Determinant-Based Fast Greedy Sensor Selection Algorithm
Determinant-Based Fast Greedy Sensor Selection Algorithm
复制标题
基于行列式的快速贪婪传感器选择算法
作者：
Y. Saito;T. Nonomura;Keigo Yamada;Kumi Nakai;T. Nagata;K. Asai;Yasuo Sasaki;Daisuke Tsubakino
本文研究了最小二乘估计的稀疏传感器配置问题，推广了稀疏传感器选择算法。在本扩展方法中，将伪逆矩阵运算中出现的矩阵行列式的最大化作为问题的目标函数。相应矩阵的行列式的最大化的过程被证明是数学上相同的先前提出的QR方法时，传感器的数量小于状态变量（欠采样）。另一方面，作者开发了一种新的算法，当传感器的数量大于状态变量（过采样）。然后，给出了这两种算法的统一形式，并利用目标函数的单调子模性给出了该算法所给出的目标函数的下界。通过与其他算法的结果比较，证明了该算法在解决真实的数据集问题上的有效性。数值结果表明，在过采样情况下，该算法的估计误差比传统方法提高了约10%，其中估计误差定义为重构数据与全观测值之差与全观测值之比.对于NOAA-SST传感器问题，该算法在3.40 GHz计算机上，在过采样情况下，需要几个小时才能在几秒钟内完成传感器位置的选择。
In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which appears in pseudo-inverse matrix operations is employed as an objective function of the problem in the present extended approach. The procedure for the maximization of the determinant of the corresponding matrix is proved to be mathematically the same as that of the previously proposed QR method when the number of sensors is less than that of state variables (undersampling). On the other hand, the authors have developed a new algorithm for when the number of sensors is greater than that of state variables (oversampling). Then, a unified formulation of the two algorithms is derived, and the lower bound of the objective function given by this algorithm is shown using the monotone submodularity of the objective function. The effectiveness of the proposed algorithm on the problem using real datasets is demonstrated by comparing with the results of other algorithms. The numerical results show that the proposed algorithm improves the estimation error by approximately 10% compared with the conventional methods in the oversampling case, where the estimation error is defined as the ratio of the difference between the reconstructed data and the full observation data to the full observation. For the NOAA-SST sensor problem, which has more than ten thousand sensor candidate points, the proposed algorithm selects the sensor positions in few seconds, which required several hours with the other algorithms in the oversampling case on a 3.40 GHz computer.
使用平衡模型缩减来选择最佳传感器和执行器
影响因子：
6.8
作者：
Manohar, Krithika;Kutz, J. Nathan;Brunton, Steven L.
通讯作者：
Brunton, Steven L.
随机和确定性采样点的离散经验插值和间隙本征正交分解的稳定性
影响因子：
3.1
作者：
Peherstorfer, Benjamin;Drmač, Zlatko;Gugercin, Serkan
通讯作者：
Gugercin, Serkan