Abstract
The inverse of the Fisher information matrix can be decided by the system input sequence and the disturbance variance if a Gaussian noise is involved. The lower bound mean-square error matrix of any unbiased estimator is given by Cramer-Rao Lemma. When a system is disturbed by some biased noises, the classical Fisher information matrix would be not valid. The bound is not fitted when a biased estimator is implemented. Signal processing for ARX model disturbed by complex noise is concerned in this paper. Cramer-Rao bound of a biased estimation is obtained. An adaptive signal processing algorithm for identification of ARX system disturbed by biased estimation is proposed. Some experiments are included to verify the efficiency of the new algorithm.
This work is supported by the National Natural Science Foundation of China No.60973049 and No.60635020.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Goodwin, G., Payne, R.L.: Dynamic system identification: Experiment design and data analysis. Academic Press, New York (1977)
Bombois, X., Scorletti, G., Gevers, M., Hildebrand, R., Van den Hof, P.: Cheapest open-loop identification for control. In: Conference on Decision and Control. IEEE, Paradise Island (2004)
Lindqvist, K., Hjalmarsson, H.: Identification for control: Adaptive input design using convex optimization. In: Proc. 40th IEEE Conf. on Decision and Control (2001)
Gerencser, L., Hjalmarsson, H., Martensson, J.: Identification of ARX systems with non-stationary inputs – asymptotic analysis with application to adaptive input design. Automatica 45, 623–633 (2009)
Cramer, H.: Mathematical methods of Statistics. Princeton University Press, Princeton (1946)
Ljung, L.: System identification: Theory for the user, 2nd edn. Prentice Hall, Englewood Cliffs (1999)
Anderson, B.D.O., Moore, J.B.: Optimal filtering. Prentice-Hall, Englewood Cliffs (1979)
Stoorvogel, A.A., Saberi, A.: The discrete algebraic riccati equation and linear matrix inequality. Linear Algebra and its Application, 274–365 (1998)
Lofberg, J.: YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference (2004)
Gerencser, L., Hjalmarsson, H.: Adaptive input design in system identification. In: Proc. of the 44th IEEE Conference on Decision and Control (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Y., Luo, G. (2010). Adaptive Signal Processing for ARX System Disturbed by Complex Noise. In: Wang, F.L., Deng, H., Gao, Y., Lei, J. (eds) Artificial Intelligence and Computational Intelligence. AICI 2010. Lecture Notes in Computer Science(), vol 6319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16530-6_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-16530-6_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16529-0
Online ISBN: 978-3-642-16530-6
eBook Packages: Computer ScienceComputer Science (R0)