Geodesic
On the consistency of generalized orthoregressive parameter estimates for a~linear dynamical system
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 87-93.

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We obtain consistency conditions for generalized orthoregressive estimates for the parameters of a linear dynamical system from the observation of a large number of independent trajectories of finite length are observed. As a consequence, we obtain the average consistency of Structured Total Least Squares estimates over the trajectory ensemble.
Keywords: linear dynamical systems, parameter identification, generalized orthoregressive estimates, STLS estimates, consistency. 
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A. A. Lomov. On the consistency of generalized orthoregressive parameter estimates for a~linear dynamical system. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 87-93. http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a7/

[1] Lomov A. A., “Variatsionnye metody identifikatsii lineinykh dinamicheskikh sistem i problema lokalnykh ekstremumov”, Upravlenie bolshimi sistemami, 39, 2012, 53–94

[2] Kukush A., Markovsky I., Van Huffel S., “Consistency of the structured total least squares estimator in a multivariate errors-in-variables model”, J. Statist. Planning and Inference, 133:2 (2005), 315–358 | DOI | MR | Zbl

[3] Aoki M., Yue P. C., “On a priori error estimates of some identificationmethods”, IEEE Trans. Automat. Control, AC-15 (1970), 541–548 | DOI | MR

[4] Osborne M. R., “A class of nonlinear regression problems”, Data Representation, Univ. of Queensland Press, St. Lucia, 1970, 94–101 | Zbl

[5] Egorshin A. O., “Vychislitelnye zamknutye metody identifikatsii lineinykh ob'ektov”, Optimalnye i samonastraivayuschiesya sistemy, Izd. IAiE SO AN SSSR, Novosibirsk, 1971, 40–53

[6] Osborne M. R., Smyth G. K., “A modified Prony algorithm for fitting functions defined by difference equations”, SIAM J. Sci. Statist. Comput., 12 (1991), 362–382 | DOI | MR | Zbl

[7] De Moor B., “Structured total least squares and $L_2$ approximation problems”, Linear Algebra Appl., 188–189 (1993), 163–207 | DOI | MR

[8] Markovsky I., Van Huffel S., “Overview of total least squares methods”, Signal Proces., 87 (2007), 2283–2302 | DOI | Zbl

[9] Aoki M., Yue P. C., “On the certain convergence questions in system identification”, SIAM J. Control, 8:2 (1970), 239–256 | DOI | MR | Zbl

[10] Lomov A. A., “Identifikatsiya lineinykh dinamicheskikh sistem po korotkim uchastkam perekhodnykh protsessov pri additivnykh izmeritelnykh vozmuscheniyakh”, Izvestiya RAN. TSU, 1997, no. 3, 20–26 | Zbl

[11] Lomov A. A., “Otsenka trendov i identifikatsiya dinamiki vremennykh ryadov na korotkikh intervalakh nablyudeniya”, Izvestiya RAN. TSU, 2009, no. 1, 25–37 | MR

[12] Gleser L. J., “Estimation in a multivariate “errors in variables” regression model: large sample results”, Ann. Statist., 9:1 (1981), 24–44 | DOI | MR | Zbl

[13] Pearson K., “On lines and planes of closest fit to systems of points in space”, Philos. Mag., 6:2 (1901), 559–572 | Zbl

[14] Kramer G., Matematicheskie metody statistiki, Nauka, M., 1975 | MR

[15] Loev M., Teoriya veroyatnostei, Izd-vo inostr. lit., M., 1962 | MR

[16] Lomov A. A., “Usloviya razlichimosti statsionarnykh lineinykh sistem”, Differents. uravneniya, 39:2 (2003), 261–266 | MR | Zbl

[17] Lomov A. A., “O razlichimosti statsionarnykh lineinykh sistem s koeffitsientami, zavisyaschimi ot parametra”, Sib. zhurn. industr. matematiki, 6:4(16) (2003), 60–66 | MR | Zbl