Approximate inference in state-space models with heavy-tailed noise

IEEE Transactions on Signal Processing

Volumn 60, Issue 10, 2012, Pages 5024-5037

  Agamennoni, Gabriel ^a   Nieto, Juan I ^a   Nebot, Eduardo M ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Bayesian outlier detection; heavy tailed noise; inverse Wishart distribution; robust estimation; robust Kalman filter; state space models; student's t distribution; sub exponential noise

Indexed keywords

HEAVY-TAILED; OUTLIER DETECTION; ROBUST ESTIMATION; STATE-SPACE MODELS; STUDENT'S T DISTRIBUTION; SUB-EXPONENTIAL NOISE; WISHART DISTRIBUTION;

ALGORITHMS; GAUSSIAN NOISE (ELECTRONIC); TARGET TRACKING;

ESTIMATION;

EID: 84866497004     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2012.2208106     Document Type: Article

References (60)

1. B. Anderson and J. Moore, Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1978.
2. R. Brown and P. Hwang, Introduction to Random Signals and Applied Kalman Filtering. New York: Wiley, 1991.
3. Y. Bar-Shalom, X. Li, and T. Kirubarajan, Estimation With Applications to Tracking and Navigation. New York: Wiley, 2001.
4. H. Durrant-Whyte and T. Bailey, "Simultaneous localization and mapping (SLAM): Part I the essential algorithms," IEEE Robot. Autom. Mag., vol. 13, pp. 99-110, 2006.
5. R. Pearson, "Outliers in process modeling and identification," IEEE Trans. Control Syst. Technol., vol. 10, no. 1, pp. 55-63, Jan. 2002.
6. F. Grubbs, "Procedures for detecting outlying observations in samples," Technometrics, vol. 11, no. 1, pp. 1-31, Feb. 1969.
7. V. Barnett and T. Lewis, Outliers in Statistical Data. New York: Wiley, 1994.
8. J. Ting, A. D'Souza, and S. Schaal, "Automatic outlier detection: A Bayesian approach," in Proc. IEEE Int. Conf. Robot. Autom., 2007.
9. J. Ting, E. Theodorou, and S. Schaal, "Learning an outlier-robust Kalman filter," in Proc. 2007 Eur. Conf. Mach. Learn., 2007.
10. A. Jepson, D. Fleet, and T. El-Maraghi, "Robust on-line appearance models for visual tracking," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 10, pp. 1296-1311, Oct. 2003.
11. J. Loxam and T. Drummond, "Student mixture filter for robust, realtime visual tracking," in Proc. 10th Eur. Conf. Comput. Vis.: Part III, 2008.
12. T. Bailey and H. Durrant-Whyte, "Simultaneous localization and mapping (SLAM): Part II," IEEE Robot. Autom. Mag., vol. 13, no. 3, pp. 108-117, Sep. 2006.
13. A. Gil, O. Reinoso, O. Mozos, C. Stachnissi, and W. Burgard, "Improving data association in vision-based SLAM," in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., Oct. 2006, pp. 2076-2081.
14. R. Kalman, "A new approach to linear filtering and prediction theory," Trans. ASME J. Basic Eng., Series D, vol. 82, pp. 35-45, 1960.
15. R. Kalman and R. Bucy, "New results in linear filtering and prediction theory," Trans. ASME J. Basic Eng., Series D, vol. 83, pp. 95-108, 1961.
16. S. Roweis and Z. Ghahramani, "A unifying review of linear-Gaussian models," Neural Comput., vol. 11, no. 2, pp. 305-345, 1999.
17. R. Shumway and D. Stoffer, Time Series Analysis and Its Applications. New York: Springer-Verlag, 2005.
18. J. Morris, "The Kalman filter: A robust estimator for some classes of linear quadratic problems," IEEE Trans. Inf. Theory, vol. 22, no. 5, pp. 526-534, Sep. 1976.
19. P. Huber, "Robust estimation of a location parameter," Annals Math. Statist., vol. 35, no. 1, pp. 73-101, 1964.
20. H. Sorenson and A. Stubberud, "Non-linear filtering by approximation of the posterior density," Int. J. Contr., vol. 8, no. 1, pp. 33-51, 1968.
21. H. Sorenson and D. Alspach, "Recursive Bayesian estimation using Gaussian sums," Automatica, vol. 7, no. 4, pp. 465-479, 1971.
22. P. Szablowski, "Elliptically-contoured random variables and their application to the extension of the Kalman filter," Comput. Math. With Appl., vol. 19, no. 2, pp. 61-72, 1990.
23. F. Girón and J. Rojano, "Bayesian Kalman filtering with elliptically-contoured errors," Biometrika, vol. 81, no. 2, pp. 390-395, Jun. 1994.
24. R. Meinhold and N. Singpurwalla, "Robustification of Kalman filter models," J. Amer. Statist. Assoc., pp. 479-486, 1989.
25. I. Arasaratnam and S. Haykin, "Cubature Kalman filters," IEEE Trans. Autom. Control, vol. 54, no. 6, pp. 1254-1269, Jun. 2009.
26. J. Ting, E. Theodorou, and S. Schaal, "A Kalman filter for robust outlier detection," in Proc. IEEE Int. Conf. Intell. Robots Syst., 2007.
27. S. Sarkka and A. Nummenmaa, "Recursive noise adaptive Kalman filtering by variational Bayesian approximations," IEEE Trans. Autom. Control, vol. 54, no. 3, pp. 596-600, Mar. 2009.
