Adaptive sensing of target signature with unknown amplitude

The problem of selecting the optimal linear measurement, subject to energy constraints, for nonlinear parameter estimation is stated. While the problem is similar to previously reported measurement selection problems for Gaussian random vectors, there are some key differences stemming from the fact that the signal amplitude is a nuisance parameter. An objective function based on minimizing the Bayesian Cramer-Rao bound is proposed. Through a linearization of the response vector and other simplifying assumptions, the objective function is reduced to a one-parameter function that is easily maximized. Simulation results comparing the optimal measurement to the traditional measurement suggest the potential for significantly improved estimator performance, although the linearization assumption is problematic when the parameter being estimated has a large prior variance.