Do the Contemporary Cubature and Unscented Kalman Filtering Methods Outperform Always the Traditional Extended Kalman Filter?

TL;DR

This paper challenges the common belief that modern cubature and unscented Kalman filters always outperform the traditional extended Kalman filter, especially in stiff stochastic systems where EKF may be more accurate.

Contribution

It demonstrates that EKF can outperform CKF and UKF in stiff stochastic systems, highlighting the importance of considering system properties in filter selection.

Findings

EKF may outperform CKF and UKF in stiff systems

Contemporary filters are not universally superior in all scenarios

Stiffness affects the relative performance of Kalman filtering methods

Abstract

This brief technical note elaborates three well-known state estimators, which are used extensively in practice. These are the rather old-fashioned extended Kalman filter (EKF) and the recently-designed cubature Kalman filtering (CKF) and unscented Kalman filtering (UKF) algorithms. Nowadays, it is commonly accepted that the contemporary techniques outperform always the traditional EKF in the accuracy of state estimation because of the higher-order approximation of the mean of propagated Gaussian density in the time- and measurement-update steps of the listed filters. However, the present paper specifies this commonly accepted opinion and shows that despite the mentioned theoretical fact the EKF may outperform the CKF and UKF methods in the accuracy of state estimation when the stochastic system under consideration exposes a stiff behavior. That is why stiff stochastic models are difficult to deal with and require effective state estimation techniques to be designed yet.