Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances

We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.Comment: Derivations for the smoother can found here: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-12070

State-Space Inference and Learning with Gaussian Processes

State-space inference and learning with Gaussian processes (GPs) is an unsolved problem. We propose a new, general methodology for inference and learning in nonlinear state-space models that are described probabilistically by non-parametric GP models. We apply the expectation maximization algorithm to iterate between inference in the latent state-space and learning the parameters of the underlying GP dynamics model. Copyright 2010 by the authors

Robust Filtering and Smoothing with Gaussian Processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of "system identification" is more robust than finding point estimates of a parametric function representation. In this article, we present a principled algorithm for robust analytic smoothing in GP dynamic systems, which are increasingly used in robotics and control. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail.Comment: 7 pages, 1 figure, draft version of paper accepted at IEEE Transactions on Automatic Contro

Probabilistic movement modeling for intention inference in human-robot interaction.

Intention inference can be an essential step toward efficient humanrobot interaction. For this purpose, we propose the Intention-Driven Dynamics Model (IDDM) to probabilistically model the generative process of movements that are directed by the intention. The IDDM allows to infer the intention from observed movements using Bayes ’ theorem. The IDDM simultaneously finds a latent state representation of noisy and highdimensional observations, and models the intention-driven dynamics in the latent states. As most robotics applications are subject to real-time constraints, we develop an efficient online algorithm that allows for real-time intention inference. Two human-robot interaction scenarios, i.e., target prediction for robot table tennis and action recognition for interactive humanoid robots, are used to evaluate the performance of our inference algorithm. In both intention inference tasks, the proposed algorithm achieves substantial improvements over support vector machines and Gaussian processes.

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an $L^2$ regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intracortical sources. In our model, the observation model is derived from the steady-state solution to Maxwell's equations while the latent model representing neural dynamics is given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org