Geometric methods for optimal sensor design
Geometric methods for optimal sensor design
复制标题
优化传感器设计的几何方法
DOI：
10.1098/rspa.2015.0312
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Belabbas
中科院分区：
文献类型：
--
作者：
M. Belabbas
卡尔曼-布希滤波是根据传感器测量数据对线性动力系统状态的最优估计器。因为它的性能受到配对的传感器的限制，所以寻找最佳传感器是很自然的。然而，由此产生的优化问题是非凸的。因此，多年来，许多特别的方法被用于设计从工程到生物再到经济的各个领域的传感器。在本文中，我们展示了如何获得卡尔曼滤波的最优传感器。准确地说，我们提供了表征最优传感器的结构方程。在此基础上，提出了一种梯度算法，并证明了该算法收敛于最优传感器。对于具有固定信噪比的测量，该最优传感器产生尽可能最低的估计误差。通过将最优传感器问题归结为Grassman流形上的最优化问题，并证明了极小化函数是具有唯一极小值的Morse函数，从而证明了本文的结果。本文的结果也适用于最优执行器设计的对偶问题。
The Kalman–Bucy filter is the optimal estimator of the state of a linear dynamical system from sensor measurements. Because its performance is limited by the sensors to which it is paired, it is natural to seek optimal sensors. The resulting optimization problem is however non-convex. Therefore, many ad hoc methods have been used over the years to design sensors in fields ranging from engineering to biology to economics. We show in this paper how to obtain optimal sensors for the Kalman filter. Precisely, we provide a structural equation that characterizes optimal sensors. We furthermore provide a gradient algorithm and prove its convergence to the optimal sensor. This optimal sensor yields the lowest possible estimation error for measurements with a fixed signal-to-noise ratio. The results of the paper are proved by reducing the optimal sensor problem to an optimization problem on a Grassmannian manifold and proving that the function to be minimized is a Morse function with a unique minimum. The results presented here also apply to the dual problem of optimal actuator design.
影响因子：
4.4
作者：
Barnes, Chris P.;Silk, Daniel;Stumpf, Michael P. H.
通讯作者：
Stumpf, Michael P. H.