传感器放置问题的近似解和性能边界

M. Uddin, A. Kuh, A. Kavcic, Toshihisa Tanaka
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引用次数: 8

摘要

本文考虑在n > m个可能位置放置m个传感器。给定噪声观测、状态相关矩阵的知识和均方误差准则,该问题可以被表述为一个整数规划问题。对于较大的m和n的解是不可行的,需要我们寻找近似算法。利用矩阵的性质,给出了最优解性能的下界和上界。我们还制定了一个贪心算法和一个动态规划算法,其运行时间分别为m和n的多项式。最后,我们通过仿真证明了贪心算法和动态规划算法非常接近最优解。传感器放置问题有许多能源应用,我们经常面临资源有限的问题。一些例子包括在有大量分布式太阳能光伏的地区放置环境传感器的位置,以及在配电微电网上放置电网监视器的位置。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximate solutions and performance bounds for the sensor placement problem
This paper considers the placement of m sensors at n > m possible locations. Given noisy observations, knowledge of the state correlation matrix, and a mean square error criterion, the problem can be formulated as an integer programming problem. The solution for large m and n is infeasible, requiring us to look at approximate algorithms. Using properties of matrices, we come up with lower and upper bounds for the optimal solution performance. We also formulate a greedy algorithm and a dynamic programming algorithm that runs in polynomial time of m and n. Finally, we show through simulations that the greedy and dynamic programming algorithms very closely approximate the optimal solution. The sensor placement problem has many energy applications where we are often confronted with limited resources. Some examples include where to place environmental sensors for an area where there are large amounts of distributed solar PV and where to place grid monitors on an electrical distribution microgrid.
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