Continuous-discrete path integral filtering

Entropy

Volumn 11, Issue 3, 2009, Pages 402-430

  Balaji, Bhashyam ^a  

^a DEFENCE RESEARCH AND DEVELOPMENT CANADA   (Canada)

Author keywords

Continuousdiscrete filters; Data assimilation; Dirac Feynman approximation; Feynman path integrals; Fokker Planck equation; Kolmogorov equation; Nonlinear filtering; Path integral filtering; Tracking; Universal nonlinear filtering

Indexed keywords

EID: 70349563759     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e110300402     Document Type: Article

References (35)

1. Jazwinski, A.H. Stochastic Processes and Filtering Theory. Dover Publications: New York, NY, USA, 1970.
2. Kalman, R.E. A new approach to linear filtering and prediction problems. Trans. ASME, J. Basic Eng. 1960, 82, 35-45.
3. Kalman, R.E.; Bucy, R.S. New results in linear filtering and prediction problems. Trans. ASME, J. Basic Eng. 1961, 83, 95-108.
4. Daum, F. Exact finite-dimensional nonlinear filters. Automatic Control, IEEE Transactions on 1986, 31, 616-622.
5. Thomée, V. Handbook of Numerical Analysis. Ciarlet, P.G., Lions, J.L., Eds., North Holland: Amsterdam, The Netherlands, 1990, Vol. 1, Chapter Finite difference methods for linear parabolic equations, pp. 5-196.
6. Marchuk, G.I. Handbook of Numerical Analysis. Ciarlet, P.G., Lions, J.L., Eds., North Holland: Amsterdam, The Netherlands, 1990, Vol. 1, Chapter Splitting and Alternating Direction Methods, pp. 197-462.
7. Canuto, C.; Hussaini, M.Y.; Quarteroni, A.; Zang, T.A. Spectral Methods: Fundamentals in Single Domains. Springer-Verlag: Berlin, Germany, 2006.
8. Thomée, V. Galerkin Finite Element Methods for Parabolic Problems, Vol. 25, Springer Series in Computational Mathematics. Springer-Verlag: Berlin, Germany, 1997.
9. Feynman, R.P.; Hibbs, A.R. Quantum Mechanics and Path Integrals. McGraw-Hill Book Company: New York, NY, USA, 1965.
10. Zinn-Justin, J. Quantum Field Theory and Critical Phenomena. International Series in Monographs on Physics. Oxford University Press: New York, NY, USA, 2002.
11. Langouche, F.; Roekaerts, D.; Tirapegui, E. Functional Integration and Semiclassical Expansions. Reidel: Dordrecht, The Netherlands, 1982.
12. Yau, S.T.; Yau, S.S.T. Explicit Solution of a Kolmogorov Equation. Appl. Math. Opt. 1996, 34, 231-266.
13. Balaji, B. Feynman Path Integrals and continuous-discrete filtering: The additive noise case. Technical Report TM 2008-343, 2009.
14. Bader, B.W.; Kolda, T.G. Algorithm 862: MATLAB tensor classes for fast algorithm prototyping. ACM Trans. Math. Software 2006, 32, 635-653.
15. Bader, B.W.; Kolda, T.G. Efficient MATLAB computations with sparse and factored tensors. Technical Report SAND2006-7592, 2006.
16. Gordon, N.; Salmond, D.; Smith, A. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc.-F Rad. Sig. Proc. 1993, 140, 107-113.
17. Budhiraja, A.; Chen, L.; Lee, C. A survey of numerical methods for nonlinear filtering problems. Physica D 2007, 230, 27-36.
18. Chen, L.; Lee, C.; Bidhiraja, A.; Mehra, R.K. PFLib -An object oriented MATLAB toolbox for particle filtering. In Proceedings to SPIE Signal Processing, Sensor Fusion, and Target Recognition XVI, 2007, Vol. 6567.
19. Lototsky, S.V.; Rozovskii, B.L. Recursive nonlinear filter for a continuous discrete-time model:separation of parameters and observations. IEEE Transactions on Automatic Control 1998, 43, 1154-1158.
20. Crisan, D.; Doucet, A. A survey of convergence results on particle filtering methods for practitioners. Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on] 2002, 50, 736-746.
21. Daum, F.; Huang, J. Curse of dimensionality and particle filters. In IEEE Aerospace Conference, 2003, Vol. 4.
22. Balaji, B. Sparse Tensors and Discrete-Time nonlinear filtering. In IEEE Radar Conference. 2008, pp. 1785-1790.
23. Balaji, B. Continuous-Discrete Filtering using the Dirac-Feynman Algorithm. In IEEE Radar Conference, Rome, Italy, 2008.
24. Montváy, I.; M̈unster, G. Quantum Fields on a Lattice. Cambridge Monographs on Mathematical Physics. Cambridge University Press: New York, USA, 1997.
25. Alicki, R.; Makoviec, D. Functional integrals for parabolic differential equations. J. Phys. A:Math. Gen. 1985, 18, 3319-3325.
26. Balaji, B. Universal Nonlinear Filtering Using Path Integrals II: The Continuous-Continuous Model with Additive Noise. PMC Physics A 2009.
27. Balaji, B. Estimation of indirectly observable Langevin states: path integral solution using statistical physics methods. J. Stat. Mech.-Theory Exp. 2008, 2008, P01014:1-P01014:17.
28. Balaji, B. Euclidean Quantum Mechanics and Universal Nonlinear Filtering. Entropy 2009, 11, 42-58.
29. Whittle, P. Likelihood and Cost as Path Integrals. J. Roy. Stat. Soc. Ser. B 1991, 53, 505-538.
30. Archambeau, C.; Cornford, D.; Lawrence, D.; Schwaighofer, A.; Quinonero, J. Gaussian process approximations of stochastic differential equations. In Journal of Machine Learning Research Workshop and Conference Proceedings, 2007.
31. Friston, K. Variational filtering. NeuroImage 2008, 41, 747-766.
32. Friston, K.; Mattout, J.; Trujillo-Barreto, N.; Ashburner, J.; Penny, W. Variational free energy and the Laplace approximation. NeuroImage 2007, 34, 220-234.
33. Friston, K.; Trujillo-Barreto, N.; Daunizeau, J. DEM: A variational treatment of dynamic systems. NeuroImage 2008, 41, 849-885.
34. Alexander, F.J.; Eynik, G.L.; Restrepo, J.M. Accelerated Monte Carlo for Optimal Estimation of Time Series. J. Statist. Phys. 2005, 119, 1331-1345.
35. Restrepo, J.M. A path integral method for data assimilation. Physica D 2008, 237, 14-27.