An Analytical Approach for Comparing Linearization Methods in EKF and UKF

Authors

Matthew Rhudy, West Virginia University
Yu Gu, West Virginia University
Marcello R. Napolitano, West Virginia University

Document Type

Article

Publication Date

2013

College/Unit

Statler College of Engineering and Mining Resources

Department/Program/Center

Mechanical and Aerospace Engineering

Abstract

The transformation of the mean and variance of a normally distributed random variable was considered through three different nonlinear functions: sin(x), cos(x), and x^k, where k is a positive integer. The true mean and variance of the random variable after these transformations is theoretically derived within, and verified with respect to Monte Carlo experiments. These statistics are used as a reference in order to compare the accuracy of two different linearization techniques: analytical linearization used in the Extended Kalman Filter (EKF) and statistical linearization used in the Unscented Kalman Filter (UKF). This comparison demonstrated the advantage of using the unscented transformation in estimating the mean after transforming through each of the considered nonlinear functions. However, the variance estimation led to mixed results in terms of which linearization technique provided the best performance. As an additional analysis, the unscented transformation was evaluated with respect to its primary scaling parameter. A nonlinear filtering example is presented to demonstrate the usefulness of the theoretically derived results.

Digital Commons Citation

Rhudy, Matthew; Gu, Yu; and Napolitano, Marcello R., "An Analytical Approach for Comparing Linearization Methods in EKF and UKF" (2013). Faculty & Staff Scholarship. 2615.
https://researchrepository.wvu.edu/faculty_publications/2615

Source Citation

Rhudy, M., Gu, Y., & Napolitano, M. R. (2013). An Analytical Approach for Comparing Linearization Methods in EKF and UKF. International Journal of Advanced Robotic Systems, 10(4), 208. https://doi.org/10.5772/56370