Nonlinear estimation with polynomial chaos and higher order moment updates

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 3142-3147

  Dutta, Parikshit ^a   Bhattacharya, Raktim ^a  

^a Department of Electrical and Computer Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY FUNCTIONAL THEORY; KALMAN FILTERS; NONLINEAR ANALYSIS; POLYNOMIALS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; UNCERTAINTY ANALYSIS;

EXTENDED KALMAN FILTERING; GENERALIZED POLYNOMIAL CHAOS; HIGHER ORDER MOMENTS; INITIAL CONDITION UNCERTAINTIES; NON-GAUSSIAN PROBABILITY DENSITY FUNCTION; NON-LINEAR ESTIMATION; NONLINEAR RANDOM PROCESS; POLYNOMIAL CHAOS THEORY;

CHAOS THEORY;

EID: 77957824003     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2010.5531023     Document Type: Conference Paper

References (33)

1. R.E. Kalman, "A new approach to linear filtering and prediction problems", Journal of basic Engineering, vol. 82, no. 1, pp. 35-45, 1960.
2. B. Anderson, J.B. Moore, and M. Eslami, "Optimal filtering", IEEE Transactions on Systems, Man and Cybernetics, vol. 12, no. 2, pp. 235-236, 1982.
3. G. Evensen, "Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model", Journal of Geophysical Research, vol. 97, no. C11, pp. 17905-17924, 1992.
4. R.N. Miller, M. Ghil, and F. Gauthiez, "Advanced data assimilation in strongly nonlinear dynamical systems", Journal of the Atmospheric Sciences, vol. 51, no. 8, pp. 1037-1056, 1994.
5. P. Gauthier, P. Courtier, and P. Moll, "Assimilation of simulated wind lidar data with a Kalman filter", Monthly Weather Review, vol. 121, no. 6, pp. 1803-1820, 1993.
6. F. Bouttier, "A dynamical estimation of forecast error covariances in an assimilation system", Monthly Weather Review, vol. 122, no. 10, pp. 2376-2390, 1994.
7. S.J. Julier and J.K. Uhlmann, "A new extension of the Kalman filter to nonlinear systems", in Int. Symp. Aerospace/Defense Sensing, Simul. and Controls, 1997, vol. 3, p. 26.
8. MS Arulampalam, S. Maskell, N. Gordon, T. Clapp, D. Sci, T. Organ, and SA Adelaide, "A tutorial on particle filters for online nonlinear/non- GaussianBayesian tracking", IEEE Transactions on signal processing, vol. 50, no. 2, pp. 174-188, 2002. (Pubitemid 34291500)
9. C. Snyder, T. Bengtsson, P. Bickel, and J. Anderson, "Obstacles to high-dimensional particle filtering", Monthly Weather Review, vol. 136, no. 12, pp. 4629-4640, 2008.
10. M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, Krieger Pub., 2006.
11. N. Wiener, "The Homogeneous Chaos", American Journal of Mathematics, vol. 60, no. 4, pp. 897-936, 1938.
12. R. H. Cameron and W. T. Martin, "The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals", The Annals of Mathematics, vol. 48, no. 2, pp. 385-392, 1947.
13. Dongbin Xiu and George Em Karniadakis, "The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations", SIAM J. Sci. Comput., vol. 24, no. 2, pp. 619-644, 2002.
14. R. Askey and J. Wilson, "Some Basic Hypergeometric Polynomials that Generalize Jacobi Polynomials", Memoirs Amer. Math. Soc., vol. 319, 1985.
15. Thomas Y. Hou, Wuan Luo, Boris Rozovskii, and Hao-Min Zhou, "Wiener Chaos Expansions and Numerical Solutions of Randomly Forced Equations of Fluid Mechanics", J. Comput. Phys., vol. 216, no. 2, pp. 687-706, 2006.
16. Dongbin Xiu and George Em Karniadakis, "Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos", J. Comput. Phys., vol. 187, no. 1, pp. 137-167, 2003.
17. Roger G. Ghanem and Pol D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag New York, Inc., New York, NY, USA, 1991.
18. Roger Ghanem and John Red-Horse, "Propagation of Probabilistic Uncertainty in Complex Physical Systems Using a Stochastic Finitek Element Approach", Phys. D, vol. 133, no. 1-4, pp. 137-144, 1999.
19. R.G. Ghanem, "Ingredients for a General Purpose Stochastic Finite Elements Implementation", Comput. Methods Appl. Mech. Eng., vol. 168, no. 1-4, pp. 19-34, 1999.
20. J. Fisher and R. Bhattacharya, "Optimal Trajectory Generation with Probabilistic System Uncertainty Using Polynomial Chaos", In Press Journal of Dynamic Systems, Measurement and Control, 2008.
21. J. Fisher and R. Bhattacharya, "Linear Quadratic Regulation of Systems with Stochastic Parameter Uncertainties", in Press Automatica, 2009.
22. J. Fisher and R. Bhattacharya, "Stability Analysis of Stochastic Systems using Polynomial Chaos", in American Control Conference, 2008.
23. Z.K. Nagy and R.D. Braatz, "Robust nonlinear model predictive control of batch processes", AIChE Journal, vol. 49, no. 7, 2003.
24. Z.K. Nagy and R.D. Braatz, "Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis", Journal of process control, vol. 14, no. 4, pp. 411-422, 2004.
25. Franz S. Hover and Michael S. Triantafyllou, "Application of Polynomial Chaos in Stability and Control", Automatica, vol. 42, no. 5, pp. 789-795, 2006.
26. C. Sandu E. D. Blanchard, A. Sandhu, "A Polynomial Chaos Based Bayesian Approach for Estimating Uncertain Parameters of Mechanical Systems Part 1: Theoretical Approach", in Computer Science Technical Report TR-07-38, 2007.
27. C. Sandu E. D. Blanchard, A. Sandhu, "A Polynomial Chaos Based Bayesian Approach for Estimating Uncertain Parameters of Mechanical Systems Part 1: Theoretical Approach", in Computer Science Technical Report TR-07-39, 2007.
28. S. Julier, J. Uhlmann, HF Durrant-Whyte, I. Ind, and J. City, "A new method for the nonlinear transformation of means andcovariances in filters and estimators", IEEE Transactions on Automatic Control, vol. 45, no. 3, pp. 477-482, 2000.
29. th Moment Extended Kalman Filtering for Estimation of Nonlinear Dynamic Systems", in AIAA Guidance, Navigation and Control Conference and Exhibit, 2008.
30. SJ Julier, JK Uhlmann, I. Ind, and MO Jefferson City, "Unscented filtering and nonlinear estimation", Proceedings of the IEEE, vol. 92, no. 3, pp. 401-422, 2004.
31. R.S. Park and D.J. Scheeres, "Nonlinear Mapping of Gaussian State Uncertainties: Theory and Applications to Spacecraft Control and Navigation", in 2005 Astrodynamics Specialist Meeting, Lake Tahoe, California, 2005.
32. Bert J. Debusschere, Habib N. Najm, Philippe P. Pébay, Omar M. Knio, Roger G. Ghanem, and Olivier P. Le Maître, "Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes", SIAM J. Sci. Comput., vol. 26, no. 2, pp. 698- 719, 2005.
33. P.E. Gill, W. Murray, and M.A. Saunders, "SNOPT: An SQP algorithm for large-scale constrained optimization", SIAM Journal on Optimization, vol. 12, no. 4, pp. 979-1006, 2002.