  Optimization for sensor placement has been intensely studied to monitor
complex, large scale systems, whereas one needs to overcome its intractable
nature of the objective function for the optimization. In this study, a fast
algorithm for greedy sensor selection is presented for a linear reduced-ordered
reconstruction under the assumption of correlated noise on the sensor signals.
The presented algorithm accomplishes the maximization of the determinant of the
Fisher information matrix in the linear inverse problem, while this study
firstly shows that the objective function with correlated noise is neither
submodular nor supermodular. Efficient one-rank computations in the greedy
selection procedure are introduced in both of the underdetermined and
oversampled problem. Several numerical experiments show the effectiveness of
the selection algorithm for its accuracy in the estimation of the states of
large dimensional measurement data.
