Feedback particle filter

IEEE Transactions on Automatic Control

Volumn 58, Issue 10, 2013, Pages 2465-2480

  Yang, Tao ^a   Mehta, Prashant G ^a   Meyn, Sean P ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b J Crayton Pruitt Family Department of Biomedical Engineering   (United States)

Author keywords

Mean field games; nonlinear filtering; optimal transportation; particle filtering

Indexed keywords

CONTINUOUS OBSERVATION; EMPIRICAL DISTRIBUTIONS; KULLBACK LEIBLER DIVERGENCE; MEAN-FIELD GAMES; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROL SOLUTION; OPTIMAL TRANSPORTATIONS; PARTICLE FILTERING;

ALGORITHMS; FEEDBACK CONTROL; NONLINEAR FILTERING; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION;

MONTE CARLO METHODS;

EID: 84884789621     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2013.2258825     Document Type: Article

References (30)

1. T. Yang, P. G. Mehta, and S. P. Meyn, "A mean-field control-oriented approach for particle filtering," in Proc. 2011 Amer. Control Conf., San Francisco, CA, USA, Jun. 2011, pp. 2037-2043.
2. T. Yang, P. G. Mehta, and S. P. Meyn, "Feedback particle filter with mean-field coupling," in Proc. 50th IEEE Conf. Decision and Control, Orlanda, FL, USA, Dec. 2011, pp. 7909-7916.
3. G. Kallianpur, Stochastic Filtering Theory. NewYork,NY,USA: Springer-Verlag, 1980.
4. A. Budhiraja, L. Chen, and C. Lee, "A survey of numerical methods for nonlinear filtering problems," Physica D: Nonlinear Phenomena, vol. 230, no. 1-2, pp. 27-36, 2007. (Pubitemid 46776906)
5. J. E. Handschin and D. Q.Mayne, "Monte Carlo techniques to estimate the conditional expectation in multi-stage nonlinear filtering," Int. J. Control, vol. 9, no. 5, pp. 547-559, 1969.
6. N. J. Gordon, D. J. Salmond, and A. F. M. Smith, "Novel approach to nonlinear/non-Gaussian Bayesian state estimation," IEEProc.FRadar Signal Process., vol. 140, no. 2, pp. 107-113, 1993.
7. A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte-Carlo Methods in Practice. New York, NY, USA: Springer-Verlag, Apr. 2001.
8. D. Crisan and A. Doucet, "A survey of convergence results on particle filtering methods for practitioners," IEEE Trans. Signal Process., vol. 50, no. 3, pp. 736-746, Mar. 2002. (Pubitemid 34295113)
9. M. Huang, P. E. Caines, and R. P. Malhame, "Large-population costcoupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized-Nash equilibria," Trans. Autom. Control, vol. 52, no. 9, pp. 1560-1571, 2007. (Pubitemid 47456068)
10. H. Yin, P. G. Mehta, S. P. Meyn, and U. V. Shanbhag, " Synchronization of coupled oscillator is a game," IEEE Trans. Autom. Control, vol. 57, no. 4, pp. 920-935, Apr. 2012.
11. L. C. Evans, Partial Differential Equations. Providence, RI, USA: Amer. Math. Soc., 1998.
12. T. Yang, R. S. Laugesen, P. G. Mehta, and S. P. Meyn, "Multivariable feedback particle filter," in Proc. 51st IEEE Conf. Decision Control, Maui, HI, USA, Dec. 2012, pp. 4063-4070.
13. J. Xiong, "Particle approximations to the filtering problem in continuous time," in The Oxford Handbook of Nonlinear Filtering, D. Crisan and B. Rozovskii, Eds. Oxford, U.K.: Oxford Univ. Press, 2011.
14. B. Øksendal, Stochastic Differential Equations (6th ed.): An Introduction With Applications. New York, NY, USA: Springer-Verlag, 2005.
15. T. S. Lee and D. Mumford, "Hierarchical Bayesian inference in the visual cortex," J. Opt. Soc. Amer., A, vol. 20, no. 7, pp. 1434-1448, 2003.
16. K. Doya, S. Ishii, A. Pouget, and R. P. N. Rao, Bayesian Brain, ser. Comput. Neurosci. Cambridge, MA, USA: MIT Press, 2007.
17. A. K. Tilton, E. T. Hsiao-Wecksler, and P. G. Mehta, "Filtering with rhythms: Application of the feedback particle filter to estimation of human gait cycle," in Proc. 2012 Amer. Control Conf., Montréal, QC, Canada, Jun. 2012, pp. 3433-3438.
18. A. K. Tilton, P. G. Mehta, and S. P. Meyn, "Multi-dimensional feedback particle filter for coupled oscillators," in Proc. 2013 Amer. Control Conf., Washington, DC, Jun. 2013.
19. D. Crisan and J.Xiong, "Approximate McKean-Vlasov representations for a class of SPDEs," Stochastics: Int. J. Probab. Stochast. Process., pp. 1-16, 2009.
20. S. K. Mitter and N. J. Newton, "A variational approach to nonlinear estimation," SIAM J. Control Optimiz., vol. 42, no. 5, pp. 1813-1833, 2003.
21. F. Daum and J. Huang, "Generalized particle flow for nonlinear filters," in Proc. SPIE, 2010, pp. 76 980I-76 980I-12.
22. H. Kunita, Stochastic Flows and Stochastic Differential Equations. Cambridge, U.K.: Cambridge Univ. Press, 1990.
23. S. Reich, "A dynamical systems framework for intermittent data assimilation," BIT Numer. Math., vol. 51, no. 1, pp. 235-249, 2011.
24. L. Greengard and V. Rokhlin, "A fast algorithm for particle simulations," J. Comput. Phys., vol. 73, pp. 325-348, Dec. 1987.
25. A. J. Chorin, "Numerical study of slightly viscous flow," J. Fluid Mech., vol. 57, pp. 785-796, 1973.
26. A. Leonard, "Vortex method for flow simulation," J. Comput. Phys., vol. 37, pp. 289-335, 1980.
27. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-Dynamic Programming. Cambridge, MA, USA: Athena Scientific, 1996.
28. A. Bain and D. Crisan, Fundamentals of Stochastic Filtering. Cambridge, MA, USA: Springer, 2010.
29. T. Yang, G. Huang, and P. G. Mehta, "Joint probabilistic data association-feedback particle filter for multiple target tracking applications," in Proc. Amer. Control Conf., Montréal, QC, Canada, Jun. 2012, pp. 820-826.
30. H. J. Kushner, "On the differential equations satisfied by conditional probability densities of Markov processes," SIAM J. Control, vol. 2, pp. 106-119, 1964.