering for dynamic systems with non-Gaussian distributions, which is incremental as it builds on existing GP and sampling methods but offers improved accuracy for specific applications like robotics.
The authors tackled the problem of stochastic dynamic filtering with complex, non-Gaussian beliefs by introducing GP-SUM, a filtering algorithm that avoids linearizations and unimodal approximations, resulting in outperformance over GP-Bayes and Particle Filters on a standard benchmark and accurate predictions in a pushing task.
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), and to states represented as a weighted sum of Gaussians. The key attribute of GP-SUM is that it does not rely on linearizations of the dynamic or observation models, or on unimodal Gaussian approximations of the belief, hence enables tracking complex state distributions. The algorithm can be seen as a combination of a sampling-based filter with a probabilistic Bayes filter. On the one hand, GP-SUM operates by sampling the state distribution and propagating each sample through the dynamic system and observation models. On the other hand, it achieves effective sampling and accurate probabilistic propagation by relying on the GP form of the system, and the sum-of-Gaussian form of the belief. We show that GP-SUM outperforms several GP-Bayes and Particle Filters on a standard benchmark. We also demonstrate its use in a pushing task, predicting with experimental accuracy the naturally occurring non-Gaussian distributions.