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In this paper, coincidence detection procedures with invariant or distribution-free false alarm rates are proposed and investigated. The only information concerning the channel statistics required by these coincidence procedures is the median of the noise under no-signal conditions. The coincidence procedures are subsequently modified so that the detectors constitute learning systems with respect to time-varying and/or unknown medians. It is shown that their false alarm rates remain distribution free for wide classes of detection problems. The distribution-free coincidence detectors are then applied to various detection problems of practical importance, and their performance evaluated and compared to the performance of comparable likelihood detectors. It is shown that the distribution-free detectors are reasonably efficient, though suboptimal, for channels with Gaussian statistics, and highly efficient for channels with a combination of Gaussian and impulse noise.