Gaussian filtering for polynomial systems based on moment homotopy

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-form solutions 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.