Sensor Selection by Greedy Method for Linear Dynamical Systems: Comparative Study on Fisher-Information-Matrix, Observability-Gramian and Kalman-Filter-Based Indices

Objective functions for sensor selection are investigated in linear time-invariant systems with a large number of sensor candidates. This study compared the performance of sensor sets obtained using three types of D-optimality-based indices as objective functions for sensor selection based on the greedy method. The compared indices are computed based on the snapshot-to-snapshot Fisher information matrix, the observability Gramian and the Kalman filter-based matrix. Both random systems and systems with eigenmodes are considered, indices for selecting the best-performing sensor set for each are identified, as well as computational complexity and corresponding wall clock times. The sensor optimized for each index works best for that index, as expected. We also clarified the trend of the sensor sets selected by the greedy method based on each objective function in terms of the other objective function.