In this paper a new synchronization technique is presented for applications using repeated measurements or experiments with periodically excited signals. The objective with repeated or periodic measurements is often to retrieve an estimate of the (noise reduced) signal and its uncertainties. However, these measurements need to be synchronized to obtain accurate estimates. Existing synchronization techniques are limited to specific signal and noise conditions, such as white Gaussian noise or narrowband signals, to achieve good performance. The proposed method, not limited by these conditions, extracts statistical information regarding the underlying signal and the noise contained in the measurements, to obtain good synchronization (asymptotically optimal). The Cramér-Rao lower bound (CRLB) is derived for the synchronization problem, including bounds for the underlying signal waveform and the covariance of the measurement noise, both considered unknown. The method, which is shown to be the maximum-likelihood estimator (MLE) in both white and colored Gaussian noise, is compared with the CRLB along with standard sub-sample estimation and aligning techniques using Monte Carlo simulations. The results show significant mean square error (MSE) improvements compared to standard synchronization techniques. Synchronization results using the proposed technique are presented for repeated ultrasonic measurements, to validate the method in a real measurement situation, and to experimentally support theoretical results.
2008. Vol. 19, no 2