Cramer-Rao lower bound for parameter estimation in nonlinear systems

Calculation of the Cramer-Rao lower bound, i.e., the inverse of the Fisher information matrix, for output data sets of a general nonlinear system is a challenging problem and is considered in this letter. It is shown that the Fisher information matrix for a data set generated by a nonlinear system with additive Gaussian measurement noise can be expressed in terms of the outputs of its derivative system that is also a nonlinear system. An example is considered arising from surface plasmon resonance experiments to determine the dynamic parameters of molecular interactions.