Nonlinear estimation with state-dependent gaussian observation noise

IEEE Transactions on Automatic Control

Volumn 55, Issue 6, 2010, Pages 1358-1366

  Spinello, Davide ^a   Stilwell, Daniel J ^b  

^a UNIVERSITY OF OTTAWA   (Canada)

^b State University   (United States)

Author keywords

Extended Kalman filter; Mobile sensors; Nonlinear estimation; State dependent noise

Indexed keywords

CONTROL PROBLEMS; ESTIMATION ALGORITHM; GAUSSIANS; ITERATED EXTENDED KALMAN FILTER; ITERATIVE ROOTS; MAXIMUM LIKELIHOOD FUNCTION; MEASUREMENT NOISE; MOBILE BEARING; MOBILE SENSORS; NON-LINEAR ESTIMATION; OBSERVATION NOISE; SEARCHING METHODS; STATE ESTIMATES; STATE-DEPENDENT; STATE-DEPENDENT NOISE;

ESTIMATION; EXTENDED KALMAN FILTERS; MAXIMUM LIKELIHOOD ESTIMATION; POSITION CONTROL; SENSORS; STATE ESTIMATION; UNMANNED AERIAL VEHICLES (UAV);

NONLINEAR ANALYSIS;

EID: 77953117482     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2042006     Document Type: Article

References (47)

