An λ 1-Laplace robust kalman smoother

IEEE Transactions on Automatic Control

Volumn 56, Issue 12, 2011, Pages 2898-2911

  Aravkin, Aleksandr Y ^a   Bell, Bradley M ^b   Burke, James V ^b   Pillonetto, Gianluigi ^c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF WASHINGTON   (United States)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

Interior point methods; Kalman filtering; Kalman smoothing; Moving horizon estimation; Robust statistics

Indexed keywords

INTERIOR POINT METHODS; KALMAN SMOOTHING; KALMAN-FILTERING; MOVING HORIZON ESTIMATION; ROBUST STATISTICS;

ALGORITHMS; KALMAN FILTERS; NEWTON-RAPHSON METHOD; STATISTICS;

LAPLACE TRANSFORMS;

EID: 83255176348     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2011.2141430     Document Type: Article

References (44)

1. A. Aravkin, "Robust methods for Kalman filtering/smoothing and bundle adjustment," Ph.D. dissertation, Univ. of Washington, Seattle, 2010.
2. B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter. Boston, MA: Artech House, 2004.
3. Y. Bar-Shalom, X. R. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation. New York: Wiley, 2001.
4. B. Bell, "The iterated Kalman smoother as a Gauss-Newton method," SIAM J. Optim., vol. 4, no. 3, pp. 626-636, Aug. 1994.
5. B. M. Bell, "The marginal likelihood for parameters in a discrete Gauss-Markov process," IEEE Trans. Signal Process., vol. 48, no. 3, pp. 626-636, Mar. 2000.
6. B. M. Bell, J. V. Burke, and G. Pillonetto, "An inequality constrained nonlinear Kalman-Bucy smoother by interior point likelihood maximization," Automatica, pp. 25-33, 2008.
7. B. M. Bell and G. Pillonetto, Matlab®/Octave Package, 2007 [Online]. Available: http://www.seanet.com/~bradbell/ckbs/ckbs.xml
8. G. E. P. Box, R. L. Launer and G. N. Wilkinson, Eds., "Robustness in the strategy of scientific model building," in Robustness Statist.: Workshop Proc., 1979.
9. J. V. Burke, "Descent methods for composite nondifferentiable optimization problems," Math. Program., vol. 33, pp. 260-279, 1985.
10. J. V. Burke, "Second order necessary and sufficient conditions for convex composite ndo," Math. Program., vol. 38, pp. 287-302, 1987.
11. A. E. Cetin and A.M.Tekalp,"Robust reduced update Kalmanfiltering," IEEE Trans. Circuits Syst., vol. 37, no. 1, pp. 155-156, Jan. 1990.
12. R. Chen and J. S. Liu, "Mixture Kalman filters," J. R. Statist. Soc. Ser. B, vol. 62, pp. 493-508, 2000.
13. T. Cipra and R. Romera, "Kalman filter with outliers and missing observations," Sociedad de Estadistica e Invastigacion Operativa, vol. 6, no. 2, pp. 379-395, 1997.
14. A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice. New York: Springer, 2001.
15. J. Durbin and S. J. Koopman, "Monte Carlo maximum likelihood estimation for non-Gaussian state space models," Biometrika, vol. 84, pp. 669-684, 1997.
16. Z. M. Durovic and B. D. Kovachevic, "Robust estimation with unknown noise statistics," IEEE Trans. Autom. Control, vol. 44, no. 6, pp. 1292-1296 Jun. 1999.
17. P. Fearnhead and P. Clifford, "On-line inference for hidden markov models via particle filters," J. R. Statist. Soc. Ser. B, vol. 65, pp. 887-899, 2003. (Pubitemid 37434236)
18. J. Gao, "Robust l1 principal component analysis and its Bayesian variational inference," Neural Comput., vol. 20, no. 2, pp. 555-572, Feb. 2008.
19. V. Gebski and D. McNeil, "A refined method of robust smoothing," J. Amer. Statist. Assoc., vol. 79, no. 387, pp. 616-623, Sep. 1984.
20. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice. London, U.K.: Chapman & Hall, 1996.
