  The topic of the paper is the position reconstruction from signals of
segmented detectors. With the help of a simple simulation, it is shown that the
position reconstruction using the centre-of-gravity method is strongly biased,
if the width of the charge (or e.g. light) distribution at the electrodes (or
photo detectors) is less than the read-out pitch. A method is proposed which
removes this bias for events with signals in two or more read-out channels and
thereby improves the position resolution. The method also provides an estimate
of the position-response function for every event. Examples are given for which
its width as a function of the reconstructed position varies by as much as an
order of magnitude.
  A fast Monte Carlo program is described which simulates the signals from a
silicon pixel detector traversed by charged particles under different angles,
and the results obtained with the proposed reconstruction method and with the
centre-of-gravity method are compared. The simulation includes the local
energy-loss fluctuations, the position-dependent electric field, the diffusion
of the charge carriers, the electronics noise and charge thresholds for
clustering. A comparison to test-beam-data is used to validate the simulation.
