In this paper, a new class of nonlinear Kalman filter is proposed to further improve filtering accuracy and efficiency for high-dimensional state estimation, which is named simplex Kalman filter (SKF). In the proposed SKF, the simplex rules of different numerical accuracy are utilized to generate two sets of sigma points that are applied to numerically compute multivariate moment integrals encountered in nonlinear Kalman filter (NKF). The proposed SKFs can achieve improvement of computational efficiency in state estimation. With the increase in the state dimension, the computational complexity of the new SKFs is lower than that of traditional NKF, which can mitigate the curse of dimension issue in high-dimensional systems. Simulations on nonlinear high-dimensional problem and bearings only tracking demonstrate that in comparison with different NKFs, the new SKFs can improve the filtering performance efficiently.
['Wenjie Zhang', 'Shiyuan Wang', 'Yali Feng']
Novel Simplex Kalman Filters