Polynomial chaos quadrature-based minimum variance approach for source parameters estimation

Procedia Computer Science

Volumn 9, Issue , 2012, Pages 1129-1138

  Madankan, R ^a   Singla, P ^a   Patra, A ^a   Bursik, M ^b   Dehn, J ^c   Jones, M ^b   Pavolonis, M ^d   Pitman, B ^b   Singh, T ^a   Webley, P ^c  

^a State University of New York   (United States)

^b UNIVERSITY AT BUFFALO   (United States)

^c UNIVERSITY OF ALASKA FAIRBANKS   (United States)

^d OFFICE OF RESEARCH AND APPLICATIONS   (United States)

Author keywords

Inverse problem; Minimum variance estimator; Polynomial chaos; Source parameter estimation

Indexed keywords

EID: 84878534149     PISSN: 18770509     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1016/j.procs.2012.04.122     Document Type: Conference Paper

References (39)

1. D. Schneider, W. Rose, L. Kelley, Tracking of 1992 eruption clouds from Crater Peak vent of Mount Spurr Volcano, Alaska using AVHRR, U. S. Geological Survey Bulletin 2139 (1995) 27-36.
2. CNN, New ash cloud could extend air travel threat, Accessed at http://www.cnn.com/2010/TRAVEL/04/19/volcano.ash/index.html.
3. D. B. Ryall, R. H. Maryon, Validation of the uk met. offices name model against the etex dataset, Atmospheric Environment 32 (1998) 4265-4276.
4. A. Jones, Assessing the meteorological uncertainties in dispersion forecasts using nwp ensemble prediction systems, in: Proceedings of the 11th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes, Cambridge, England, UK, 2007, pp. 246-250, http://www.harmo.org/Conferences/Proceedings/Cambridge/publishedSections/ Op246-250.pdf.
5. R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems 1, Transactions of the ASME-Journal of Basic Engineering 82 (Series D) (1960) 35-45.
6. A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, 1970.
7. S. F. Schmidt, Application of State-Space Methods to Navigation Problems, Advanced Control Systems 3 (1966) 293-340.
8. B. D. O. Anderson, J. B. Moore, Optimal Filtering, Prentice-Hall, 1979, 277-297.
9. S. J. Julier, New extension of the Kalman filter to nonlinear systems, Proceedings of SPIE (1997) 182-193 doi:10.1117/12.280797. URL http://link.aip.org/link/?PSI/3068/182/1&Agg=doi
10. F. E. Daum, Bounds on performance for multiple target tracking, Automatic Control, IEEE Transactions on 35 (4) (1990) 443-446. doi:10.1109/9.52299.
11. F. Daum, S.-T. Yau, S. Yau, Comments on "finite-dimensional filters with nonlinear drift," [and addendum], Aerospace and Electronic Systems, IEEE Transactions on 34 (2) (1998) 689-692. doi:10.1109/7.670361.
12. I. H. Sloan, H. Woniakowski, When are quasi-monte carlo algorithms efficient for high dimensional integrals?, Journal of Complexity (1998) 1-33.
13. Special issue on monte carlo methods for statstical signal processing, IEEE Trasactions on Signal Processing 50 (2).
14. F. Daum, J. Huang, Curse of dimensionality and particle filters, Aerospace Conference, 2003. Proceedings. 2003 IEEE 4 (March 8-15, 2003) 1979-1993.
15. J. Li, D. Xiu, A generalized polynomial chaos based ensemble Kalman filter with high accuracy, Journal of Computational Physics 228 (15) (2009) 5454-5469. doi:10.1016/j.jcp.2009.04.029. URL http://linkinghub.elsevier.com/ retrieve/pii/S0021999109002137
16. B. L. Pence, H. K. Fathy, J. L. Stein, A Maximum Likelihood Approach To Recursive Polynomial Chaos Parameter Estimation, in: 2010 American Control Conference, Marriott Waterfront, Baltimore, MD, USA, 2010, pp. 2144-2151.
