In this paper, we analyze two subspace identification methods. The
one is an N4SID-like algorithm which performs poorly in certain
conditions where the past input signal and future input spaces are
nearly parallel. The other method, based on a preliminary orthogonal
decomposition of output data space, is more robust and reliable than
the first method in critical cases. Numerical results demonstrate
a substantial improvement of performance in such a parallel case.
Keywords: canonical correlation analysis, orthogonal decomposition,
parallel case, LQ factorization