1. A. Farina, "Target tracking with bearings-only measurements," Signal Processing, vol.78, pp. 61-78, 1999.
2. A. Logothetis, A. Isaksson, and R. J. Evans, "An information theoretic approach to observer path design for bearings-only tracking," in Proc. 36th Conf. Decision Control, San Diego, CA, Dec. 1997, pp. 3132-3137.
3. S. Thrun, Y. Liu, K. D. , and A. Y. Ng, "Simultaneous localization and mapping with sparse extended information filters," Int. J. Robot. Res., vol.23, no.7-8, pp. 693-716, Jul./Aug. 2004.
4. K. X. Zhou and S. I. Roumeliotis, "Optimal motion strategies for rangeonly distributed target tracking," in Proc. Amer. Control Conf., Minneapolis, MN, Jun. 14-16, 2006, pp. 5195-5200.
5. T. H. Chung, J. W. Burdick, and R. M. Murray, "Decentralized motion control of mobile sensing agents in a network," in Proc. IEEE Int. Conf. Robot. Autom., Orlando, FL, May 2006, pp. 2416-2422.
6. T. H. Chung, V. Gupta, J. W. Burdick, and R. M. Murray, "On a decentralized active sensing strategy using mobile sensor platforms in a network," in Proc. IEEE Conf. Decision Control, Paradise Island, Bahamas, Dec. 2004, pp. 1914-1919.
7. S. Martínez and F. Bullo, "Optimal sensor placement and motion coordination for target tracking," Automatica, vol.42, no.4, pp. 661-668, 2006.
8. P. Yang, R. A. Freeman, and K. M. Lynch, "Distributed cooperative active sensing using consensus filters," in Proc. IEEE Int. Conf. Robot. Autom., Roma, Italy, Feb. 2007, pp. 405-410.
9. C. Belta and V. Kumar, "Abstraction and control for groups of robots," IEEE Trans. Robotics, vol.20, no.5, pp. 865-875, Oct. 2004.
10. J. Cortés, S. Martínez, T. Karatas, and F. Bullo, "Coverage control for mobile sensing networks," IEEE Trans. Robot. Autom., vol.20, no.2, pp. 243-255, Feb. 2004.
11. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Trans. Autom. Control, vol.49, no.9, pp. 1465-1476, Sep. 2004.
12. R. A. Freeman, P. Yang, and K. M. Lynch, "Distributed estimation and control of swarm formation statistics," in Proc. Amer. Control Conf., Minneapolis, MN, Jun. 14-16, 2006, pp. 749-755.
13. M. Porfiri, D. G. Roberson, and D. J. Stilwell, "Tracking and formation control of multiple autonomous agents: A two-level consensus approach," Automatica, vol.43, no.8, pp. 1318-1328, 2007.
14. S. Simic and S. Sastry, "Distributed environmental monitoring using random sensor networks," in Proc. 2nd Int. Workshop Inform. Processing Sensor Networks, Palo Alto, CA, 2003, pp. 582-592.
15. S. Susca, S. Martínez, and F. Bullo, "Monitoring environmental boundaries with a robotic sensor network," in Proc. Amer. Control Conf., 2006, pp. 2072-2077.
16. Y. Bar-Shalom and T. E. Fortman, Tracking and Data Association. New York: Academic Press, 1988.
17. M. Zakai, "On the optimal filtering of diffusion processes," Zeitschrift Fur Wahrscheinlichkeitstheorie Und Verwandte Gebiete, vol.11, pp. 230-243, 1969.
18. R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes. New York: Springer Verlag, 1977, vol.I, II.
19. A. Üstnel and M. Zakai, Transformation of Measure on Wiener Space. Berlin, Germany: Springer, 2000.
20. X. R. Li and V. P. Jilkov, "A survey of maneuvering target tracking- Part III: Measurement models," in Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, San Diego, CA, Jul./Aug. 2001, p. 4473-4541
21. J. Manyika and H. Durrant-Whyte, Data Fusion and Sensor Management: A Decentralized Information-Theoretic Approach. London, U.K.: Ellis Horwood, 1994.
22. P. S. Maybeck, Stochastic Models, Estimation, and Control, ser. Mathematics in Science and Engineering, R. Bellman, Ed. NewYork: Academic Press, 1982, vol.2.
23. A. G. O. Mutambara, Decentralized Estimation and Control for Multisensor Systems. Boca Raton, FL: CRC Press LLC, 1998.
24. T. Lefebvre, H. Bruyninckx, and J. De Schutter, "Comment on 'A new method for the nonlinear transformation of means and covariances in filters and estimators'," IEEE Trans. Autom. Control, vol.47, no.8, pp. 1406-1408, Aug. 2002.
25. T. Schei, "A finite-difference method for linearisation in nonlinear estimation algorithms," Automatica, vol.33, no.11, pp. 2053-2058, 1997.
26. M. Nørgaard, N. Poulsen, and O. Ravn, "New developments in state estimations for nonlinear systems," Automatica, vol.36, no.11, pp. 1627-1638, 2000.
27. S. J. Julier and J. K. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proc. SPIE Int. Symp. Aerosp./Defense Sens., Simul., Controls, 1997, pp. 182-193.
28. J. Julier, S. Uhlmann, and H. F. Durrant-Whyte, "A new method for the nonlinear transformation of means and covariances in filters and estimators," IEEE Trans. Autom. Control, vol.45, no.3, pp. 477-482, Mar. 2000.
29. R. van der Merve, "Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models," Ph.D. dissertation, OGI School Sci. Eng., Oregon Health & Science Univ., , 2004.
30. G. Sibley, G. Suckhatme, and L. Matthies, "The iterated sigma point Kalman filter with application to long range stereo," in Proc. Robot.: Sci. Syst., Philadelphia, PA, Aug. 2006 [Online]. Available: http://www. roboticsproceedings.org/rss02/p34.html
31. R. Zhan and J. Wan, "Iterated unscented Kalman filter for passive target tracking," IEEE Trans. Aerosp. Electron. Syst., vol.43, no.3, pp. 1155-1163, Jul. 2007.
32. T. Lefebvre, H. Bruyninckx, and J. De Shutter, "Kalman filters for nonlinear systems: A comparison of performance," Int. J. Control, vol.77, no.7, pp. 639-653, 2004.
33. K. Ito and K. Xiong, "Gaussian filters for nonlinear filtering problems," IEEE Trans. Autom. Control, vol.45, no.5, pp. 910-927, May 2000.
34. B. M. Bell and F. W. Cathey, "The iterated Kalman filter update as a Gauss-Newton method," IEEE Trans. Autom. Control, vol.38, no.2, pp. 294-297, Feb. 1993.
35. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods. Englewood Cliffs, NJ: Prentice Hall, 1989.
36. R. A. Iltis and K. L. Anderson, "A consistent estimation criterion for multisensor bearing-only tracking," IEEE Trans. Aerosp. Electron. Syst., vol.32, no.1, pp. 108-120, Jan. 1996.
37. J. P. Le Cadre and C. Jauffret, "On the convergence of iterative methods for bearing-only tracking," IEEE Trans. Aerosp. Electron. Syst., vol.35, no.3, pp. 801-818, Jul. 1999.
38. J. Shao, Mathematical Statistics, ser. Springer Texts in Statistics. New York: Springer Verlag, 1999.
39. Y. Oshman and P. Davidson, "Optimization of observer trajectories for bearings-only target localization," IEEE Trans. Aerosp. Electron. Syst., vol.35, no.3, pp. 892-902, 1999.
40. D. S. Bernstein, Matrix Mathematics. Princeton, NJ: Princeton Univ. Press, 2005.
41. A. Gadre, M. Roan, and D. J. Stilwell, "Sensor Model for a Uniform Linear Array," VaCAS, Tech. Rep., 2008 [Online]. Available: http:// www.unmanned.vt.edu/discovery/reports/VaCAS-2008-01.pdf
42. A. Logothetis, A. Isaksson, and R. J. Evans, "Comparison of suboptimal strategies for optimal own-ship maneuvers in bearing-only tracking," in Proc. Amer. Control Conf., Philadelphia, PA, Jun. 1996, pp. 3334-3338.
43. A. Gadre, D. Makcza, D. Spinello, B. McCarter, D. Stilwell, W. Neu, M. Roan, and J. Hennage, Cooperative Localization of an Acoustic Target Using a Team of AUVs. Woods Hole, MA, Oct. 12-13, 2008.
44. D. Spinello and D. J. Stilwell, "Nonlinear Estimation With State-Dependent Gaussian Observation Noise," VaCAS, Tech. Rep. 2, 2008 [Online]. Available: http://www.unmanned.vt.edu/discovery/reports/ VaCAS-2008-02.pdf
45. Z.Wang, F. Yang, D. W. C. Ho, and X. Liu, "Robust finite-horizon filtering for stochastic systems with missing measurements," IEEE Signal Processing Lett., vol.12, no.6, pp. 437-440, Jun. 2005. (Pubitemid 40794876)
46. B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan, and S. S. Sastry, "Kalman filtering with intermittent observations," IEEE Trans. Autom. Control, vol.49, no.9, pp. 1453-1464, Sep. 2004.
47. B. Shen, Z.Wang, H. Shu, and G.Wei, "On nonlinear filtering for discrete-time stochastic systems with missing measurements," IEEE Trans. Autom. Control, vol.53, no.9, pp. 2170-2180, Oct. 2008.