A robust Kalman filter is proposed for the discrete-time system with norm-bounded parametric uncertainties. The uncertainties are described by the energy bound constraint, i.e. the sum quadratic constraint (SQC). It is shown that the SQC can be converted into an indefinite quadratic cost function to be minimised in the Krein space, and it is found that the Krein space Kalman filter is a solution of the minimisation problem. After introducing a Krein space state-space model, which includes the uncertainty, one can easily write a robust version of the Krein space Kalman filter by modifying the measurement matrix and the variance of measurement noises in the original Krein space Kalman filter. Since the resulting robust Kalman filter has the same recursive structure as a conventional Kalman filter, a robust filtering scheme can be readily designed using the proposed method. A numerical example demonstrates that the proposed filter achieves robustness against parameter variation and improvement in performance when compared with a conventional Kalman filter and an existing robust Kalman filter, respectively.
References
-
-
1)
-
S.H. Jin ,
J.B. Park ,
K.K. Kim ,
T.S. Yoon
.
Krein space approach to decentralized H∞ state estimation.
IEE Proc. Control Theory Appl.
,
6 ,
502 -
508
-
2)
-
B. Hassibi ,
A.H. Sayed ,
T. Kailath
.
(1999)
Indefinite-quadratic estimation and control: a unified approach to \calH2 and \calH∈fty theories.
-
3)
-
B. Hassibi ,
A.H. Sayed ,
T. Kailath
.
Linear estimation in Krein spaces – Part II: applications.
IEEE Trans. Autom. Control
,
1 ,
34 -
49
-
4)
-
J. Bognar
.
(1974)
Indefinite inner product spaces.
-
5)
-
B. Hassibi ,
A.H. Sayed ,
T. Kailath
.
Linear estimation in Krein spaces – part I: theory.
IEEE Trans. Autom. Control
,
1 ,
18 -
33
-
6)
-
A.V. Savkin ,
I.R. Petersen
.
Robust state estimation and model validation for discrete-time uncertain systems with a deterministic description of noise and uncertainty.
Automatica
,
2 ,
271 -
274
-
7)
-
L. Xie ,
Y.C. Soh ,
C.E. de Souza
.
Robust Kalman filtering for uncertain discrete-time systems.
IEEE Trans. Autom. Control
,
6 ,
1310 -
1314
-
8)
-
I.R. Petersen ,
A.V. Savkin
.
(1999)
Robust Kalman filtering for signals and systems with large uncertainties.
-
9)
-
X. Zhu ,
Y.C. Soh ,
L. Xie
.
Design and analysis of discrete-time robust Kalman filters.
Automatica
,
6 ,
1069 -
1077
-
10)
-
V.I. Istratescu
.
(1987)
Inner product structures: theory and applications.
-
11)
-
Y. Theodor ,
U. Shaked
.
Robust discrete-time minimum-variance filtering.
IEEE Trans. Signal Process.
,
2 ,
181 -
189
-
12)
-
I.R. Petersen ,
D.C. McFarlane
.
Optimal guaranteed cost filtering for uncertain discrete-time linear systems.
Int. J. Robust Nonlinear Control
,
4 ,
267 -
280
-
13)
-
S.P. Boyd ,
C.H. Barratt
.
(1991)
Linear controller design: limit of performance.
-
14)
-
M. Fu ,
C.E. de Souza ,
Z. Luo
.
Finite-horizon robust Kalman filter design.
IEEE Trans. Signal Process.
,
9 ,
2103 -
2112
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cta_20040064
Related content
content/journals/10.1049/ip-cta_20040064
pub_keyword,iet_inspecKeyword,pub_concept
6
6