The original q-Markov COVariance Equivalent Realization (q-Markov Cove
r) method for identification required white noise test signals, which
cannot be generated exactly. This paper replaces the unrealizable whit
e-noise signal with a realizable signal (the pseudo-random binary sign
al, PRBS), and proves that when the period of the PRBS approaches infi
nity the q-Markov Cover algorithm, operating with PRBS, matches the fi
rst q Markov and covariance parameters (as in the original theory with
white-noise test signals). The existing q-Markov Cover algorithm will
fail to match covariance and Markov parameters exactly due to non-whi
te test signals. The new algorithm will fail to match covariance and M
arkov parameters exactly due to the finite period of PRBSs. We demonst
rate however that the results with PRBSs are far superior to results w
ith 'white' noise signals. Apparently, the 'non-whiteness' of the test
signal degrades the identification performance worse than the 'non-in
finite' period of the PRBS.