© The Institution of Engineering and Technology
This note presents the problem of designing the linear-minimum-mean-square-error observer for a class of multi-rate sensor fusion systems with missing measurements. Under the casuality constraint because of the multi-rate nature, the covariances of the equivalent noises in the estimation error system are obtained via multi-rate recursive computation. Through minimising the traces of the covariances of the estimation errors, the optimal observer is obtained. Fortunately, all the observer parameters can be calculated off-line. A numerical example is given to show the effectiveness of the proposed observer.
References
-
-
1)
-
6. Plarre, K., Bullo, F.: ‘On kalman filtering for detectable systems with intermittent observations.’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 386–390 (doi: 10.1109/TAC.2008.2008347).
-
2)
-
M. Sahebsara ,
T. Chen ,
S.L. Shah
.
Optimal H∞ filtering in networked control systems with multiple packet dropouts.
Syst. Control Lett.
,
9 ,
696 -
702
-
3)
-
4. Xia, Y., Fu, M., Liu, G.: ‘Analysis and synthesis of netwoked Control Systems’ (Springer, New York, 2011).
-
4)
-
S. Sun ,
L. Xie ,
W. Xiao ,
Y.C. Soh
.
Optimal linear estimation for systems with multiple packet dropouts.
Automatica
,
1333 -
1342
-
5)
-
J. Hespanha ,
P. Naghshtabrizi ,
Y. Xu
.
A survey of recent results in networked control systems.
Proc. IEEE
,
1 ,
138 -
162
-
6)
-
2. Zhang, H., Basin, M., Skliar, M.: ‘Ito-volterra optimal state estimation with continuous, multi-rate, randomly sampled, and delayed measurements’, IEEE Trans. Autom. Control, 2007, 52, (3), pp. 401–416 (doi: 10.1109/TAC.2007.892383).
-
7)
-
M. Huang ,
S. Dey
.
Stability of Kalman filtering with Markovian packet losses.
Automatica
,
598 -
607
-
8)
-
10. Censi, A.: ‘Kalman filtering with intermittent observations: convergence for semi-Markov chains and instrinsic measure’, IEEE Trans. Autom. Control, 2011, 55, (2), pp. 376–381 (doi: 10.1109/TAC.2010.2097350).
-
9)
-
Z. Wang ,
F. Yang ,
D.W.C. Ho ,
X. Liu
.
Robust H∞ filtering for stochastic time-delay systems with missing measurements.
IEEE Trans. Signal Process.
,
7 ,
2579 -
2587
-
10)
-
9. Kluge, S., Reif, K., Brokate, M.: ‘Stochastic stability of the extended Kalman filter with intermittent observations’, IEEE Trans. Autom. Control, 2010, 55, (2), pp. 514–518 (doi: 10.1109/TAC.2009.2037467).
-
11)
-
14. Sun, S., Xie, L., Xiao, W., Soh, Y.C.: ‘Optimal filtering for systems with multiple packet dropouts’, IEEE Trans. Circuits Syst. II: Express Briefs, 2008, 55, (7), pp. 695–699.
-
12)
-
Y. Liang ,
T. Chen ,
Q. Pan
.
Multi-rate stochastic H∞ filtering for networked multi-sensor fusion.
Automatica
,
2 ,
437 -
444
-
13)
-
20. Zhang, W., Feng, G., Yu, L.: ‘Multi-rate distributed fusion estimation for sensor networks with packet losses’, Automatica, 2012, 48, (9), pp. 2016–2028 (doi: 10.1016/j.automatica.2012.06.027).
-
14)
-
S.L. Sun ,
L.H. Xie ,
W.D. Xiao
.
Optimal full-order and reduced-order estimators for discrete-time systems with multiple packet dropouts.
IEEE Trans. Signal Process.
,
4031 -
4038
-
15)
-
L.P. Yan ,
D.H. Zhou ,
M.Y. Fu ,
Y.Q. Xia
.
State estimation for asynchronous multirate multisensory dynamic systems with missing measurements.
IET Signal Process.
,
6 ,
728 -
739
-
16)
-
7. Jin, Z., Gupta, V., Murray, R.: ‘State estimation over packet dropping networks using multiple-description coding’, Automatica, 2006, 42, (9), pp. 1441–1452 (doi: 10.1016/j.automatica.2006.03.020).
-
17)
-
H. Gao ,
T. Chen
.
H∞ estimation for uncertain systems with limited communication capacity.
IEEE Trans. Autom. Control
,
2070 -
2084
-
18)
-
Y. Liang ,
T. Chen ,
Q. Pan
.
Optimal linear state estimator with multiple packet dropouts.
IEEE Trans. Autom. Control
,
1428 -
1433
-
19)
-
B. Sinopoli ,
L. Schenato ,
M. Franceschetti ,
K. Poolla ,
M.I. Jordan ,
S.S. Sastry
.
Kalman filtering with intermittent observations.
IEEE Trans. Autom. Control
,
9 ,
1453 -
1464
-
20)
-
19. Chen, T., Francis, B.: ‘Optimal sampled-data control systems’, (Springer-Verlag, New York, 1995).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0972
Related content
content/journals/10.1049/iet-cta.2013.0972
pub_keyword,iet_inspecKeyword,pub_concept
6
6