ABSTRACT
This chapter outlines some of the main ideas behind unscented Kalman filter (UKF), which has become established as a very useful set of heuristics for real time filtering. It describes some of the standard UKF algorithms and looks at the properties of sigma point generation algorithms based on computing a square root of the covariance matrix. The main difference between the UKF and the extended Kalman filter (EKF) is the point where linearization is performed; however, both the filters assume a jointly Gaussian update and share the same risk of divergence if the system dynamics is strongly nonlinear. If the EKF is seen as a ‘linearize first, then evaluate covariance matrices’ approach, the UKF may be seen as an ‘evaluate covariance matrices first, then linearize’ approach. The deterministic sample points, or sigma points in the UKF are computed purely with an objective of matching the leading order terms in the Taylor expansion of the first two moments.
