A solution is presented to the H2 optimal deconvolution filtering, smoothing and prediction problems for multivariable, discrete, linear signal processing problems. A weighted H2 cost-function is minimized where the dynamic weighting function can be chosen for robustness improvement. The signal and noise sources can be correlated and signal channel dynamics can be included in the system model. The estimation of the thickness of steel strip given X-ray gauge measurements is then considered. The deconvolution problem arises because the thickness at the roll gap is required for control purposes whereas the measurement occurs some time later when the strip reaches the X-ray gauge.

1.
Byrne, J. C., 1989, “Polynomial Systems Control Design with Marine Applications,” PhD thesis, Industrial Control Unit, Dept. of Electronic and Electrical Eng., Univ. of Strathclyde, Glasgow.
2.
Mendel
J. M.
,
1977
, “
White Noise Estimators for Seismic Data Processing in Oil Exploration
,”
IEEE Trans on Auto. Contr.
,
AC-22
,
5
, pp.
694
707
.
3.
Chi
C-Y
, and
Mendel
J. M.
,
1984
, “
Performance of Minimum Variance Deconvolution Filter
,”
IEEE Trans on Acoustics, Speech and Signal Processing
, Vol.
ASSP-32
(
6)
, pp.
1145
1152
.
4.
Moir
T. J.
,
1986
, “
Optimal Deconvolution Smoother
,”
IEEE Proc.
,
133
, Part D,
1
, pp.
13
18
.
5.
Chisci, L., and Mosca, E., 1992, “MMSE Multichannel Deconvolution Via Polynomial Equations,” To be publ., Automatica.
6.
Grimble, M. J., and Fairbairn, N. A., 1989, “The F-Iteration Approach to H∞ Control,” presented at IFAC Conf. Glasgow, Adaptive Control and Signal Processing.
7.
Kucˇera, V., 1979, Discrete Linear Control, John Wiley and Sons.
8.
Hagander
P.
, and
Wittenmark
B.
,
1977
, “
A Self-Tuning Filter for Fixed-Lag Smoothing
,”
IEEE Trans. on Inform. Theory
, Vol.
IT-23
, No.
3
, pp.
377
384
.
9.
Moir
T. J.
and
Grimble
,
1984
, “
Optimal Self-Tuning Filtering, Prediction and Smoothing for Discrete Multivariable Processes
,”
IEEE Trans. on Auto. Contr.
, Vol.
AC-29
,
2
, pp.
128
137
.
10.
Kwakernaak H., and Sivan, R., 1991, Modern, Signals and Systems, Prentice Hall.
11.
Grimble
M. J.
,
1980
, “
A Finite-Time Linear Filter for Discrete-Time Systems
,”
Int. J. of Control
, Vol.
31
, No.
3
, pp.
413
432
.
12.
Grimble
M. J.
,
1980
, “
A New Finite-Time Linear Smoothing Filter
,”
Int. J. Systems Sci.
, Vol.
11
, No.
10
, pp.
1189
1212
.
13.
Grimble, M.J., and Johnson, M.A., 1988, Optimal Control and Stochastic Estimation Theory and Applications, Vol. 1 and 2, John Wiley.
14.
Ahlen
A.
, and
Sternad
M.
,
1989
, “
Optimal Deconvolution Based on Polynomial Methods
,”
IEEE Trans. ASSP
, Vol.
37
, No.
2
, pp.
217
226
.
15.
Grimble, M. J., 1994, Robust Industrial Control, Prentice Hall International, Hemel Hempstead.
16.
Oppenheim, A. V., Willsky, A. S., and Young, I. T., 1983, Signals and Systems, Prentice Hall.
17.
Stearns, S. D., and Hush, D. R., 1990, Digital Signal Analysis, Prentice Hall.
18.
Haddad, R. A., and Pearsons, T. W., 1991, Digital Signal Processing, Computer Science Press.
19.
Kalouptsidis, N., and Theodoridis, S., 1993, Adaptive System Identification and Signal Processing Algorithms, Prentice Hall.
20.
Choi, S. G., Johnson, M. A., and Grimble, M. J., 1994, “Polynomial LQG Control of Back-Up-Roll Eccentricity Gauge Variations in Cold Rolling Mills”, to be published, Automatica.
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