Design of optimal probing signals for vector parameter estimation.

In the design of optimal inputs or probing signals for parameter estimation, it is more natural to consider functions of the Fisher information matrix as the criterion of optimality instead of some function of the error covariance matrix. The input which maximizes the Fisher information measure for efficient estimation of a scalar parameter also provides the minimum error variance. The information is thus a logical choice for the optimality criterion in scalar problems. No such obvious choice is apparent for vector parameter estimation. A number of performance measures are examined and compared in the present study, and a useful criterion is selected. The design of an optimal probing signal using this criterion is shown to be equivalent to an optimal control problem in which certain equality constraints must be satisfied. This problem may be solved by conventional techniques of deterministic or stochastic optimal control.