Truncated Moment Problem for Dirac Mixture Densities with Entropy Regularization

We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous coverage of the state space.Comment: 18 pages, 6 figure

Deterministic Sampling of Multivariate Densities based on Projected Cumulative Distributions

We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate settings. Simple solutions are restricted to the one-dimensional case. In this paper, we propose to employ one-dimensional density projections. These are the Radon transforms of the densities. For every projection, we compute their cumulative distribution function. These Projected Cumulative Distributions (PCDs) are compared for all possible projections (or a discrete set thereof). This leads to a tractable distance measure in multivariate space. The proposed approximation method is efficient as calculating the distance measure mainly entails sorting in one dimension. It is also surprisingly simple to implement.Comment: 21 pages, 10 figure

Probabilistic Framework for Sensor Management

A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions

Dual Quaternion Sample Reduction for SE(2) Estimation

We present a novel sample reduction scheme for random variables belonging to the SE(2) group by means of Dirac mixture approximation. For this, dual quaternions are employed to represent uncertain planar transformations. The Cramér–von Mises distance is modified as a smooth metric to measure the statistical distance between Dirac mixtures on the manifold of planar dual quaternions. Samples of reduced size are then obtained by minimizing the probability divergence via Riemannian optimization while interpreting the correlation between rotation and translation. We further deploy the proposed scheme for nonparametric modeling of estimates for nonlinear SE(2) estimation. Simulations show superior tracking performance of the sample reduction-based filter compared with Monte Carlo-based as well as parametric model-based planar dual quaternion filters