Continuous-time and continuous-discrete-time unscented Rauch-Tung-Striebel smoothers

Signal Processing

Volumn 90, Issue 1, 2010, Pages 225-235

  Särkkä, Simo ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Continuous time smoother; Unscented Kalman smoother; Unscented Rauch Tung Striebel smoother; Unscented transformation

Indexed keywords

CONTINUOUS TIME; CONTINUOUS-TIME SMOOTHER; DISCRETE-TIME; NON-LINEAR; SMOOTHING ALGORITHMS; STOCHASTIC DYNAMIC SYSTEMS; UNSCENTED KALMAN SMOOTHER; UNSCENTED RAUCH-TUNG-STRIEBEL SMOOTHER; UNSCENTED TRANSFORMATION; UNSCENTED TRANSFORMATIONS;

ANALOG TO DIGITAL CONVERSION; DIFFERENTIAL EQUATIONS; DYNAMIC PROGRAMMING; DYNAMICAL SYSTEMS;

CONTINUOUS TIME SYSTEMS;

EID: 69249221260     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2009.06.012     Document Type: Article

References (37)

1. Bar-Shalom Y., Li X.-R., and Kirubarajan T. Estimation with Applications to Tracking and Navigation (2001), Wiley, New York
2. Fong W., Godsill S.J., Doucet A., and West M. Monte Carlo smoothing with application to audio signal enhancement. IEEE Transactions on Signal Processing 50 2 (2002) 438-449
3. Z. Ghahramani, S.T. Roweis, Learning nonlinear dynamical systems using an EM algorithm, in: Neural Information Processing Systems, vol. 11, NIPS'98, 1999, pp. 431-437.
4. Kitagawa G. Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics 5 (1996) 1-25
5. Särkkä S., Vehtari A., and Lampinen J. Rao-Blackwellized particle filter for multiple target tracking. Information Fusion Journal 8 1 (2007) 2-15
6. Meditch J. Stochastic Optimal Linear Estimation and Control (1969), McGraw-Hill, New York
7. Crassidis J.L., and Junkins J.L. Optimal Estimation of Dynamic Systems (2004), Chapman & Hall, CRC, London, Boca Raton, FL
8. S.J. Julier, J.K. Uhlmann, A general method of approximating nonlinear transformations of probability distributions, Technical Report, Robotics Research Group, Department of Engineering Science, University of Oxford, 1995.
9. Julier S.J., Uhlmann J.K., and Durrant-Whyte H.F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control 45 3 (2000) 477-482
10. Wan E.A., and Van der Merwe R. The unscented Kalman filter. In: Haykin S. (Ed). Kalman Filtering and Neural Networks (2001), Wiley, New York (Chapter 7)
11. Särkkä S. Unscented Rauch-Tung-Striebel smoother. IEEE Transactions on Automatic Control 53 3 (2008) 845-849
12. Särkkä S. On unscented Kalman filtering for state estimation of continuous-time nonlinear systems. IEEE Transactions on Automatic Control 52 9 (2007) 1631-1641
13. Karatzas I., and Shreve S.E. Brownian Motion and Stochastic Calculus (1991), Springer, New York
14. Øksendal B. Stochastic Differential Equations: An Introduction with Applications. sixth ed. (2003), Springer, New York
15. Stratonovich R.L. Conditional Markov Processes and their Application to the Theory of Optimal Control (1968), American Elsevier Publishing Company, Inc.
16. Kalman R.E. A new approach to linear filtering and prediction problems. Transactions of the ASME, Journal of Basic Engineering 82 (1960) 35-45
17. Kalman R.E., and Bucy R.S. New results in linear filtering and prediction theory. Transactions of the ASME, Journal of Basic Engineering 83 (1961) 95-108
18. H.J. Kushner, On the differential equations satisfied by conditional probability densities of Markov processes, with applications, SIAM Journal on Control Series A 2 (1) (1964).
19. Bucy R.S. Nonlinear filtering theory. IEEE Transactions on Automatic Control 10 (1965) 198
20. Jazwinski A.H. Stochastic Processes and Filtering Theory (1970), Academic Press, New York
21. Gelb A. Applied Optimal Estimation (1974), The MIT Press, Cambridge, MA
22. Anderson B.D.O., and Moore J.B. Optimal Filtering (1979), Prentice-Hall, Englewood Cliffs, NJ
23. S.J. Julier, J.K. Uhlmann, H.F. Durrant-Whyte, A new approach for filtering nonlinear systems, in: Proceedings of the 1995 American Control, Conference, Seattle, Washington, 1995, pp. 1628-1632.
24. Julier S.J., and Uhlmann J.K. Unscented filtering and nonlinear estimation. Proceedings of the IEEE 92 3 (2004) 401-422
25. Doucet A., de Freitas N., and Gordon N. Sequential Monte Carlo Methods in Practice (2001), Springer, New York
26. Ristic B., Arulampalam S., and Gordon N. Beyond the Kalman Filter (2004), Artech House, Norwood, MA
27. Rauch H.E. Solutions to the linear smoothing problem. IEEE Transactions on Automatic Control AC-8 (1963) 371-372
28. Rauch H.E., Tung F., and Striebel C.T. Maximum likelihood estimates of linear dynamic systems. AIAA Journal 3 8 (1965) 1445-1450
29. Fraser D., and Potter J. The optimum linear smoother as a combination of two optimum linear filters. IEEE Transactions on Automatic Control 14 4 (1969) 387-390
30. Sage A.P., and Melsa J.L. Estimation Theory with Applications to Communications and Control (1971), McGraw-Hill Book Company, New York
31. Maybeck P. Stochastic Models, Estimation and Control vol. 2 (1982), Academic Press, New York
32. Cox H. On the estimation of state variables and parameters for noisy dynamic systems. IEEE Transactions on Automatic Control 9 1 (1964) 5-12
33. C.T. Leondes, J.B. Peller, E.B. Stear, Nonlinear smoothing theory, IEEE Transactions on Systems Science and Cybernetics 6 (1) (1970).
34. Meditch J. A survey of data smoothing for linear and nonlinear dynamic systems. Automatica 9 (1973) 151-162
35. S. Särkkä, Recursive Bayesian inference on stochastic differential equations, Doctoral Dissertation, Helsinki University of Technology, Department of Electrical and Communications Engineering, 2006.
36. Stengel R.F. Optimal Control and Estimation (1994), Dover Publications, New York
37. Kloeden P.E., and Platen E. Numerical Solution to Stochastic Differential Equations (1999), Springer, New York