24,645 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
DualSMC: Tunneling Differentiable Filtering and Planning under Continuous POMDPs
A major difficulty of solving continuous POMDPs is to infer the multi-modal
distribution of the unobserved true states and to make the planning algorithm
dependent on the perceived uncertainty. We cast POMDP filtering and planning
problems as two closely related Sequential Monte Carlo (SMC) processes, one
over the real states and the other over the future optimal trajectories, and
combine the merits of these two parts in a new model named the DualSMC network.
In particular, we first introduce an adversarial particle filter that leverages
the adversarial relationship between its internal components. Based on the
filtering results, we then propose a planning algorithm that extends the
previous SMC planning approach [Piche et al., 2018] to continuous POMDPs with
an uncertainty-dependent policy. Crucially, not only can DualSMC handle complex
observations such as image input but also it remains highly interpretable. It
is shown to be effective in three continuous POMDP domains: the floor
positioning domain, the 3D light-dark navigation domain, and a modified Reacher
domain.Comment: IJCAI 202
An introduction to quantum filtering
This paper provides an introduction to quantum filtering theory. An
introduction to quantum probability theory is given, focusing on the spectral
theorem and the conditional expectation as a least squares estimate, and
culminating in the construction of Wiener and Poisson processes on the Fock
space. We describe the quantum It\^o calculus and its use in the modelling of
physical systems. We use both reference probability and innovations methods to
obtain quantum filtering equations for system-probe models from quantum optics.Comment: 41 pages, 1 figur
- …