Optimal inputs for linear system identification

This paper considers the design of optimal inputs for identifying parameters in linear dynamic systems. The criterion used for optimization is the sensitivity of the system output to the unknown parameters as expressed by the weighted trace of the Fisher information matrix. It is shown that the optimal energy constrained input is an eigenfunction of a positive self-adjoint operator corresponding to its largest eigenvalue. Several different representations of the optimal input and several methods for its numerical computation are considered. The results are extended to systems with process noise, and the relationship to other criteria for input design are brought out. Three analytical examples are solved in closed form which show that the optimal input is a sum of sine and cosine functions at appropriate frequencies. Optimal elevator deflections for identifying the short period parameters of C-8 aircraft are computed numerically and compared with the doublet input currently in use.