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

TL;DR

This paper addresses the optimal design of sensors for continuous-time vector Gauss-Markov processes to minimize mutual information while satisfying estimation error constraints, using semidefinite programming techniques.

Contribution

It introduces a tractable semidefinite programming approach for optimal sensor design in continuous-time Gaussian processes, linking it to zero-delay source coding.

Findings

Sensor design problem is solvable via semidefinite programming.

Optimal sensors minimize mutual information under estimation error constraints.

Connection established between sensor design and zero-delay source coding.

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.