  Detecting the presence of target subspace signals with unknown clutters is a
well-known hard problem encountered in various signal processing applications.
Traditional methods fails to solve this problem because prior knowledge of
clutter subspace is required, which can not be obtained when target and clutter
are intimately mixed. In this paper, we propose a novel subspace detector that
can detect target signal buried in clutter without knowledge of clutter
subspace. This detector makes use of the geometrical relation between target
and clutter subspaces and is derived based upon the calculation of volume of
high dimensional geometrical objects. Moreover, the proposed detector can
accomplish the detection simultaneously with the learning processes of clutter,
a property called "detecting while learning". The performance of detector was
showed by theoretical analysis and numerical simulation.
