  Optical beam center position on an array of detectors is an important
(hidden) parameter that is essential not only from a tracking perspective, but
is also important for optimal detection of Pulse Position Modulation symbols in
free-space optical communications. In this paper, we have examined the beam
position estimation problem for photon-counting detector arrays, and to this
end, we have proposed and analyzed a number of non-Bayesian beam position
estimators. These estimators are compared in terms of their mean-square error,
bias and the probability of error performance. Additionally, the Cramer-Rao
Lower Bounds (CRLB) of the tracking error is also derived, and the CRLB curves
give us additional insights concerning the effect of number of detectors and
the beam radius on mean-square error performance. Finally, the effect of beam
position estimation on the probability of error performance is investigated,
and our study concludes that the probability of error of the system is
minimized when the beam position on the array is estimated as accurately as
possible.
