Optimal Sensor Design and Zero-Delay Source Coding for Continuous-Time Vector Gauss-Markov Processes

2017/09/10 by Tanaka, Takashi, Skoglund, Mikael, Ugrinovskii, Valeri
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1709.03026

Abstract

We consider the situation in which a continuous-time vector Gauss-Markov process is observed through a vector Gaussian channel (sensor) and estimated by the Kalman-Bucy filter. Unlike in standard filtering problems where a sensor model is given a priori, we are concerned with the optimal sensor design by which (i) the mutual information between the source random process and the reproduction (estimation) process is minimized, and (ii) the minimum mean-square estimation error meets a given distortion constraint. We show that such a sensor design problem is tractable by semidefinite programming. The connection to zero-delay source-coding is also discussed.

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