Abstract
Identification of a system, in which the generating mechanisms are unknown, has been a central issue in the field of signal processing for many years. The aim of this paper is two-fold: first to investigate and present a method for simultaneously selecting the order and identifying the time-varying parameters of an AutoRegressive Moving Average model with eXogenous input (ARMAX), and second to evaluate the method via computer experiments. The proposed algorithm is based on the reformulation of the problem in the standard state space form and the subsequent implementation of a bank of Kaiman filters, each fitting a different order model. Then the problem is reduced to selecting the true model, using the well-known multi-model partitioning theory for general (not necessarily Gaussian) data pdf’s. Simulations illustrate that the proposed method selects the correct model order and identifies the model parameters in a sufficiently small number of iterations, even when the true model order does not belong to the bank of Kaiman filters. Furthermore, the method is adaptive, in the sense that it can successfully track changes in the model structure in real time. Finally, the algorithm can be implemented in parallel and a VLSI implementation is also feasible.
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
H. Akaike. Fitting autoregressive models for prediction. Ann. Inst. Of Stat Math, 21:243–347, 1969.
H. Akaike. Information theory and an extension of the maximum likelihood principle. In Proc. 2nd Int. Symp. Inform. Theory. Budapest, Hungary: Akademia Kiado, pp. 267–281, 1973.
H. Akaike. A new look at the statistical model identification. IEEE Trans. Automat. Conr., 26:1–18, 1977.
B. D. O. Anderson and J. B. Moore. Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ,, 1979.
Richard M. Hawkes and John B. Moore. Performance Bounds for Adaptive Estimation. IEEE Proceedings, 64(8): 1143–1150, 1976.
S. K. Katsikas, S. D. Likothanassis, and D. G. Lainiotis. AR model identification with unknown process order. IEEE Trans. A.S.S.P., 38(5):872–876, 1990.
D. G. Lainiotis. Optimal adaptive estimation: Structure and parameter adaptation and parameter adaptation. IEEE Trans. Automat. Contr., AC-16:160–170, 1971.
D. G. Lainiotis. Partitioning: A unifying framework for adaptive systems I: Estimation. Proc. IEEE, 64:1126–1143, 1976.
D. G. Lainiotis. Partitioning: A unifying framework for adaptive systems II: Estimation. Proc. IEEE, 64:1182–1198, 1976.
D. G. Lainiotis, S. K. Katsikas, and S. D. Likothanassis. Adaptive deconvolution of seismic signals: Performance, computational analysis, parallelism. IEEE Trans. Acoust., Speech, Signal Processing, 36(11):1715–1734, 1988.
Gang Liang, D. Mitchell Wilkes, and James A. Cadzow. ARMA Model Order Estimation Based on the Eigenvalues of the Covariance Matrix. IEEE Trans. On Signal Processing, 41(10):3003–3009, 1993.
S. D. Likothanassis and S.K. Katsikas. Multivariable AR model identification and control. In Proc. IASTED Int. Symp. Modeling, Identification and Control, Grindelwald, Switzerland, pp. 248–252, 1987.
A. K. Mahalanabis and S. Prasad. On the application of the fast kalman algorithm to adaptive deconvolution of seismic data. IEEE Trans. Geosci. Remote Sensing, GE-21(4):426–433, 1983.
J. Rissanen. Modeling by shortest data description. Automatica, 14:465–471, 1978.
S. K. Katsikas. Optimal algorithms for geophysical signal processing. Ph. D. Thesis, University of Patras, Dept. of Computer Engineering and Informatics, Greece, 1986.
G. Schwarz. Estimation of the dimension of a model. Ann. Stat., 6:461–464, 1978.
R. L. Shengbush and D. G. Lainiotis. Simplified parameter quantization procedure for adaptive estimation. IEEE Trans. Automat. Contr., AC-14:424–425, 1969.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Likothanassis, S.D., Demiris, E.N. (1998). ARMAX Model Identification with Unknown Process Order and Time-Varying Parameters. In: Procházka, A., Uhlíř, J., Rayner, P.W.J., Kingsbury, N.G. (eds) Signal Analysis and Prediction. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1768-8_12
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1768-8_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7273-1
Online ISBN: 978-1-4612-1768-8
eBook Packages: Springer Book Archive