This is an open access article published by the IET under the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/3.0/)
The authors consider non-linear state filtering problem in continuous–discrete systems, where the system dynamics is modelled by a stochastic differential equation, and noisy measurements of the system are obtained at discrete time instances. A novel particle method is proposed based on sequential importance sampling. This approach uses a bank of the continuous–discrete unscented Kalman filters (CDUKFs) to obtain the importance proposal distribution, retaining the advantage of the CDUKF in continuous–discrete systems as well as the accuracy of particle filter in highly non-linear systems. Simulation results show that the algorithm outperforms some other benchmarks substantially in estimation accuracy.
References
-
-
1)
-
4. Julier, S.J., Uhlmann, J.K.: ‘Unscented filtering and nonlinear estimation’, Proc. IEEE, 2004, 92, (3), pp. 401–422 (doi: 10.1109/JPROC.2003.823141).
-
2)
-
18. Doucet, A., Godsill, S., Andrieu, C.: ‘On sequential Monte Carlo sampling methods for Bayesian filtering’, Stat. Comput. (Kluwer), 2000, 10, (3), pp. 197–208 (doi: 10.1023/A:1008935410038).
-
3)
-
21. Sarkka, S.: ‘On unscented Kalman filtering for state estimation of continuous-time nonlinear systems’, IEEE Trans. Autom. Control, 2007, 52, (9), pp. 1631–1641 (doi: 10.1109/TAC.2007.904453).
-
4)
-
14. Wan, E.A., Van Der Merwe, R.: ‘The unscented Kalman filter’, in Haykin, S. (Ed.): ‘Kalman filtering and neural networks’ (Wiley, New York, 2001), pp. 221–280.
-
5)
-
5. VanTrees, H.L.: ‘Detection, estimation, and modulation theory part II’ (John Wiley Sons, New York, 1971).
-
6)
-
3. Stengel, R.F.: ‘Optimal control and estimation’ (Dover Publications, Inc., New York,1994).
-
7)
-
7. Gelb, A. (Ed.): ‘Applied optimal estimation’ (The MIT Press, Cambridge, 1974).
-
8)
-
6. Jazwinski, A.H.: ‘Stochastic processes and filtering theory’ (Academic Press, New York, 1970).
-
9)
-
2. Grewal, M.S., Weill, L.R., Andrews, A.P.: ‘Global positioning systems, inertial navigation and integration’ (Wiley Inter science, New York, 2001).
-
10)
-
12. Julier, S.J., Uhlmann, J.K.: ‘New extension of the Kalman filter to nonlinear systems’. AeroSense'97, 1997, pp. 182–193.
-
11)
-
8. Grewal, M.S., Andrews, A.P.: ‘Kalman filtering, theory and practice using MATLAB’ (Wiley Inter science, New York, 2001).
-
12)
-
13. Wan, E.A., Van Der Merwe, R.: ‘The unscented Kalman filter for nonlinear estimation’. IEEE Adaptive Systems for Signal Processing, Communications, and Control Symp. , 2000, pp. 153–158.
-
13)
-
S.J. Julier ,
J.K. Uhlmann
.
Unscented filtering and nonlinear estimation.
Proc. IEEE
,
3 ,
401 -
422
-
14)
-
1. Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: ‘Estimation with applications to tracking and navigation’ (Wiley Inter science, New York, 2001).
-
15)
-
17. Kloeden, P.E., Platen, E.: ‘Numerical solution to stochastic differential equations’ (Springer, 1999).
-
16)
-
4. VanTrees, H.L.: ‘Detection, estimation, and modulation theory part I’ (John Wiley Sons, New York, 1968).
-
17)
-
A. Doucet ,
S. Godsill ,
C. Andreu
.
On sequential Monte-Carlo sampling methods for Bayesian filtering.
Stat. Comput.
,
197 -
208
-
18)
-
10. Tommi, S., Simo, S.: ‘Application of Girsanov theorem to particle filtering of discretely observed continuous-time non-linear systems’, Bayesian Anal., 2008, 3, (3), pp. 555–584.
-
19)
-
S. Sarkka
.
On unscented Kalman filtering for state estimation of continuous-time nonlinear systems.
IEEE Trans. Autom. Control
,
9 ,
1631 -
1641
-
20)
-
15. Van der Merwe, R., Doucet, A., de Freitas, N., Wan, E.: ‘The unscented particle filter’. , 2000.
http://iet.metastore.ingenta.com/content/journals/10.1049/joe.2014.0076
Related content
content/journals/10.1049/joe.2014.0076
pub_keyword,iet_inspecKeyword,pub_concept
6
6