Measurement strategies for input estimation in linear systems

In this work, we present a mathematical approach for some of the measurement problems arising in optics, which is also applicable to other contexts. We see the measurement problem as the problem of determining the best measurement strategy to estimate an unknown stochastic process by noisy measurements. The number of measurement devices, their positions and qualities characterize the measurement strategies. The model we use also includes a cost function based on resolving powers of sensors. We are unable to offer a solution to this problem in such generality; but for the metrical problem in which the number and locations of the measurement devices are fixed, we present an efficient numerical approach.