Linear filtering with wide-band noise disturbances

We consider the analog of the linear (Kalman-Bucy) filtering problem when the observation and driving noises are random processes with large, but finite, bandwidths. We show that as the bandwidth of the noise tends to infinity there is a natural limiting Kalman filtering problem whose solution is suboptimal for the original problem. When the Kalman-Bucy filter is used as an estimator in the original problem an error proportional to the inverse of the bandwidth of the actual system noises is incurred. We compute this error and outline a design procedure based on it. The results of numerical experiments are reported to illustrate the analytical work.