A new method for identification of time-varying ARMAX systems is introduced. This method is based on expansion of time-varying parameters of the ARMAX model onto a set of basis functions. A recursive formulation for updating the coefficients of the basis functions of the time-varying parameters of the system is proposed. Similar to non-real-time basis-function methods, the proposed real-time method has the capability of tracking fast changes in the parameters of a time-varying system much better than the standard Kalman and recursive least-squares (RLS) methods. A computationally efficient version of the algorithm is also presented with a small degradation in tracking properties of the original algorithm. Selection of different types of basis functions makes the new method very flexible for different applications.

References

References
1.
Mercere
,
G.
,
Palsson
,
H.
, and
Poinot
,
T.
,
2011
, “
Continuous-Time Linear Parameter-Varying Identification of a Cross Flow Heat Exchanger: A Local Approach
,”
IEEE Trans. Control Syst. Technol.
,
19
, pp.
64
76
.10.1109/TCST.2010.2071874
2.
Deng
,
F.
,
Remond
,
D.
, and
Gaudiller
,
L.
,
2011
, “
Self-Adaptive Modal Control for Time-Varying Structures
,”
J. Sound Vib.
,
330
(
14
), pp.
3301
3315
.10.1016/j.jsv.2011.01.004
3.
Sandberg
,
H.
,
2006
, “
A Case Study in Model Reduction of Linear Time-Varying Systems
,”
Automatica
,
42
, pp.
467
472
.10.1016/j.automatica.2005.10.016
4.
Giannakis
,
G.
, and
Tepedelenlioglu
,
C.
,
1998
, “
Basis Expansion Models and Diversity Techniques for Blind Identification and Equalization of Time-Varying Channels
,”
IEEE Proc.
,
86
(
10
), pp.
1969
1986
.10.1109/5.720248
5.
Tugnait
,
J. K.
, and
Luo
,
W.
,
2004
, “
Blind Identification of Time-Varying Channels Using Multistep Linear Predictors
,”
IEEE Trans. Signal Process.
,
52
(
6
), pp.
1739
1749
.10.1109/TSP.2004.827174
6.
Zou
,
R.
, and
Chon
,
K.
,
2004
, “
Robust Algorithm for Estimation of Time-Varying Transfer Functions
,”
IEEE Trans. Biomed. Eng.
,
51
(
2
), pp.
219
228
.10.1109/TBME.2003.820381
7.
Wang
,
H.
,
Siu
,
K.
,
Ju
,
K.
,
Moore
,
L. C.
, and
Chon
,
K. H.
,
2005
, “
Identification of Transient Renal Autoregulatory Mechanisms Using Time-Frequency Spectral Technique
,”
IEEE Trans. Biomed. Eng.
,
52
(
6
), pp.
1033
1039
.10.1109/TBME.2005.846720
8.
Ljung
,
L.
, and
Soderstrom
,
T.
,
1987
,
Theory and Practice of Recursive Identification
, Prentice-Hall, Upper Saddle River, NJ.
9.
Soderstrom
,
T.
, and
Stoica
,
P.
,
1989
,
System Identification
,
Prentice–Hall
,
Englewood Cliffs, NJ
.
10.
Niedzwiecki
,
M.
,
2000
,
Identification of Time-Varying Systems
,
John-Wiley & Sons
, New York.
11.
Toth
,
R.
,
2010
,
Modeling and Identification of Linear Parameter-Varying Systems
,
Springer
,
New York
.
12.
Tsatsanis
,
M. K.
, and
Giannakis
,
G. B.
,
1993
, “
Time-Varying System Identification and Model Validation Using Wavelets
,”
IEEE Trans. Signal Process.
,
41
(
12
), pp.
3512
3523
.10.1109/78.258089
13.
Niedzwiecki
,
M.
, and
Kaczmarec
,
P.
,
2005
, “
Identification of Quasi-Periodically Varying Systems Using the Combined Nonparametric/Parametric Approach Systems
,”
IEEE Trans. Signal Process.
,
53
(
12
), pp.
4599
4609
.10.1109/TSP.2005.859223
14.
Niedzwiecki
,
M.
, and
Klaput
,
T.
,
2003
, “
Fast Algorithms for Identification of Periodically Varying Systems
,”
IEEE Trans. Signal Process.
,
51
(
12
), pp.
3270
3279
.10.1109/TSP.2003.819007
15.
Bao
,
C.
,
Hao
,
H.
,
Lia
,
Z-X.
, and
Zhu
,
X.
,
2009
, “
Time-Varying System Identification Using a Newly Improved HHT Algorithm
,”
Elsevier J. Comput. Struct.
,
87
(
23
), pp.
1611
1623
.10.1016/j.compstruc.2009.08.016
16.
Paleologu
,
C.
, and
Benesty
,
J.
,
2008
, “
A Robust Variable Forgetting Factor Recursive Least-Squares Algorithm for System Identification
,”
IEEE Signal Process. Lett.
,
15
, pp.
597
600
.10.1109/LSP.2008.2001559
17.
Cooper
,
J. E.
, and
Worden
,
K.
,
2000
, “
On-Line Physical Parameter Estimation With Adaptive Forgetting Factors
,”
Elsevier J. Mech. Syst. Signal Process.
,
14
(
5
), pp.
705
730
.10.1006/mssp.2000.1322
18.
Xu
,
X.
, and
You
,
Q.
,
2012
, “
Identification of Linear Time-Varying Systems Using a Wavelet-Based State-Space Method
,”
Elsevier J. Mech. Syst. Signal Process.
,
26
, pp.
91
103
.10.1016/j.ymssp.2011.07.005
19.
Lataire
,
J.
,
Pintelon
,
R.
, and
Louarroudi
,
E.
,
2012
, “
Non-Parametric Estimate of the System Function of a Time-Varying System
,”
Automatica
,
48
(
4
), pp.
666
672
.10.1016/j.automatica.2012.01.013
20.
Hsiao
,
T.
,
2008
, “
Identification of Time-Varying Autoregressive Systems Using Maximum a Posteriori Estimation
,”
IEEE Trans. Signal Process.
,
56
(
8
), pp.
3497
3509
.10.1109/TSP.2008.919393
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