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A method, based on adaptive filtering, is proposed to detect dim small moving targets in strong undulant clutter background. This method utilizes the difference between target and clutter with regard to statistical characteristics, the consistency of the moving target's trajectory, and the random fluctuation of noise. After the elimination of clutter, the original correlated image is reduced to an independent random signal with Gaussian distribution. This is desirable yet difficult for some usual algorithms, such as the LMS filter. A test based on infrared sequence images captured outdoors is presented. The results indicate that this method can suppress the strong undulant clutter and enhance targets efficiently; therefore, it can greatly improve the performance for detecting small targets.