Parameter estimation of quasi-periodic sequences

Measurements of a process described by t(i)=k_iT+τ+η( i), (i=1, 2, . . .), where k_i are unknown integers and {η(i)} is a white noise, are considered. The estimation of the `period´ T and `phase´ τ of such processes is often required in communications and radar. Popular linear regression techniques for this estimation problem are shown to fail and new algorithms are derived. Statistical properties of the estimators are presented, under reasonable assumptions. The suggested procedure is illustrated in the digital communications symbol timing recovery from eye-diagram zero crossings. The new bit synchronizer obtained is shown to be superior in many practical situations to known maximum-likelihood-type algorithms