Unscented Filtering and Nonlinear Estimation

Abstract

The extended Kalman filter (EKF) is probably the most widely

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

“…In principle, for the nonlinearities in the SV model observation equation, extensions to the popular KF, such as the extended Kalman filter (EKF) [19], the unscented Kalman filter (UKF) [54], and other SigmaPoint Kalman filters [55] should be applicable. However, as reported in [56], these methods fail when addressing the SV model since they are unable to update their prior beliefs for such model (the Kalman gain is always null).…”

A Bayesian Approach to Model Calibration and Parameter Estimation in Potential Drop Measuring

“…The unscented Kalman filter (UKF) [26][27][28] as well as the unscented Rauch-Tung-Striebel smoother (URTSS) [19] address the filtering and smoothing problem by utilising the unscented transform as a way of deterministic sampling [14] in a Gaussian framework. Considering two random variables ξ and υ with a nonlinear model function υ = g(ξ), an approximation to the joint distribution can be obtained by estimating the mean µ υ and covariance Σ υυ by means of a minimal set of weighted samples.…”

Performance Comparison of the Kalman Filter Variants for Dynamic Mobile Localization in Urban Area Using Cellular Network

“…Therefore, the degree of accuracy of the EKF relies on the validity of the linear approximation and is not suitable for highly non-Gaussian conditional probability density functions, since it only updates the first two moments (mean and covariance) [13]. In addition, the calculation of the Jacobian matrix, used to linearize the nonlinear function in an EKF algorithm, can be complex causing implementation difficulties [14], [15]. In order to overcome these limitations, the Unscented Kalman Filter (UKF) has been proposed by Julier and Uhlmann [14], [15].…”

“…In addition, the calculation of the Jacobian matrix, used to linearize the nonlinear function in an EKF algorithm, can be complex causing implementation difficulties [14], [15]. In order to overcome these limitations, the Unscented Kalman Filter (UKF) has been proposed by Julier and Uhlmann [14], [15]. Based on EKF and UKF, adaptive Kalman filters have been developed to achieve much better estimation performance for non linear systems by adjusting the noise covariance matrices during estimation [16].…”