Adaptive observer for discrete linear time-invariant systems

This paper considers the problem of estimating the state of a discrete linear time-invariant system when the noise statistics are unknown. In the absent of any knowledge of the noise statistics, an observer with a fixed gain can be used in estimating the state. When more observation information is accumulated, the estimation performance can be improved by directly adjusting the gain of the observer adaptively. An adaptive observer is developed which will converge in mean square to the optimum filter asymptotically.