Abstract
This paper considers the problem of filtering data sequences generated by errors-in-variables processes where all measured signals, differently from the classical Kalman filtering context, are affected by additive noise.
The design of optimal (minimal variance) filters leading to estimates of the process inputs and outputs is first carried out in a behavioural context.
The state-space context where EIV filtering can be performed relying on modified Kalman filtering techniques is then considered and a Monte Carlo simulation is finally proposed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R.E. Kalman, A new approach to linear filtering and prediction problems, Transactions of the ASME, 82: 35–45, 1960.
B.D.O. Anderson and J.B. Moore, Optimal filtering, Prentice-Hall, Englewood Cliffs, New Jersey, 1979.
T. Söderström, Identification of stochastic linear systems in presence of input noise, Automatica, 17: 713–725, 1981.
M. Deistler, Linear errors-in-variables models, on Time Series and Linear Systems, S. Bittanti ed., 37–68, Springer-Verlag, Berlin, 1986.
S. Beghelli, R.P. Guidorzi and U. Soverini, The Frisch scheme in dynamic system identification, Automatica, 26 (1): 171–176, 1990.
W.X. Zheng and C.B. Feng, Unbiased parameter estimation of linear systems in the presence of input and output noise, Int. J. of Adaptive Control and Signal Processing, 3: 231–251, 1989.
P. Guidorzi and R. Guidorzi, Frisch filtering of noisy signals, Proceedings of EUSIPCO g8, vol. IV, 2117–2120, Rhodes, September 1998.
J.C. Willems, From time series to linear system, part I: Finite dimensional linear time invariant systems; part II: Exact modelling; part III: Approximate modelling, Automatica, 22/23:561–580, 675–694, 87–115, 1986, 1987.
R. Guidorzi, R. Diversi and U. Soverini, Optimal Errors-in-Variables filtering, under review.
R. Diversi, R. Guidorzi and U. Soverini, Algorithms for optimal Errors-inVariables filtering, under review.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Guidorzi, R., Diversi, R., Soverini, U. (2002). Errors-In-Variables Filtering in Behavioural and State-Space Contexts. In: Van Huffel, S., Lemmerling, P. (eds) Total Least Squares and Errors-in-Variables Modeling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3552-0_25
Download citation
DOI: https://doi.org/10.1007/978-94-017-3552-0_25
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5957-4
Online ISBN: 978-94-017-3552-0
eBook Packages: Springer Book Archive