Paper D. Gaussian Filtering for Polynomial Systems Based on Moment Homotopy. Edited version of the paper: M. F. Huber and U. D. Hanebeck. Gaussian Filtering for Polynomial Systems Based on Moment Homotopy. In Proceedings to the 16th International Conference on Information Fusion (Fusion), pages 1080-1087, Istanbul, Turkey, July 2013

This paper proposes Gaussian filters for polynomial systems with efficient solutions for both the prediction and the filter step. For the prediction step, computationally efficient closed-formsolutions are derived for calculating the exact moments. In order to achieve a higher estimation quality, the filter step is solved without the usual additional assumption that state and measurement are jointly Gaussian distributed. As this significantly complicates the required moment calculation, a homotopy continuation method is employed that yields almost optimal results.