Abstract
For the unique solution of the problem of calculation of the inputs and outputs of a linear system from observations comprising additive quasipolynomial additives (trends) with unknown parameters, the existence conditions were established. Formulas to calculate the system signals and trends from the observations of the total signal were presented.
Similar content being viewed by others
References
Pollock, D.S.G., Trend Estimation and De-trending via Rational Square-wave Filters, J. Econom., 2000, vol. 99, no. 2, pp. 317–334.
Rogov, S.N., Sobolev, L.G., and Khrutskii, O.V., On Some Methods of Smoothing and Identification of the Experimental Trands, Avtom. Telemekh., 2005, no. 5, pp. 134–145.
Lomov, A.A., Orthoregression Methods of Parameter Estomation and Problems of Trend Separation in Linear Systems, Diff. Uravn. Prots. Upravlen., 2005, no. 2 (manuscript at http://www.neva.ru/journal).
Lomov, A.A., Trend Sepration in Linear Systems, in Proc. V Int. Conf. “System Identificaiton and Problems of Control” SICPRO’06, Moscow: Inst. Probl. Upravlen., 2006, pp. 1980–2009.
Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988. Translated into English under the title Theory of Matrices, New York: Chelsea, 1959.
Pontryagin, L.S., Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations), Moscow: Nauka, 1974.
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.A. Lomov, 2008, published in Avtomatika i Telemekhanika, 2008, No. 7, pp. 29–36.
This work was supported by the Russian Foundation for Basic Research, project no. 06-01-00776.
Rights and permissions
About this article
Cite this article
Lomov, A.A. Signal restoration in linear systems with trends. Autom Remote Control 69, 1126–1132 (2008). https://doi.org/10.1134/S0005117908070035
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117908070035