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Authors
Straka, Ondrej; Flídr, Miroslav; Dunik, Jindrich; Simandl, Miroslav

Identifier
10.3182/20090706-3-FR-2004.00084

Index Terms
Toolboxes; Bayesian Methods; Filtering and Smoothing

Abstract
The goal of the article is to describe a software framework designed for nonlinear state estimation of discrete time dynamic systems. The framework was designed with the aim to facilitate implementation, testing and use of various nonlinear state estimation methods in mind. The main strength of the framework is its versatility due to the possibility of either structural or probabilistic description of the problem. Besides the well-known basic nonlinear estimation methods such as the extended Kalman filter, the divided difference filters and the unscented Kalman filter, the framework implements particle filter with advanced features as well. As the framework is designed on the object oriented basis, further extension by user-specified nonlinear estimation algorithms is extremely easy. The paper provides a brief introduction into nonlinear state estimation problem and describes the individual components of the framework, their key features and use. The strengths of the framework are presented in two examples.

References

M. Flidr, J. Dunik, O. Straka, Svacha, J., and M. Simandl.
Framework for implementing and testing nonlinear filters.
In Preprints of the 7th IFAC Symposium on advances in
control education, Madrid, Spain, 2006. http://nft.kky.zcu.cz/nftools.

N. Gordon, D. Salmond, and A.F.M. Smith. Novel approach
to nonlinear/non-Gaussian Bayesian state estimation. IEE
proceedings-F, 140:107–113, 1993.

K. Ito and K. Xiong. Gaussian Filters for Nonlinear Filtering
Problems. Automatica, 45(5):910–927, 2000.

A.H. Jazwinski. Stochastic Processes and filtering Theory.
Academic Press, 1970.

S.J. Julier, J.K. Uhlmann, and H.F. Durrant-White. A new
method for the nonlinear transformation of means and
covariances in filters and estimators. IEEE Trans. on AC, 45
(3):477–482, 2000.

M. Norgaard, N.K. Poulsen, and O. Ravn. New developments
in state estimation for nonlinear systems. 36(11):1627–1638,
2000.

M. Norgaard, N. K. Poulsen, and O. Ravn. Kalmtool for
use with matlab. In Proceedings of the 13th IFAC Sympo-
sium on System Identification, SYSID03, pages 1490–1495,
Rotterdam. Rotterdam, 2003. IFAC. 
http://server.oersted.dtu.dk/personal/or/kalmtool3/.

S. Sarkka and J. Hartikainen. EKF/UKF toolbox, 2007. http:
//www.lce.hut.fi/research/mm/ekfukf/.

M. Simandl. State Estimation For Non-Gaussian Models. In
Preprints of the 13th world congress, volume 2, pages 463–
468, San Francisco, USA, 1996. IFAC, Elsevier Science.

M. Simandl. Multi-process models and outliers elimination. In
Proceedings of IASTED Int. Conf. SIP’97, pages 320–325,
New Orleans, USA, 1997. IASTED.

M. Simandl and M. Flidr. Nonlinear nonnormal dynamic
models: State estimation and software.
In Computer-Intensive Methods in Control and Signal Processing.
Birkhauser, Boston, 1997.

M. Simandl and O. Straka. Functional sampling density design
for particle filters. Signal Processing, 88(11):2784–2789,
2008.

M. Simandl, J. Kralovec, and T. Soderstrom. Anticipative
Grid Design in Point-Mass Approach to Nonlinear State
Estimation. IEEE Trans. on AC, 47(4):699–702, 2002.

H.W. Sorenson. Bayesian Analysis of Time Series and Dynamic
Models, chapter Recursive Estimation for Nonlinear
Dynamic Systems, pages 127–165. Marcel Dekker, New York, 1988.

H.W. Sorenson and D.L. Alspach. Recursive Bayesian Estimation
Using Gaussian Sums. Automatica, 7:465–479, 1971.

R. van der Merwe and E. A. Wan. Rebel - Recursive Bayesian
Estimation Library, 2006. http://choosh.csee.ogi.edu/rebel/.