Polynomial Based Kalman Filter Result Fitting to Data

A Kalman based trajectory estimate always has an associated uncertainty characterized by its covariance. A way to reduce this uncertainty consists in the adaptive selection of parameters during the filtering process. Different informed strategies for automatically tuning the parameters in Kalman smoothers were already proposed. We propose here a different semi-blind post processing approach, which is faster and more robust. Starting from the conjecture that the trajectory is polynomial in cartesian coordinates, our method supposes to fit the data obtained at the output of Kalman filter to a polynomial. We propose a new polynomial fitting method based on wavelets in two steps: denoising and polynomial part extraction and we compare favorably its performance with the performance of classical polynomial fitting method in an experiment using real data.