2016/03/14 by Stavrou, Photios A., Charalambous, Themistoklis, Charalambous, Charalambos D. +1
#Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1603.04172
In this paper, we develop finite-time horizon causal filters using the nonanticipative rate distortion theory. We apply the developed theory to design optimal filters for time-varying multidimensional Gauss-Markov processes, subject to a mean square error fidelity constraint. We show that such filters are equivalent to the design of an optimal \texttt\encoder, channel, decoder\, which ensures that the error satisfies a fidelity constraint. 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 filter developed is characterized by a reverse-waterfilling algorithm, which ensures that the fidelity constraint is satisfied. The theoretical results are demonstrated via illustrative examples.