A new perspective on Gaussian sigma-point Kalman filters

ABSTRACT

There are a variety of Gaussian sigma-point Kalman filters (GSPKF) existing in the literature which are based on different quadrature rules. Their performances are always compared with each other on accuracy and robustness from the numerical-integration perspective, where the number of the sigma points and their corresponding weights are the main reasons resulting in the different accuracy. A new perspective on the GSPKF is proposed in this paper, which is the Mahalanobis distance ellipsoid (MDE). From the MDE perspective, GSPKFs differ from each other on accuracy and robustness mainly because they enclose different probability concentrations. This characteristic is evident when using the high-degree GSPKFs to filter the low-dimensional nonlinear systems. Two classical nonlinear system examples are used to demonstrate the proposed point of this paper. Moreover, some suggestions are given on how to select an appropriate GSPKF for a given nonlinear system.

KEYWORDS:

• Gaussian sigma-point Kalman filters
• mahalanobis distance ellipsoid
• nonlinear filter

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61703228].

Notes on contributors

Yongfang Nie

Yongfang Nie was born in 1976. She received the M.S degree in weapon system engineering from Naval Aeronautical Engineering Institute in 2002. She received the Ph.D. degree from Tsinghua University, Beijing, China in 2019. She is currently a lecturer of Naval Submarine Academy. Her current research activity is focused on nonlinear filtering and adaptive control.E-mail: [email protected]

Tao Zhang

Tao Zhang was born in 1969. He received the B.S. degree, M.S. degree and Ph.D. degree from Tsinghua University, Beijing, China, in 1993, 1995 and 1999 respectively. He received his second Ph.D. degree from Saga University, Saga, Japan, in 2002. He is currently a Professor and Deputy Head of the Department of Automation, School of Information Science and Technology, Tsinghua University, Beijing, China. He is the author or coauthor of more than 200 papers and three books. His current research includes robotics, control theory, artificial intelligent, navigation and control of spacecraft, fault diagnosis and reliability analysis, body signal extraction and recognition.E-mail: [email protected]

Qianxia Ma

Qianxia Ma was born in 1992. She received the B.S. degree in automation from Beihang University in 2015 and Now she is pursing Ph.D. at Tsinghua University. Her current research activity is focused on speech recognition and multi-modal deep learning.E-mail: [email protected]