Computationally Efficient Simplex Unscented Kalman Filter Based on Numerical Integration

Abstract

AbstractThis paper concerns the computationally efficient unscented Kalman filter (UKF) for nonlinear dynamic systems. From the numerical integration viewpoint, it is proved for the first time that the spherical simplex unscented transformation (UT) cannot be derived from the integration rule of degree 2, which is inconsistent with well‐known previous works. Then a novel simplex UT consisting of n + 1 equally weighted points, which can construct a numerical integration formula of degree 2, is investigated. By embedding the proposed simplex UT into the Kalman filtering framework, a computationally efficient simplex UKF is derived. Compared with the spherical simplex UT based UKF, the proposed algorithm is more rigorous and more accurate.