  This paper addresses the problem of detecting multidimensional subspace
signals, which model range-spread targets, in noise of unknown covariance. It
is assumed that a primary channel of measurements, possibly consisting of
signal plus noise, is augmented with a secondary channel of measurements
containing only noise. The noises in these two channels share a common
covariance matrix, up to a scale, which may be known or unknown. The signal
model is a subspace model with variations: the subspace may be known or known
only by its dimension; consecutive visits to the subspace may be unconstrained
or they may be constrained by a prior distribution. As a consequence, there are
four general classes of detectors and, within each class, there is a detector
for the case where the scale between the primary and secondary channels is
known, and for the case where this scale is unknown. The generalized likelihood
ratio (GLR) based detectors derived in this paper, when organized with
previously published GLR detectors, comprise a unified theory of adaptive
subspace detection from primary and secondary channels of measurements.
