Book excerpt: In this report, we study procedures for robust detection of slowly fading narrowband signals in nearly Gaussian noise, a common model for radar/sonar systems. For the classical quadrature matched filter test, we introduce an uncertainty about the envelope statistic and develop a robust test for this one-sample situation. It is demonstrated that this test is capable of protecting only against relatively weak contaminations. With uncertainty taken directly on the noise samples, we develop an estimation-detection theoretic approach: The detection statistic preserves the structure of the quadrature matched filter, but in place of the linear sample mean, a minimax robust estimator of the random amplitude is substituted. This test is shown to be asymptotically maximin optimal (in the sense of Huber) for a wide family of decision rules and for several common target signal models. Originator supplied keywords include: robust detection; non-Gaussian detection; fading narrow-band signals; combined robust estimation-detection; scale invariance; and adaptive threshold.