28. G. Agamennoni, J. Nieto, and E. Nebot, "An outlier-robust Kalman filter," in Proc. IEEE Int. Conf. Robot. Autom., 2011.
29. M. Beal, "Variational algorithms for approximate Bayesian inference," Ph.D. dissertation, Gatsby Computational Neuroscience Unit, Univ. College, London, U.K., 2003.
30. A. Doucet, S. Godsill, and C. Andrieu, "On sequential Monte Carlo sampling methods for Bayesian filtering," Dept. Eng., Cambridge Univ., Tech. Rep. CUED/F-INFENG/TR310, 1998.
31. A. Doucet, N. De Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001.
32. N. Lawrence, "Variational inference in probabilistic models," Ph.D. dissertation, Univ. Cambridge Computer Lab., Cambridge, U.K., 2000.
33. M. Grewal and A. Andrews, Kalman Filtering: Theory and Practice. Englewood Cliffs, NJ: Prentice-Hall, 1993.
34. A. Dawid, "Some matrix-variate distribution theory: Notational considerations and a Bayesian application," Biometrika, vol. 68, pp. 265-274, 1981.
35. R. Muirhead, Aspects of Multivariate Statistical Theory. New York: Wiley, 1982.
36. P. Diaconis and D. Ylvisaker, "Conjugate priors for exponential families," Annal. Statist., vol. 7, no. 2, pp. 269-281, 1979.
37. J. Wishart, "The generalized product moment distribution in samples from a normal multivariate population," Biometrika, vol. 20A, no. 1, pp. 32-52, Jul. 1928.
38. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, With Formulas, Graphs and Mathematical Tables. New York: Dover, 1974.
39. W. Gosset, "The probable error of a mean," Biometrika, vol. 6, no. 1, pp. 1-25, 1908.
40. S. Kotz and S. Nadarajah, Multivariate Distributions and Their Applications. Cambridge, U.K.: Cambridge Univ. Press, 2004.
41. F. Hampel, E. Ronchetti, P. Rousseeuw, and W. Stahel, Robust Statistics: The Approach Based on Influence Functions. New York: Wiley, Mar. 1986.
42. J. Jensen, "Sur les fonctions convexes et les iné galités entre les valeurs moyennes," Acta Mathematica, vol. 30, no. 1, pp. 175-193, Dec. 1906.
43. A. O'Hagan, "A moment of indecision," Biometrika, vol. 68, no. 1, pp. 329-330, 1981.
44. J. Drèze, "Bayesian regression analysis using poly-densities," J. Econometr., vol. 6, no. 3, pp. 329-354, Nov. 1977.
45. R. Neal and G. Hinton, "A view of the EM algorithm that justifies incremental, sparse, and other variants," in Proc. NATO Adv. Study Inst. Learn. Graphical Models, M. Jordan, Ed., 1998.
46. S. Kullback and R. Leibler, "On information and sufficiency," Annal. Math. Statist., vol. 22, no. 1, pp. 79-86, 1951.
47. P. Naveau, M. Genton, and X. Shen, "A skewed Kalman filter," J. Mul-tivariate Anal., vol. 94, no. 2, pp. 382-400, Jun. 2005.
48. R. Bucy and P. Joseph, "Filtering for stochastic processes with applications to guidance," in Proc. Amer. Math. Soc. Chelsea, 2005.
49. S. Julier and J. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proc. Int. Symp. Aerospace Defense Sensing, Simulation, Contr., 1997.
50. M. Verhaegen and P. Van Dooren, "Numerical aspects of different Kalman filter implementations," IEEE Trans. Autom. Control, vol. 31, no. 10, pp. 907-917, Oct. 1986.
51. P. Park and T. Kailath, "New square-root smoothing algorithms," IEEE Trans. Autom. Control, vol. 41, no. 5, pp. 727-732, May 1996.
52. H. Akaike, "A new look at the statistical model identification, " IEEE Trans. Autom.Control, vol. 19, no. 6, pp. 716-723, Dec. 1974.
53. G. Schwarz, "Estimating the dimension of a model," Annal. Statist., vol. 6, no. 2, pp. 461-464, 1978.
54. F. Liu, "Bayesian time series: Analysis methods using simulation-based computation," Ph.D. dissertation, Inst. Statist. Decision Sci., Graduate School of Duke Univ., Durham, NC, 2000.
55. C. Carvalho and M. West, "Dynamic matrix-variate graphical models," Bayesian Anal., vol. 2, no. 1, pp. 69-98, 2007.
56. K. Murphy, Switching Kalman Filters Univ. California, Berkeley, CA, Compaq Cambridge Res. Lab. Tech. Rep. 98-10, 1998.
57. Z. Ghahramani and G. Hinton, "Variational learning for switching state-space models," Neural Comput., vol. 12, no. 4, pp. 831-864, 2000.
58. D. Barber, "Expectation correction for smoothed inference in switching linear dynamical systems," J. Mach. Learn. Res., vol. 7, pp. 2515-2540, Dec. 2006.
59. A. Roverato, "Cholesky decomposition of a hyper-inverse Wishart matrix," Biometrika, vol. 87, no. 1, pp. 99-112, 2000.
60. G. Letac and H. Massam, "Wishart distributions for decomposable graphs," Annal. Statist., vol. 35, no. 3, pp. 1278-1323, 2007.