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

摘要

This paper elaborates three well-known state estimators, which are used extensively in practice. These are the classical continuous-discrete extended Kalman filter (EKF) and the continuous-discrete cubature Kalman filtering (CKF) and unscented Kalman filtering (UKF) algorithms designed recently. Nowadays, it is commonly accepted that the contemporary filters always outperform the traditional EKF in the accuracy of state estimation because of their higher-order approximation of the mean of propagated Gaussian density in the time- and measurement-update steps of the modern techniques. 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 algorithms to be devised yet.