A fast least-squares arrival time estimator for scintillation pulses

The true weighted least-squares (WLS) arrival time estimator for scintillation pulse detection was previously found to out-perform conventional arrival time estimators such as leading-edge and constant-fraction timers, but has limited applications because of its complexity. A new diagonalized version of the weighted least-squares (DWLS) estimator has been developed which, like the true WLS, incorporates the statistical properties of the scintillation detector. The new DWLS reduces estimator complexity at the expense of fundamental timing resolution. The advantage of the DWLS implementation is that only scalar multiplications and additions are needed instead of the matrix operations used in the true WLS. It also preserves the true WLS´s ability to effectively separate piled-up pulses. The DWLS estimator has been applied to pulses which approximate the response of BGO and NaI(Tl) scintillation detectors. The timing resolution obtained with the DWLS estimator is then compared to conventional analog timers along with the Cramer-Rao lower bound on achievable timing error. The DWLS out-performs the conventional arrival time estimators but does not provide optimal performance compared to the lower bound; however, it is more robust than the true WLS estimator