Title: Kalman Filter Tutorial

Speaker: Nick West, Stanford University, ICME (Institute for Computational and Mathematical Engineering)

Date/Time: Wednesday, July 22, 10:00-11:30 (NM)

Location: CSRI Room 90 (Sandia NM)

Brief Abstract: The Kalman Filter is a classical filtering technique for state estimation of systems with linear dynamics and Gaussian noise (in both the observations and the dynamics). The 'filtering' problem can be viewed as an inverse problem for a random process over a state-space evolving in time. Given incomplete, noisy, observations of the process at different times, we wish to estimate the current state as and/or make predictions of the future state. When the state evolution is linear and the underlying randomness is Gaussian, the Kalman Filter is the optimal (in an L^2 sense) filter; when the randomness is arbitrary the Kalman Filter is the optimal affine predictor/estimator.

In this tutorial, a theoretical derivation of the Kalman filter will be presented with an emphasis on the use of the innovation sequence and Hilbert Space projections. The Kalman filter is an attractive tool for many filtering problems due to its recursive nature and the fact that it produces confidence intervals for the estimates. Several examples will be presented that will demonstrate applicability of the Kalman Filter both in the Linear/Gaussian setting and in other situations.

This is the first part of a two-part tutorial. The next lecture will discuss nonlinear filtering and extensions of the Kalman filter such as ensemble Kalman filters.

CSRI POC: Laura Swiler, (505) 844-8093