Parameter Estimation in Distributed Systems: Optimal Design

We formulate a very general optimal design problem for the selection of best states to observe and optimal sampling times and locations (i.e., selections of what, when, and where to observe) for parameter estimation or inverse problems involving complex nonlinear partial differential systems. A theoretical framework along with a detailed iterative algorithm for implementation of the resulting methodology are proposed and the algorithm’s successful use on several examples of wide interest are noted.