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Experimental results of estimating the delay of optical pulses in the presence of background noise based on the occurrence times of photoelectrons emitted by a direct detection photoelectric effect receiver are presented. Both minimum mean square error (MMSE) and maximum likelihood estimation techniques were used. The MMSE estimates of the delay of both Gaussian and rectangular optical pulses were obtained from the evolution of the posterior conditional probability density of the pulse delay given the photocount occurrence times. For signal to noise intensity ratios as low as 10 dB, it was found that the experimental performance of the MMSE delay estimates remained near performance lower bounds and that a rectangular pulse gave better performance than a Gaussian pulse of equal signal energy and equal peak signal intensity. At lower signal to noise ratios, the performance of the estimates for both pulse shapes deteriorated rapidly. It is shown that, in the absence of background noise, MMSE and ML estimation are equivalent.