连续时间向量Gauss-Markov过程的最优传感器设计与零延迟信源编码
Optimal Sensor Design and Zero-Delay Source Coding for Continuous-Time Vector Gauss-Markov Processes
摘要：
我们考虑的情况下，连续时间向量高斯-马尔可夫过程是通过一个矢量高斯信道（传感器）观察和估计的卡尔曼-布西滤波器。与标准滤波问题中的传感器模型是先验给定的不同，我们关注的是最优传感器设计，其中（i）源随机过程和再现（估计）过程之间的互信息最小化，以及（ii）最小均方估计误差满足给定的失真约束。我们表明，这样的传感器设计问题是听话的半定规划。零延迟源编码的连接也进行了讨论。
英文摘要：
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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