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Global Total Least Squares
Isometric State Representations
7 other sections not shown
Appendix approximate modelling approximation error asymptotically stable auxiliary inputs basis transformation canonical correlations consider corresponding dashed line defined Definition degree of freedom denote described determine deterministic deviations difference equations dimension dynamic effect equals equivalent external behaviour finite intervals follows Gauss-Newton algorithm given system GTLS approach GTLS criterion GTLS method GTLS problem Hankel matrices i/s/o-representation impulse response initial models input/output instant isometric state representations ISR's iterative Lemma linear space locally optimal minimal model class model improvement constructions norm observation interval observed time series optimal approximation order GTLS model orthogonal complement orthogonal projection output parameters past and future periodic phenomenon Proof of Proposition recursive relative misfit restrictions sample interval Section shift-invariant singular values SR's stabilizable static stationary point stochastic system identification system trajectory term interest rates Theorem time-invariant total least squares unitary unitary matrix validation interval white noise zero