**Uncertainty Quantification Working Group**

February 5, 2004, 11:30 AM, CNLS Conf. Room, TA-3, Bldg. 1690

## Tutorial on the Kalman filter and the extended Kalman filter - Part II

John M. Finn, T-15

(slides)

### Abstract

I will briefly review my conclusions from the first tutorial, and go on to show yet another alternative approach to the random walk problem, the simplest prototype for a system with dynamical noise. I will show a generalization of the minimum variance approach to higher dimensional systems with a nontrivial covariance matrix. I will go into more detail on the Bayesian approach. The remaining topics are 1) the general formulation for a linear stochastic system in higher dimension, with dynamical and measurement noise, 2) the separation theorem in control theory (separation of state estimation by a Kalman filter from the control applied), and 3) the Extended Kalman Filter, which deals with nonlinear stochastic systems.