Kalman Filtering under Wide Band Noises

Kalman filtering is a powerful estimation method. One of its weaknesses is related to the white or colored nature of the disturbing noises in the Kalman filtering model. At the same time, real noises are rarely white or colored. They are mostly wide band. In this regard, white or colored noise Kalman filtering makes concessions on adequacy. This pushes system scientists to develop mathematical methods of estimation for systems corrupted by wide band noises. In applications, wide band noises are detected by their autocovariance and cross-covariance functions which do not allow modeling them uniquely. Therefore, it becomes important to develop estimation methods which are independent of a class of wide band noises, but dependent on the unique autocovariance and cross-covariance functions. Such results are called invariant results. In this paper, we prove a complete set of invariant equations for Kalman type filter for a linear signal-observation system corrupted by correlated wide band noises. This filter has a ready form to be used in applications, just respective numerical methods must be developed. We also discuss an application scenario for the proposed filter. Keywords: Wiener process, white noise, wide band noise, Kalman filter.