论文标题
最小信息的连续时间通道增益控制Kalman-Bucy滤波
Continuous-Time Channel Gain Control for Minimum-Information Kalman-Bucy Filtering
论文作者
论文摘要
我们考虑了通过具有可调通道增益矩阵的矢量高斯通道观察到的连续时间高斯 - 马尔科夫源过程的问题。对于给定的（通常是时间变化的）通道增益矩阵，我们提供公式来计算（i）经典的kalman-bucy滤波器可实现的均方估计误差，以及（ii）源过程与其Kalman-Bucy-bucy-bucy估算之间的相互信息。然后，我们制定了一种新颖的“最佳通道增益控制问题”，其中目的是从策略上控制频道增益矩阵，以最大程度地减少这两个性能指标的加权总和。为了发展对最佳解决方案的见解，我们首先考虑在有限的时间间隔内控制时间变化的通道增益的问题。必要的最佳条件是根据Pontryagin的最低原则得出的。对于标量系统，我们表明最佳通道增益是零件的常数信号，最多是两个开关。我们还考虑了设计最佳时间不变增益的问题，以最大程度地降低无限时间范围内的平均成本。提出了一种新型的半决赛编程（SDP）启发式，并讨论了解决方案的精确性。
We consider the problem of estimating a continuous-time Gauss-Markov source process observed through a vector Gaussian channel with an adjustable channel gain matrix. For a given (generally time-varying) channel gain matrix, we provide formulas to compute (i) the mean-square estimation error attainable by the classical Kalman-Bucy filter, and (ii) the mutual information between the source process and its Kalman-Bucy estimate. We then formulate a novel "optimal channel gain control problem" where the objective is to control the channel gain matrix strategically to minimize the weighted sum of these two performance metrics. To develop insights into the optimal solution, we first consider the problem of controlling a time-varying channel gain over a finite time interval. A necessary optimality condition is derived based on Pontryagin's minimum principle. For a scalar system, we show that the optimal channel gain is a piece-wise constant signal with at most two switches. We also consider the problem of designing the optimal time-invariant gain to minimize the average cost over an infinite time horizon. A novel semidefinite programming (SDP) heuristic is proposed and the exactness of the solution is discussed.
