This letter shows by digital simulation that a simple rule applied to one-dimensional self-organized maps for integrating sensory perceptions from two identical sources yielding position information as integers, corrupted by independent noise sources, yields almost statistically optimal results for position estimation as determined by maximum likelihood estimation. There is no learning of the corrupting noise sources nor is any information about the statistics of the noise sources available to the integrating process. The simple rule employed yields a measure of the quality of the estimated position of the source. The letter also shows that if the Bayesian estimates, which are rational numbers, are rounded in order to comply with the stipulation that integers be identified, the Bayesian estimation will have a larger variance than the proposed integration.