Simultaneous estimation of the input and output frequencies of nonlinear systems

In this paper, the simultaneous estimation of the input and output frequencies of nonlinear systems is considered. As the output frequencies are generated from the input frequencies, and are integer combinations of these frequencies, it is shown in this paper that the simultaneous estimation of both the input and output frequencies can therefore be formulated as a constrained estimation problem. First, the constrained Cramér-Rao lower bound, an important general property of any unbiased estimator, is derived. The procedure and algorithm for estimating the input and output frequencies are devised based on the periodogram method. Numerical examples are presented to illustrate the performance and implementation of the proposed estimation procedure and algorithm.