TY - JOUR

T1 - A Scaled Spherical Simplex Filter (S3F) with a decreased n + 2 sigma points set size and equivalent 2n + 1 Unscented Kalman Filter (UKF) accuracy

AU - Papakonstantinou, Konstantinos G.

AU - Amir, Mariyam

AU - Warn, Gordon P.

N1 - Funding Information:
This material is based upon work supported by the U.S. National Science Foundation under CAREER Grant No. 1751941.
Publisher Copyright:
© 2020 Elsevier Ltd

PY - 2021

Y1 - 2021

N2 - 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 2n + 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.

AB - 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 2n + 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.

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U2 - 10.1016/j.ymssp.2020.107433

DO - 10.1016/j.ymssp.2020.107433

M3 - Article

AN - SCOPUS:85105023438

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 107433

ER -