A detector for the case of a radar target with known Doppler and unknown complex amplitude in complex Gaussian noise with unknown parameters has been derived. The detector assumes that the noise is an Auto-Regressive (AR) process with Gaussian autocorrelation function which is a suitable model for ground clutter in most scenarios involving airborne radars. The detector estimates the unknown parameters by Maximum Likelihood (ML) estimation for the use in the Generalized Likelihood Ratio Test (GLRT). By computer simulations, it has been shown that for large data records, this detector is Constant False Alarm Rate (CFAR) with respect to AR model driving noise variance. Also, measurements show the detector excellent performance in a practical setting. The detector’s performance in various simulated and actual conditions and the result of comparison with Kelly’s GLR and AR-GLR detectors are also presented.