The

This paper points out the flaws in using the EKF, and introduces an
improvement, the * Unscented Kalman Filter* (UKF), proposed by Julier and
Uhlman [1]. A central and vital operation performed in the Kalman
Filter is the propagation of a Gaussian random variable (GRV) through
the system dynamics. In the EKF, the state distribution is
approximated by a GRV, which is then propagated analytically through
the first-order linearization of the nonlinear system. This can introduce
large errors in the true posterior mean and covariance of the
transformed GRV, which may lead to sub-optimal performance and
sometimes divergence of the filter. The UKF addresses this problem by
using a deterministic sampling approach. The state distribution is
again approximated by a GRV, but is now represented using a minimal
set of carefully chosen sample points. These sample points completely
capture the true mean and covariance of the GRV, and when propagated
through the * true* non-linear system, captures the posterior mean and
covariance accurately to the 3rd order (Taylor series expansion) for
* any* nonlinearity. The EKF, in contrast, only achieves first-order
accuracy. Remarkably, the computational complexity of the UKF is the
same order as that of the EKF.

Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. Our preliminary results were presented in [2]. In this paper, the algorithms are further developed and illustrated with a number of additional examples.

- Introduction
- The EKF and its Flaws
- The Unscented Kalman Filter
- Applications and Results
- Conclusions and future work
- Bibliography
- About this document ...