Some remarks on the lattice form of the Steiglitz-McBride iteration

It is shown that the offline Steiglitz-McBride (1965) identification method may present stable limit cycles and even chaotic behavior when implemented in lattice form. Moreover, we also show that even under ideal conditions (i.e., with an adaptive filter of sufficient order and with noiseless measurements), the stationary point corresponding to identification of the unknown system need not be a convergent point of the lattice version of the online SM algorithm.