Measurement optimization

A methodology is developed for determining the optimum measurement strategy for processes which can be represented by linear, discrete plant and measurement equations. The optimum values of the observation matrices are determined by minimizing a cost function which contains a quadratic form of the observation matrices. The class of problems considered is referred to as combined optimization problems whose solution requires the determination of the best estimate of the state, the optimum plant control and the optimum observation control. The plant equation is linear in the state and plant control, and contains an additive white Gaussian noise term. The measurement equation is linear in the state and contains additive white Gaussian noise. The cost function to be minimized is quadratic in the state and plant control, and contains a scalar valued quadratic form of the observation matrix.