Several areas of machine learning including classification and regression, nonlinear signal processing, and adaptive control, rely heavily on the extended Kalman filter (EKF). For example, the EKF plays a central role in nonlinear state estimation required by complex control applications, and is used as a parameter, estimation algorithm in neural network training for pattern recognition, and for identification of dynamic systems. The EKF also plays an important role in the simultaneous modeling and estimation (known as dual estimation) of noisy time-series, with applications ranging from speech enhancement, to financial forecasting and environmental modeling.
The central approximation used in the EKF is a linearization of the nonlinear system dynamics. While this is done in order to propagate the mean and covariance of the state variables being estimated, the EKF can introduce considerable errors between the estimates produced by the algorithm and the true statistics of the state. However, the computational expense of the algorithm is considerably lower than that of more accurate Markov-Chain Monte Carlo (MCMC) sampling methods, and produces excellent results in many circumstances. The benefit of good results at low cost is primarily responsible for the widespread use of the EKF.
In 1997, Julier and Uhlman introduced a new approach called the Unscented Kalman Filter By avoiding a linearization of the system, the UKF offers increased accuracy in the estimation of the mean and covariance of the state variables, resulting in a substantial performance improvement. The implementation of the UKF requires no analytic derivation of Jacobians (gradients) as in the EKF, and most importantly, the improved accuracy is achieved without an increase in computational expense.
The prior application of the UKF focused only on state-estimation problems in the context of nonlinear control. The objective of this project is to extend the use of the UKF to the full breadth of machine learning applications that currently depend on the EKF. This will entail the systematic development of algorithmic extensions and application evaluations as detailed in the proposal. Although numerous theoretical and practical problems must be overcome before this goal is achieved. Preliminary investigations have shown that the potential advantages of the UKF in these contexts are significant. Clearly, the diversity of applications that currently employ the EKF suggests that the proposed research aching impact on a wide variety of fields. ***
