  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.
