The CRLB for Bilinear Systems and Its Biomedical Applications

Abstract

The Cramer Rao lower bound (CRLB) provides a lower bound on the covariance matrix of any unbiased estimator of unknown parameters. It is shown in this paper that the CRLB for a data set generated by a bilinear system with additive Gaussian measurement noise can be expressed explicitly in terms of the outputs of its derivative system which is also bilinear. For bilinear systems with piecewise constant inputs, the CRLB for uniformly sampled data can be efficiently computed by solving certain Lyapunov equations. The theoretical results are illustrated through an example arising from surface plasmon resonance experiments for the determination of the kinetic parameters of protein-protein interactions.