Robust Semiparametric Efficient Estimator for Time Delay and Doppler Estimation
Lorenzo Ortega, Stefano Fortunati · IEEE Signal Processing Letters · 2025
This paper explores time-delay and Doppler estimation in the presence of unknown heavy-tailed disturbance. Conventional methods for achieving optimal mean squared error performance rely on the maximum likelihood estimator (MLE), which is consistent and asymptotically efficient under the unrealistic assumption of a perfect a-priori knowledge of the noise distribution. However, in practical situations, the noise distribution is often unknown, and classical parametric estimation procedures are no longer able to guarantee the statistical efficiency. In this work, by relying on the semiparametric theory, we present an originalrank-basedanddistribution-free$R$-estimator which have the remarkable property to beparametrically efficient, i.e. it attains the “classical” Cramér-Rao Bound,irrespective of the unknown noise distribution, provided that the latter belongs to the family of Complex Elliptically Simmetric (CES) distributions.