In classical detection framework, the parameter space is usually discretized, so that in reality received parameter dependent signals are never perfectly aligned with the signal model under test: it leads to the off-grid signal mismatch. In a Gaussian adaptive context (i.e. the noise covariance is unknown), Kelly GLRT and AMF detectors are well established techniques that can suffer severe performance degradation in presence of this kind of mismatch. We propose here to use adaptive subspace detectors to solve this issue, a suitable sub-space (that coincides with the Discrete Prolate Spheroidal Sequences basis when the signal model is that of sinusoids in noise) is proposed that offers robust performance. The interest lies in the fact that such detectors are really easy to implement and we are able to derive their analytic performance.