21. S. Gillijns, O. B. Mendoza, J. Chandrasekar, B. L. R. De Moor, D. S. Bernstein, and A. Ridley, "What is the ensemble Kalman filter and how well does itwork?," in Proc. Amer. Control Conf., 2006, pp. 4448-4453. (Pubitemid 46531519)
22. S. J. Godsill, A. Doucet, and M. West, "Monte Carlo smoothing for nonlinear time series," J. Amer. Statist. Assoc., vol. 99, pp. 156-168, 2004. (Pubitemid 38545203)
23. F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel, Robust Statistics. : Wiley, 1986.
24. W. K. Hastings, "Monte Carlo sampling methods using Markov chain and their applications," Biometrika, vol. 57, pp. 97-109, 1970.
25. G. A. Hewer, R. D. Martin, and J. Zeh, "Robust preprocessing for Kalman filtering of glint noise," IEEE Trans. Aerosp. Electron. Syst., vol. AES-23, no. 1, pp. 120-128, Jan. 1987. (Pubitemid 17582689)
26. P. J. Huber, Robust Statistics. New York: Wiley, 2004.
27. B. Jungbacker and S. J. Koopman, "Monte Carlo estimation for nonlinear non-Gaussian state space models," Biometrika, vol. 94, pp. 827-839, 2007.
28. R. Kandepu, B. Foss, and L. Imsland, "Applying the unscented Kalman filter for nonlinear state estimation," J. Process Control, vol. 18, pp. 753-768, 2008.
29. S. A. Kassam and H. V. Poor, "Robust techniques for signal processing: A survey," Proc. IEEE, vol. 73, no. 3, pp. 433-481, Mar. 1985. (Pubitemid 15110686)
30. R. L. Kirlin and A. Moghaddamjoo, "Robust adaptive Kalman filtering for systems with unknown step inputs and non-Gaussian measurement errors," IEEE Trans. Acoust. , Speech, Signal Process., vol. ASSP-34, no. 2, pp. 252-263, Mar. 1986. (Pubitemid 16576057)
31. S. Kotz, T. J. Kozubowski, and K. Podgorski, The Laplace Distribution and Generalizations. Cambridge, MA: Birkhauser, 2001.
32. J. S. Liu and R. Chen, "Sequential Monte Carlo methods for dynamic systems," J. Amer. Statist. Assoc., vol. 93, pp. 1032-1044, 1998.
33. R. A. Maronna, D. Martin, and Yohai, Robust Statistics. New York: Wiley, 2006, Wiley Series in Probability and Statistics.
34. C. J. Masreliez and R. D. Martin, "Robust Bayesian estimation for the linear model and robustifying the Kalman filter," IEEE Trans. Autom. Control, vol. AC-22, no. 3, pp. 361-371 Jun. 1977.
35. R. J. Meinhold and N. D. Singpurwalla, "Robustification of Kalman filter models," J. Amer. Statist. Assoc., vol. 84, no. 406, pp. 479-486 Jun. 1989.
36. K. Murphy, Matlab® Toolbox for Kalman Filtering, 1998, [Online]. Available: http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html
37. I. R. Petersen and A. V. Savkin, Robust Kalman Filtering for Signals and Systems with Large Uncertainties. Cambridge, MA: Birkhauser, 1999.
38. G. Pillonetto and B. M. Bell, "Optimal smoothing of non-linear dynamic systems via Monte Carlo Markov chains," Automatica, vol. 44, pp. 1676-1685, 2008.
39. R. T. Rochafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.
40. R. T. Rochafellar and R. J. B.Wets, Variational Analysis. New York: Springer, 1998.
41. P. Ruckdechel and B. Spangl, An R-Package for Robust Kalman Filtering, 2008, [Online]. Available: http://robkalman.r-forge.r-project. org/
42. I. C. Schick and S. K. Mitter, "Robust recursive estimation in the presence of heavy-tailed observation noise," Ann. Statist., vol. 22, no. 2, pp. 1045-1080 Jun. 1994.
43. M. W. Seeger, "Bayesian inference and optimal design for the sparse linear model," J. Mach. Learn. Res., vol. 9, pp. 759-813, 2008.
44. J. C. Spall, "Estimation via Markov chain Monte Carlo," IEEE Control Syst. Mag., vol. 23, no. 2, pp. 34-45, Apr. 2003.