We present a novel estimation algorithm for filtering and regression with a number of advantages over existing methods. The algorithm has wide application in robotics as no assumptions are made about the underlying distributions, it can represent non-Gaussian multi-modal posteriors, and learn arbitrary non-linear models from noisy data. Our method is a generalisation of the Kernel Bayes' Rule that produces multi-modal posterior estimates represented as Gaussian mixtures. The algorithm learns non-linear state transition and observation models from data and represents all distributions internally as elements in a reproducing kernel Hilbert space. Inference occurs in the Hilbert space and can be performed recursively. When an estimate of the posterior distribution is required, we apply a quadratic programming pre-image method to determine the Gaussian mixture components of the posterior representation. We demonstrate our algorithm with two filtering experiments and one regression experiment; a multi-modal tracking simulation, a real tracking problem involving a miniature slot-car with an attached inertial measurement unit, and a regression problem of estimating the velocity field of a set of pedestrian paths for robot path-planning. Our algorithm compares favourably with the Gaussian process in the regression case, and a particle filter with learned process and observation models (the “GP-BayesFilter” particle filter).

This paper presents a distributed algorithm for performing joint localisation of a team of robots. The mobile robots have heterogeneous sensing capabilities, with some having high quality inertial and exteroceptive sensing, while others have only low quality sensing or none at all. By sharing information, a combined estimate of all robot poses is obtained. Inter-robot range-bearing measurements provide the mechanism for transferring pose information from well-localised vehicles to those less capable. In our proposed formulation, high frequency egocentric data (e.g., odometry, IMU, GPS) is fused locally on each platform. This is the distributed part of the algorithm. Inter-robot measurements, and accompanying state estimates, are communicated to a central server, which generates an optimal minimum mean-squared estimate of all robot poses. This server is easily duplicated for full redundant decentralisation. Communication and computation are efficient due to the sparseness properties of the information-form Gaussian representation. A team of three indoor mobile robots equipped with lasers, odometry and inertial sensing provides experimental verification of the algorithms effectiveness in combining location information.