An intuitive look at the unscented Kalman filter

Abstract

The Unscented Kalman Filter or UKF is a powerful and easily used modification to the Kalman filter that permits it use in the case of a nonlinear process or measurement model. Its power lies in its ability to allow the mean and covariance of the data to be correctly passed through a nonlinearity, regardless of the form of the nonlinearity. There is a great deal of literature on the UKF that describes the method and gives instruction on its use, but there are no clear descriptions on why it works. In this paper, we show that by computing the mean and covariance as the expectations of a Gaussian process, passing the results through a nonlinearity and solving the resulting integrals using Gauss-Hermite quadrature, the reason for the ability of the UKF to maintain the correct mean and covariance is explained by the fact that the Gauss-Hermite quadrature uses the same abscissas and weights regardless of the form of the integrand.