POLYFILTER: A new state estimation filter for nonlinear systems

In this paper, we propose a new state estimation filter called POLYFILTER, which is based on polynomial approximation of the nonlinear transformation obtained using particular multidimensional extension of Stirling´s Interpolation Formula (SIF). In contrast to the Extended Kalman Filtering, no derivatives are needed in the interpolation formula; only function evaluations are needed during interpolation. This accommodates easy implementation of the filter, and it enables the state estimation even when there are singular points in which the derivatives are undefined.