Optimal Nonanticipative Estimation Schemes for Time-Varying Gauss-Markov Processes
Photios A. Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey L. Loyka · arXiv (Cornell University) · 2016
In this paper, we derive recursive filters for time-varying multidimensional Gauss-Markov processes, which satisfy a mean square error fidelity, using the concept of Finite Time Horizon (FTH) Nonanticipative Rate Distortion Function (NRDF) and its connection to real-time realizable filtering theory. Moreover, we derive a universal lower bound on the mean square error of any estimator of time-varying multidimensional Gauss-Markov processes in terms of conditional mutual information. Unlike classical Kalman filters, the proposed filter is constructed from the solution of a reverse-waterfilling problem, which ensures that the mean square error fidelity is met. Our theoretical results are demonstrated via illustrative examples.