Cyclic Barankin-type bounds for non-Bayesian periodic parameter estimation

In many practical periodic parameter estimation problems, the appropriate performance criteria are periodic in the parameter space. The existing mean-square-error (MSE) lower bounds, such as Cramér-Rao bound (CRB) and Barankin-type bounds do not provide valid lower bounds in such problems. In this paper, cyclic versions of the CRB and the Barankin-type bounds, Hammersley-Chapman-Robbins and McAulay-Seidman, are derived for non-Bayesian parameter estimation. The proposed bounds are lower bounds on the mean cyclic error (MCE) of any cyclic-unbiased estimator, where the cyclic-unbiasedness is defined by using Lehmann-unbiasedness. These MCE lower bounds can be readily obtained from existing MSE lower bounds and thus, can be easily calculated. The cyclic Barankin-type bounds and the performance of the maximum-likelihood (ML) estimator are compared in terms of MCE in Von-Mises distributed measurements problem and for frequency and amplitude estimation with Gaussian noise. In these problems, the ML estimator is found to be cyclic unbiased.