Major Development Under Gaussian Filtering Since Unscented Kalman Filter

Filtering is a recursive estimation of hidden states of a dynamic system from noisy measurements. Such problems appear in several branches of science and technology, ranging from target tracking to biomedical monitoring. A commonly practiced approach of filtering with nonlinear systems is Gaussian filtering. The early Gaussian filters used a derivative-based implementation, and suffered from several drawbacks, such as the smoothness requirements of system models and poor stability.A derivative-free numerical approximation-based Gaussian filter,named the unscented Kalman filter(UKF), was introduced in the nineties, which offered several advantages over the derivativebased Gaussian filters. Since the proposition of UKF, derivativefree Gaussian filtering has been a highly active research area.This paper reviews significant developments made under Gaussian filtering since the proposition of UKF. The review is particularly focused on three categories of developments: i)advancing the numerical approximation methods; ii) modifying the conventional Gaussian approach to further improve the filtering performance; and iii) constrained filtering to address the problem of discrete-time formulation of process dynamics. This review highlights the computational aspect of recent developments in all three categories. The performance of various filters are analyzed by simulating them with real-life target tracking problems.