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We address the problem of matched filter and subspace detection in the presence of arbitrary noise and interference or interfering signals that may lie in an arbitrary unknown subspace of the measurement space. A minmax methodology developed to deal with this uncertainty can also be adapted to situations where partial information on the interference or other uncertainties is available. This methodology leads to a hypothesis test with adequate levels of false alarm robustness and signal detection sensitivity. The robust test is applicable to a large class of noise density functions. In addition, generalized likelihood ratio (GLR) detectors are derived for the class of generalized Gaussian noise. The detectors are generalizations of the χ2, t, and F statistics used with Gaussian noise, which are themselves motivated in a new way by the robust test. For matched filter detection, these expressions are simpler and computationally efficient. The robust test reduces to the conventional test when unlearned subspace interference is known to be absent. The results demonstrate that when compared with the conventional detector, the robust one trades off some detection performance in the absence of interference for the sake of robustness in its presence.