A Scaled Spherical Simplex Filter (S3F) with a decreased n + 2 sigma points set size and equivalent 2n + 1 Unscented Kalman Filter (UKF) accuracy. (15th January 2022) - Papakonstantinou, Konstantinos G.; Amir, Mariyam; Warn, Gordon P.
Highlights: The Scaled Spherical Simplex Filter (S3F) is presented with n + 2 sigma points. Equivalent accuracy with the 2 n + 1 points Unscented Kalman Filter (UKF) is achieved. Accuracy is equivalent for all functions and all distribution types. Spherical simplex sigma points, weights and scaling factors are generally suggested. Detailed derivations are provided and the S3F can be used wherever UKF is applicable. Abstract: The computational efficiency of a sampling based nonlinear Kalman filtering process is mainly conditional on the number of sigma/sample points required by the filter at each time step to effectively quantify statistical properties of related states and parameters. Efficaciously minimizing the needed number of points would therefore have important implications, especially for large n -dimensional nonlinear systems. A set of minimum number of n + 1 sigma points is necessary in each filtering application in order to provide mean and nonsingular covariance estimates. Incorporating additional sigma points than this minimum set improves the accuracy of the estimates and can take advantage of a richer information content that can possibly exist, but at the same time increases the computational demand. To this end, by adding one more sigma point to this minimum set, and assigning general, well defined weights and scaling factors, a new Scaled Spherical Simplex Filter (S3F) with n + 2 sigma points set size is presented in this work, and it is theoretically proven that it can practically achieve in all cases the same accuracy and numerical stability as the typical 2 n + 1 sigma points Unscented Kalman Filter (UKF), with almost 50% less computational requirements. A comprehensive study of the suggested filter is presented, including detailed derivations, theoretical examples and numerical results, demonstrating the efficiency, robustness, and accuracy of the S3F.