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Optimization of sensor selection has been studied to monitor complex andlarge-scale systems with data-driven linear reduced-order modeling. Analgorithm for greedy sensor selection is presented under the assumption ofcorrelated noise in the sensor signals. A noise model is given using truncatedmodes in reduced-order modeling, and sensor positions that are optimal forgeneralized least squares estimation are selected. The determinant of thecovariance matrix of the estimation error is minimized by efficient one-rankcomputations in both underdetermined and overdetermined problems. The presentstudy also reveals that the objective function with correlated noise is neithersubmodular nor supermodular. Several numerical experiments are conducted usingrandomly generated data and real-world data. The results show the effectivenessof the selection algorithm in terms of accuracy in the estimation of the statesof large-dimensional measurement data.

Greedy Sensor Selection for Weighted Linear Least Squares Estimation under Correlated Noise