Periodic CRB for non-Bayesian parameter estimation

In many practical parameter estimation problems, the appropriate criterion is periodic in the parameter space. This paper considers the mean square periodic error (MSPE) criterion combined with periodic unbiasedness for which the conventional Cramer-Rao bound (CRB) does not provide a valid bound. The periodic unbiasedness is defined using the Lehmann-unbiasedness concept, and a Cramer-Rao type bound on the MSPE of any periodic unbiased estimator is derived. The proposed bound and performance of some periodic unbiased estimators for phase estimation problem are compared in terms of MSPE in a phase estimation problem with Gaussian noise.