Observations preprocessing and quantization for nonlinear filters

SIAM Journal on Control and Optimization

Volumn 38, Issue 2, 2000, Pages 482-502

  Newton, Nigel J ^a  

^a UNIVERSITY OF ESSEX   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; MATHEMATICAL MODELS; OPTIMIZATION; SPURIOUS SIGNAL NOISE;

HIDDEN MARKOV MODELS (HMM);

NONLINEAR FILTERING;

EID: 0033885338     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012997331147     Document Type: Article

References (19)

1. J. F. BENNATON, Discrete-time Galerkin approximations to the nonlinear filtering solution, J. Math. Anal. Appl., 110 (1985), pp. 364-383.
2. J. M. C. CLARK, The design of robust approximations to the stochastic differential equations of nonlinear filtering, in Communication Systems and Random Process Theory, J. K. Skwirzynski, ed., NATO Advanced Study Institute Series, Sijthoff and Noordhoff, Alphen aan den Rijn, 1978, pp. 721-734.
3. D. CRISAN AND T. LYONS, Nonlinear filtering and measure-valued processes, Probab. Theory Related Fields, 109 (1997), pp. 217-244.
4. M. H. A. DAVIS, A pathwise solution of the equations of nonlinear filtering, Theory Probab. Appl., 27 (1983), pp. 167-175.
5. G. B. DI MASI, M. PRATELLI, AND W. J. RUNGGALDIER, An approximation for the nonlinear filtering problem with error bound, Stochastics, 14 (1985), pp. 247-271.
6. S. N. ETHIER AND T. G. KURTZ, Markov Processes: Characterisation and Convergence, John Wiley, New York, 1986.
7. M. FUJISAKI, G. KALLIANPUR, AND H. KUNITA, Stochastic differential equations for the nonlinear filtering problem, Osaka J. Math., 9 (1972), pp. 19-40.
8. G. KALLIANPUR AND C. STRIEBEL, Estimation of stochastic systems: Arbitrary system process with additive white noise observation errors, Ann. Math. Statist., 39 (1968), pp. 785-801.
9. R. KHAS'MINSKII AND B. LAZAREVA, On some filtration procedure for jump Markov process observed in white Gaussian noise, Ann. Statist., 20 (1992), pp. 2153-2160.
10. R. KHASMINSKII AND O. ZEITOUNI, Asymptotic filtering for finite state Markov chains, Stochastic Process. Appl., 63 (1996), pp. 1-10.
11. H. J. KUSHNER, Dynamical equations for non-linear filtering, J. Differential Equations, 3, (1967), pp. 179-190.
12. H. J. KUSHNER, A robust discrete-state approximation to the optimal nonlinear filter for a diffusion, Stochastics, 3 (1979), pp. 75-83.
13. H. J. KUSHNER, Approximation and Weak Convergence Methods for Random Processes, With Application to Stochastic Systems Theory, MIT Press, Cambridge, MA, 1984.
14. F. LE GLAND, Splitting-up approximation for SPDEs and SDEs with application to nonlinear filtering, in Stochastic Partial Differential Equations and Their Applications, Lecture Notes in Control and Inform. Sci. 176, Springer-Verlag, Berlin, 1992, pp. 177-187.
15. R. S. LIPTSER AND A. N. SHIRYAYEV, Statistics of Random Processes 1 - General Theory, Springer-Verlag, New York, 1977.
16. N. J. NEWTON, Observation sampling and quantisation for continuous-time estimators, to appear in Stochastic Process. Appl.
17. J. PICARD, Approximation of nonlinear filtering problems and order of convergence, in Filtering and Control of Random Processes (E.N.S.T.-C.N.E.T. 1983), Lecture Notes in Control and Informat. Sci. 61, H. Korezlioglu, G. Mazziotto, and J. Szpirglas, eds., Springer-Verlag, New York, 1984, pp. 219-236.
18. W. M. WONHAM, Some applications of stochastic differential equations to optimal nonlinear filtering, SIAM J. Control, 2 (1964), pp. 347-369.
19. M. ZAKAI, On the optimal filtering of diffusion processes, Z. Wahrscheinlichkeitstheorie und Verw Gebiete, 11 (1969), pp. 230-243.