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A very rapidly convergent solution (in the form of a likelihood ratio test) for the problem of detecting a discrete-time stochastic process in additive white Gaussian noise has been derived. This likelihood ratio test is applied to the problem of moving-target detection as encountered in an airport-surveillance radar system. Using real radar data, the receiver operating characteristics are obtained for two different implementations of this adaptive detection algorithm, and for the three generations of the classical moving-target-detection algorithm presently in use in modern radar systems. The best of the two implementations of the adaptive detection algorithm employs Kalman prediction tapped delay-line filters and attains a minimum of 3 dB average performance improvement relative to the classical moving-targer-detection algorithms.