Performance limits for distance and thickness estimation in an ultrasonic parameter identification problem

This paper explores the limits of performance for the estimation of two parameters simultaneously in an ultrasonic sensing application. The two parameters are the transmitter-receiver distance and the thickness of a plate through which the wave is travelling. The Cramer-Rao lower bound is applied to yield bounds on the variance of unbiased estimates. Since the bound depends upon the input signal, convex optimization can be used to determine the tightest lower bound over all allowable input signals