TABLE OF CONTENTS In this section we develop a subspace identification solution for the output-error estimation problem of Section 7.7, where the additive perturbation was considered to be a colored stochastic process. From Section 9.4 we know that, to deal with this case, we need to find an instrumental-variable matrix Z N that satisfies both of the conditions (9.37) and (9.38). If we take for example Z N =U i,s,N, Equation (9.37) is satisfied, because u k and ? k are uncorrelated, but Equation (9.38) is clearly violated for all possible input sequences, since 
. Hence, Z N =U i,s,N is not an appropriate choice for this purpose. However, if we take a shifted version of the input to construct Z N , like, for example, Z N= U 0, s,N and i= s, condition (9.37) holds, and, as explained below, there exist certain types of input sequences for which (9.38) also holds. Usually, to construct a suitable matrix Z N , the data available for identification are split up into two overlapping parts. Among the many choices possible for splitting the data into two parts (Jansson, 1997), one that is often used is described below. The first part, from time instant 0 up to N+ s ?2, is used to construct the data matrix U 0, s,N ; this can be thought of as the past input. The second part,...
