MMSE Estimation of Arrival Time with Application to Ultrasonic Signals Johan Jaap van de Beek ∗, † Per Ola Börjesson ∗ H˚akan

Abstract

This paper deals with arrival time estimation of a narrow-band signal disturbed by white gaussian noise. In order to estimate the distance between a transmitting source and a reflecting target an estimator, based on the criterion of minimum mean square error (MMSE), is investigated. The MMSE-estimator is implemented in an experimental ultrasound pulse-echo system, and results of comparative simulations between the MAP-estimator and the MMSE-estimator are given. The results are compared to the theoretical Weiss-Weinstein lower bound. As expected, the MMSE-estimator has smaller mean square error than the MAP-estimator. For high SNRs, however, the mean square error obtained by the MAP-estimator manages to approach that of the MMSE-estimator. Other differences between the two estimators are revealed in additional experiments in which the range estimates are used to generate 3-dimensional surface pictures. Chapter