Gaussian filtering for polynomial systems based on moment homotopy
Marco F. Huber, Uwe D. Hanebeck · 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-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.