Abstract
Nonlinear filtering problems in discrete-time are studied using the Bayesian approach. The concept of a generalized finite-dimensional filter is introduced and it is shown that under suitable assumptions such a filter exists and can be implemented in a recursive way. The resulting technique is successfully applied to various situations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.L. Alspach and H.W. Sorenson, “Nonlinear Bayesian estimation using Gaussian sum approximations”. IEEE Trans. AC 17, pp. 439–448 (1972).
A. Aoki, “Optimmization of stochastic systems”. Academic Press (1967).
B. Barozzi “Filtri a tempo discrete di dimensione finite generalizzati”. Thesis, Università di Padova (1982).
G.B. Di Masi and W.J. Runggaldier, “On measure transformations for combined filtering and parameter estimation in discrete time”. Systems & Control Letters (to appear).
G.B. Di Masi and W.J. Runggaldier, “Approximations and bounds for discrete-time nonlinear filtering”. Preprint (1982).
G. Sawitzki, “Exact filtering in exponential families: discrete time”, in “Stochastic control theory and stochastic differential systems” (M. Kohlmann and W. Vogel eds.). L.N. in Contr. and Inf. Sci. 16, Springer-Verlag (1979).
G. Sawitzki, “Finite-dimensional filter systems in discrete time”. Stochastics 5, pp. 107–114 (1981).
H.W. Sorenson and D.L. Alspach, “Recursive Bayesian estimation using Gaussian sums”. Automatica 7, pp. 465–479 (1971).
J.H. Van Schuppen, “Stochastic filtering theory: a discussion of concepts, methods and results”, in “Stochastic control theory and stochastic differential systems” (M. Kohlmann and W. Vogel eds.). L.N. in Contr. and Inf. Sci. 16, Springer Verlag (1979).
J.H. Van Schuppen, “A study of estimation and filtering by the Bayesian method”, SSM-Report 7607, Washington University, St. Louis (1976).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 D. Reidel Publishing Company
About this chapter
Cite this chapter
Di Masi, G.B., Runggaldier, W.J., Barozzi, B. (1983). Generalized Finite-Dimensional Filters in Discrete Time. In: Bucy, R.S., Moura, J.M.F. (eds) Nonlinear Stochastic Problems. NATO ASI Series, vol 104. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7142-4_21
Download citation
DOI: https://doi.org/10.1007/978-94-009-7142-4_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7144-8
Online ISBN: 978-94-009-7142-4
eBook Packages: Springer Book Archive