3 research outputs found
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), 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.Comment: WAFR 2018, 16 pages, 7 figure
Non-Oscillatory Pattern Learning for Non-Stationary Signals
This paper proposes a novel non-oscillatory pattern (NOP) learning scheme for
several oscillatory data analysis problems including signal decomposition,
super-resolution, and signal sub-sampling. To the best of our knowledge, the
proposed NOP is the first algorithm for these problems with fully
non-stationary oscillatory data with close and crossover frequencies, and
general oscillatory patterns. NOP is capable of handling complicated situations
while existing algorithms fail; even in simple cases, e.g., stationary cases
with trigonometric patterns, numerical examples show that NOP admits
competitive or better performance in terms of accuracy and robustness than
several state-of-the-art algorithms