A Frequency Domain Analysis of the Linear Discrete Kalman Filter

摘要

The linear discrete Kalman filter was analyzed using a frequency domain approach. Process and measurement noise covariances are shown to be critical design parameters which, together with the assumed prior state and covariance estimates, completely determine the gain schedule of the linear Kalman filter. Several relevant design techniques are illustrated and discussed. The concepts of smoothing and sharpening are demonstrated. Extensions to adaptive, non-linear, and non-parametric filtering are briefly discussed, as are applications to inventory management, estimation of time-varying mean functions, and multiple regression. (Author)