×

zbMATH — the first resource for mathematics

Recursive Bayesian estimation under memory limitation. (English) Zbl 0721.62031
A new approach is considered to the approximation of recursive Bayes estimation schemes for models without linearity and normality. The posterior probability density of the unknown parameter is evaluated by probabilistic tools because this density is interpreted as uncertain. From a philosophical point of view such interpretation is questionable.

MSC:
62F15 Bayesian inference
62B10 Statistical aspects of information-theoretic topics
62E17 Approximations to statistical distributions (nonasymptotic)
PDF BibTeX XML Cite
Full Text: EuDML Link
References:
[1] V. Peterka: Bayesian approach to system identification. Trends and Progress in System Identification (P. Eykhoff, Pergamon Press, Oxford 1981. · Zbl 0451.93059
[2] A. H. Jazwinski: Stochastic Processes and Filtering Theory. Academic Press, New York 1970. · Zbl 0203.50101
[3] H. W. Sorenson, A. R. Stubberud: Non-linear filtering by approximation of the a poste- riori density. Internat. J. Control 8 (1968), 33-51. · Zbl 0176.08302
[4] K. Srinivasan: State estimation by orthogonal expansion of probability distributions. IEEE Trans. Automat. Control AC-15 (1970), 3-10.
[5] R. S. Bucy, K. D. Senne: Digital synthesis of non-linear filters. Automatica 7 (1971), 287-298. · Zbl 0269.93070
[6] H. W. Sorenson, D. L. Alspach: Recursive Bayesian estimation using Gaussian sums. Automatica 7 (1971), 465-479. · Zbl 0219.93020
[7] D. L. Alspach: Gaussian sum approximations in nonlinear filtering and control. Esti- mation Theory (D. G. Lainiotis, American Elsevier, New York 1974. · Zbl 0291.93053
[8] J. L. Center: Practical nonlinear filtering of discrete observations by generalized least- squares approximation of the conditional probability distribution. Proc. of 2nd Symp. on Nonlinear Estimation, San Diego 1971. · Zbl 0314.93031
[9] R. J. P. de Figueiredo, J. G. Jan: Spline filters. Proc. of 2nd Symp. on Nonlinear Estimation, San Diego 1971. · Zbl 0314.93037
[10] D. G. Lainiotis, J. G. Deshpande: Parameter estimation using splines. Estimation Theory (D. G. Lainiotis, American Elsevier, New York 1974. · Zbl 0309.62072
[11] H. W. Sorenson: On the development of practical nonlinear filters. Estimation Theory (D. G. Lainiotis, American Elsevier, New York 1974. · Zbl 0291.93052
[12] A. H. Wang, R. L. Klein: Implementation of nonlinear estimators using monospline. Proc. of 13th IEEE Conf. on Decision and Control, 1976.
[13] D. V. Lindley: Approximate Bayesian methods. Bayesian Statistics (J. M. Bernardo. M. H. DeGroot, D. V, Lindley and A. F. M. Smith, University Press, Valencia 1980. · Zbl 0458.62002
[14] O. L. R. Jacobs: Recursive estimation for non-linear Wiener systems by on-line implementation of Bayes’ rule. Trans. Inst. M. C. 7 (1985), 245-250.
[15] M. Karny, K. M. Hangos: Approximation of the Bayes rule. Proc. of 7th IFAC/ IFORS Symp. on Identification and System Parameter Estimation, York 1985.
[16] A. R. Stubberud, G. H. Xia: A fixed complexity nonlinear estimation technique. Proc. of 25th Conf. on Decision and Control, Athens 1986.
[17] M. Karny, K. M. Hangos: One-sided approximation of Bayes rule: theoretical background. Proc. of 10th IFAC Congress, Munich 19S7.
[18] S. C. Kramer, H. W. Sorenson: Bayesian parameter estimation. Proc. of 1987 Amer. Control. Conf., Minneapolis 1987. · Zbl 0633.93066
[19] J. M. Bernardo: Approximations in statistics from a decision theoretical viewpoint. Probability and Bayesian Statistics (R. Viertl, Plenum Press, New York 1987.
[20] B. de Finetti: Theory of Probability: A Critical Introductory Treatment. Wiley, New York 1970 (Vol. 1), Chichester 1972
[21] I. J. Good: The Estimation of Probabilities: An Essay on Modern Bayesian Methods. MIT Press, Cambridge 1965. · Zbl 0168.39603
[22] I. J. Good: Some history of the hierarchical Bayesian methodology. Bayesian Statistics (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, University Press, Valencia 1980. · Zbl 0467.62002
[23] N. N. Chentsov: Statistical Decision Rules and Optimal Inference (in Russian). Nauka, Moscow 1972,
[24] R. Larsen: Functional Analysis: An Introduction. Dekker, Ner York 1973. · Zbl 0261.46001
[25] R. Kulhavý: A Bazes-closed approximation of recursive nonlinear estimation. Internat. J. Adaptive Control and Signal Processing
[26] L. J. Savage: The Foundations of Statistics. Wiley, New York 1954. · Zbl 0055.12604
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.