  The focus of this paper is on detection theory for union of subspaces (UoS).
To this end, generalized likelihood ratio tests (GLRTs) are presented for
detection of signals conforming to the UoS model and detection of the
corresponding "active" subspace. One of the main contributions of this paper is
bounds on the performances of these GLRTs in terms of geometry of subspaces
under various assumptions on the observation noise. The insights obtained
through geometrical interpretation of the GLRTs are also validated through
extensive numerical experiments on both synthetic and real-world data.
