论文标题
传感器放置最小化状态估计均方误差：贪婪解决方案的性能保证
Sensor placement minimizing the state estimation mean square error: Performance guarantees of greedy solutions
论文作者
论文摘要
本文研究了选择系统输出子集的一部分，以最大程度地减少状态估计均方误差（MSE）。这导致在可能的传感器选择上定义的设置函数的最大化问题受到基数约束。我们考虑通过贪婪的搜索大致解决它。由于MSE函数不是次模构和超模型，因此在本情况下，贪婪解决方案的众所周知的性能保证不得。因此，我们使用数量---弯曲比和曲率 - - 评估目标函数的表达和超模样的程度。通过使用MSE函数的属性，我们将大约计算这些数量并获得贪婪溶液的性能保证。结果表明，保证不如现有结果中的保证。
This paper studies selecting a subset of the system's output to minimize the state estimation mean square error (MSE). This results in the maximization problem of a set function defined on possible sensor selections subject to a cardinality constraint. We consider to solve it approximately by a greedy search. Since the MSE function is not submodular nor supermodular, the well-known performance guarantees for the greedy solutions do not hold in the present case. Thus, we use the quantities---the submodularity ratio and the curvature---to evaluate the degrees of submodularity and supermodularity of the objective function. By using the properties of the MSE function, we approximately compute these quantities and derive a performance guarantee for the greedy solutions. It is shown that the guarantee is less conservative than those in the existing results.
