On the bias of the modified output error algorithm

In a recent work by Betser and Zeheb (1995), a modified adaptive output error algorithm for identification was proposed. In this paper, we prove that the solution is biased for most practical types of disturbance noise, including the white noise case. Bias can be avoided in certain cases, under the verification of a relation between the spectrum of the noise and the noise-free solution, specified in the form of a theorem.