Nonstationary consistency of subspace methods
Albert Benveniste and
Laurent Mével
In this paper we study ``nonstationary consistency'' of subspace
methods for eigenstructure identification, \ie the ability of subspace
algorithms to converge to the true eigenstructure despite
nonstationarities in the excitation and measurement noises. Note that
such nonstationarities may result in having time-varying zeros for the
underlying system, so the problem is nontrivial. In particular,
likelihood and prediction error related methods do not ensure
consistency under such situation, because estimation of poles and
estimation of zeros are tightly coupled. We show in turn that subspace
methods ensure such consistency. Our study carefully separates
statistical from non-statistical arguments, therefore enlightening the
role of statistical assumptions in this story.