Abstract
In Chapter 3, we derived convergent estimators of the system parameters using binary-valued observations. Our aim here is to obtain further bounds on estimation errors from unmodeled dynamics. In this book, unmodeled dynamics are treated as a deterministic uncertainty which is unknown but has a known bound in an appropriate space. Due to the coexistence of deterministic uncertainty from unmodeled dynamics and stochastic disturbances, we are treating necessarily a mixed environment. Consequently, estimation error characterization has a probabilistic measure that is compounded with a worst-case scenario over unmodeled dynamics, an idea introduced in our earlier work [101, 102].
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.
L.Y. Wang, J.F. Zhang, and G. Yin, System identification using binary sensors, IEEE Trans. Automat. Control, 48 (2003), 1892–1907.
L.Y. Wang, Persistent identification of time varying systems, IEEE Trans. Automatic Control, 42 (1997), 66–82.
J.C. Aguero, G.C. Goodwin, J.I. Yuz, System identification using quantized data, in Proc. 46th IEEE Conf. Decision Control, 4263–4268, 2007.
E.R. Caianiello and A. de Luca, Decision equation for binary systems: Application to neural behavior, Kybernetik, 3 (1966), 33–40.
H.F. Chen and G. Yin, Asymptotic properties of sign algorithms for adaptive filtering, IEEE Trans. Automat. Control, 48 (2003), 1545–1556.
C.R. Elvitch, W.A. Sethares, G.J. Rey, and C.R. Johnson Jr., Quiver diagrams and signed adaptive fiters, IEEE Trans. Acoustics, Speech, Signal Process., 30 (1989), 227–236.
E. Eweda, Convergence analysis of an adaptive filter equipped with the sign-sign algorithm, IEEE Trans. Automat. Control, 40 (1995), 1807–1811.
A. Gersho, Adaptive filtering with binary reinforcement, IEEE Trans. Information Theory, 30 (1984), 191–199.
K. Gopalsamy and I.K.C. Leung, Convergence under dynamical thresholds with delays, IEEE Trans. Neural Networks, 8 (1997), 341–348.
K. Pakdaman and C.P. Malta, A note on convergence under dynamical thresholds with delays, IEEE Trans. Neural Networks, 9 (1998), 231–233.
M. Vidyasagar, Learning and Generalization: With Applications to Neural Networks, 2nd ed., Springer, London, 2003.
G. Yin, V. Krishnamurthy, and C. Ion, Iterate-averaging sign algorithms for adaptive filtering with applications to blind multiuser detection, IEEE Trans. Information Theory, 49 (2003), 657–671.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Wang, L.Y., Yin, G.G., Zhang, JF., Zhao, Y. (2010). Estimation Error Bounds: Including Unmodeled Dynamics. In: System Identification with Quantized Observations. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4956-2_4
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4956-2_4
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4955-5
Online ISBN: 978-0-8176-4956-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)