Major development under Gaussian filtering since unscented Kalman filter

Abstract

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 &#x0028 UKF &#x0029 , was introduced in the nineties, which offered several advantages over the derivative-based Gaussian filters. Since the proposition of UKF, derivative-free 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 &#x0029 advancing the numerical approximation methods; ii &#x0029 modifying the conventional Gaussian approach to further improve the filtering performance; and iii &#x0029 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.