  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.