17. E. Blanchard, A Polynomial-chaos based Bayesian approach for estimating uncertain parameters of mechanical systems, in: Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2007, 2007, pp. 1-9.
18. R. Madankan, Polynomial Chaos Based Method for State and Parameter Estimation, Ph.D. thesis, State University of New York at Buffalo (2011).
19. S. Carey, R. Sparks, Quantitative models of the fallout and dispersal of tephra from volcanic eruption columns, Bull. Volcanology 48 (1986) 109-125.
20. T. Suzuki, A theoretical model for dispersion of tephra, Terra Scientific Publishing, Tokyo, 2005, pp. 95-116.
21. H. Tanaka, Development of a prediction scheme for the volcanic ash fall from redoubt volcano, in: First Int'l Symposium on Volcanic Ash and Aviation Safety, Seattle, 1991, p. 58.
22. C. Searcy, K. Dean, B. Stringer, PUFF: A volcanic ash tracking and prediction model, J. Volcanology and Geophysical Research 80 (1998) 1-16.
23. P. Webley, K. Dean, J. Dehn, J. Bailey, R. Peterson, Volcanic ash dispersion modeling of the 2006 eruption of Augustine Volcano, USGS Professional Paper: Augustine Volcano 2006 eruption.
24. R. S. J. Sparks, M. I. Bursik, S. N. Carey, J. S. Gilbert, L. S. Glaze, H. Sigurdsson, A. W. Woods, Volcanic Plumes, John Wiley & Sons, London, 1997, 574p.
25. M. Bursik, S. Kobs, A. Burns, O. Braitseva, L. Bazanova, I. Melekestsev, A. Kurbatov, D. Pieri, Volcanic plumes and the wind: jetstream interaction examples and implications for air traffic, J. of Volcanology and Geothermal Research 186 (2009) 60-67.
26. M. Bursik, Effect of wind on the rise height of volcanic plumes, Geophys. Res. Lett. 18 (2001) 3621-3624.
27. B. Morton, J. Turner, G. Taylor, Gravitational turbulent convection from maintained and instantaneous sources, Proceedings Royal Soc. London Ser. A 234 (1956) 1-23.
28. A. Doucet, N. de Freitas, N. Gordon, Sequential Monte-Carlo Methods in Practice, Springer-Verlag, 2001, 6-14.
29. R. N. Iyengar, P. K. Dash, Study of the random vibration of nonlinear systems by the gaussian closure technique, Journal of Applied Mechanics 45 (1978) 393-399.
30. J. B. Roberts, P. D. Spanos, Random Vibration and Statistical Linearization, Wiley, 1990, 122-176.
31. D. Xiu, G. Karniadakis, The wiener-askey polynomial chaos for stochastic differential equations, SIAM J. Scientific Computation 24 (2002) 619-644.
32. N. Wiener, The Homogeneous Chaos, American Journal of Mathematics 60 (4) (1938) 897-936.
33. K. Dalbey, A. Patra, E. Pitman, M. Bursik, M. Sheridan, Input uncertainty propagation methods and hazard mapping of geophysical mass flows, J. of Geophysical Research 113 (2008) B05203.
34. E. W. Cheney, D. Kincaid, Numerical Mathematics and Computing, Brooks/Cole, Pacific Grove, CA, 1999.
35. C. W. Clenshaw, A. R. Curtis, A method for numerical integration on an automatic computer, Numerische Mathematik 2 (1960) 197-205.
36. A. Gelb, Applied Optimal Estimation, MIT Press, 1974.
37. M. Ripepe, S. D. Angelis, G. Lacanna, B. Voight, Observation of infrasonic and gravity waves at soufriere hills volcano, montserrat, Geophysical Research Letters 37 (2010) L00E14, doi:10.1029/2010GL042557.
38. A. W. Woods, M. I. Bursik, Particle fallout, thermal disequilibrium and volcanic plumes, Bulletin of Volcanology 53 (1991) 559-570.
39. S. Scollo, M. Prestilippo, M. Coltelli, R. Peterson, G. Spata, A statistical approach to evaluate the tephra deposit and ash concentration from PUFF model forecasts, Journal of Volcanology and Geothermal Research 200 (2011) 129-142.