Robust M-ary detection filters and smoothers for continuous-time jump Markov systems

IEEE Transactions on Automatic Control

Volumn 49, Issue 7, 2004, Pages 1046-1055

  Elliott, Robert J ^a   Malcolm, W P ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; INTEGRAL EQUATIONS; LINEAR EQUATIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; ORDINARY DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION; PROBABILITY; STATE SPACE METHODS;

JUMP MARKOV SYSTEMS; M-ARY DETECTION; REFERENCE PROBABILITY; STOCHASTIC INTEGRAL EQUATION; TAYLOR EXPANSION; WIENER PROCESS;

TIME VARYING SYSTEMS;

EID: 3843088448     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.831188     Document Type: Article

References (19)

1. N. Bergman, A. Doucet, and N. Gordon, "Optimal estimation and the cramér-rao bounds for partial nongaussian state space models," Ann. Inst. Statist. Math., vol. 53, no. 1, pp. 97-112, 2001.
2. H. A. P. Blom, "An efficient filter for abruptly changing systems," presented at the IEEE Conf. Decision Control, Las Vegas, NV, Dec. 1984.
3. J. M. C. Clark, "The design of robust approximations to the stochastic differential equations for nonlinear filtering," in Communications Systems and Random Process Theory, J. K. Skwirzynski, Ed. Alphen aan den Rijn, The Netherlands: Sijthoff and Noorhoff, 1978, pp. 721-734.
4. R. J. Elliott, Stochastic Calculus and Its Applications. New York: Springer-Verlag, 1982.
5. R. J. Elliott, "New finite dimensional filters and smoothers for noisily observed markov chains," IEEE Trans. Inform. Theory, vol. 39, pp. 265-271, Jan. 1993.
6. R. J. Elliott, "Exact adaptive filters for markov chains observed in gaussian noise," Automatica, vol. 30, no. 9, pp. 1399-1408, Sept. 1994.
7. R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models Estimation and Control. New York: Springer-Verlag, 1995, Applications of Mathematics.
8. R. J. Elliott and W. P. Malcolm, "Reproducing gaussian densities and linear gaussian detection," Syst. Control Lett., no. 40, pp. 133-138, 2000.
9. R. J. Elliott and W. P. Malcolm, "Robust smoother dynamics for poisson processes driven by an itô diffusion," in IEEE Conf. Decision Control, Orlando, FL, Dec. 2001.
10. M. R. James, V. Krishnamurthy, and F. L. Gland, "Time discretization for continuous time filters and smoothers for hmm parameter estimation," IEEE Trans. Inform. Theory, vol. 42, pp. 593-605, Mar. 1998.
11. P. E. Kloeden and E. Platen, Numerical Solutions for Stochastic Differential Equations. New York: Springer-Verlag, 1995, Applications of Mathematics.
12. W. P. Malcolm and R. J. Elliott, "A general smoothing equation for poisson observations," presented at the IEEE Conf. Decision Control, Phoenix, AZ, Dec. 1999.
13. W. P. Malcolm and R. J. Elliott, "Robust detection filters for jump markov systems with doubly stochastic poisson process models," presented at the IEEE Conf. Information Decision Control, Adelaide, South Australia, Feb. 2002.
14. D. D. Sworder, J. Boyd, and R. J. Elliott, "Modal estimation in hybrid systems," J. Math. Anal. Applicat., no. 245, pp. 225-247, 2000.
15. E. Wong and B. Hajek, Stochastic Processes in Engineering Systems. New York: Springer-Verlag, 1985.
16. W. M. Wonham, "Some applications of stochastic differential equations to nonlinear filtering," SIAM J. Control Optim., no. 2, 1965.
17. W. P. Malcolm, "Robust filtering and estimation with Poisson observations," Ph.D. dissertation, The Australian National University, Canberra, Australia, 1999.
18. W. P. Malcolm, R. J. Elliott, and J. van der Hock, "On the numerical stability of time-discretised state estimation via Clark transformations," in Proc. 42nd IEEE Conf. Decision Control, vol. 2, Dec. 2003, pp. 1406-1412.
19. R. J. Elliott, F. Dufour, and D. D. Sworder, "Exact hybrid filters in discrete time," IEEE Trans. Automat. Contr., vol. 41, pp. 1807-1810, Dec. 1996.