相关噪声下加权线性最小二乘估计的贪婪传感器选择
Greedy Sensor Selection for Weighted Linear Least Squares Estimation under Correlated Noise
摘要：
研究了传感器选择的优化问题，以利用数据驱动的线性降阶建模来监测复杂的大规模系统。在传感器信号中存在相关噪声的假设下，提出了一种贪婪传感器选择算法。在降阶建模中使用截断模式给出噪声模型，并选择广义最小二乘估计的最佳传感器位置。估计误差的协方差矩阵的行列式最小化的有效的一秩计算在欠定和超定问题。本研究还揭示了相关噪声的目标函数既不是次模也不是超模。使用随机生成的数据和真实世界的数据进行了几个数值实验。结果表明，选择算法的有效性在精度方面的状态估计的大规模测量数据。
英文摘要：
Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in the sensor signals. A noise model is given using truncated modes in reduced-order modeling, and sensor positions that are optimal for generalized least squares estimation are selected. The determinant of the covariance matrix of the estimation error is minimized by efficient one-rank computations in both underdetermined and overdetermined problems. The present study also reveals that the objective function with correlated noise is neither submodular nor supermodular. Several numerical experiments are conducted using randomly generated data and real-world data. The results show the effectiveness of the selection algorithm in terms of accuracy in the estimation of the states of large-dimensional measurement data.
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