The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Nonlinear Bayesian estimation using Gaussian sum approximations
Abstract
Knowledge of the probability density function of the state conditioned on all available measurement data provides the most complete possible description of the state, and from this density any of the common types of estimates (e.g., minimum variance or maximum a posteriori) can be determined. Except in the linear Gaussian case, it is extremely difficult to determine this density function. In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem. In particular, it is noted that a weighted sum of Gaussian probability density functions can be used to approximate arbitrarily closely another density function. This representation provides the basis for procedure that is developed and discussed.
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Citations
Cites
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Kalman, R. E. (1960) · Journal of Basic Engineering · doi:10.1115/1.3662552 · Cited by 31,751
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Recursive bayesian estimation using gaussian sums
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Self-citationOptimization of stochastic systems
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Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurements
Athans, M., Wishner, R., & Bertolini, A. (1968) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1968.1098986 · Cited by 395
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Self-citationJazwinski, A. H. (1969) · Automatica · doi:10.1016/0005-1098(69)90109-5 · Cited by 198
Introduction to sequential smoothing and prediction
Kashyap, R. (1971) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1971.1099663 · Cited by 167
Recursive fading memory filtering
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Cited by
Arasaratnam, I., & Haykin, S. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2019800 · Cited by 3,380
Fuzzy logic systems for engineering: a tutorial
Mendel, J. M. (1995) · Proceedings of the IEEE · doi:10.1109/5.364485 · Cited by 2,110
The Gaussian Mixture Probability Hypothesis Density Filter
Vo, B.-N., & Ma, W.-K. (2006) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2006.881190 · Cited by 1,919
Gaussian filters for nonlinear filtering problems
Ito, K., & Xiong, K. (2000) · IEEE Transactions on Automatic Control · doi:10.1109/9.855552 · Cited by 1,498
Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models
van der Merwe, R. (2004) · doi:10.6083/m4z60kz5 · Cited by 1,017
Metadata
- Authors
- Alspach, D., & Sorenson, H.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1972-08
- Volume
- 17
- Issue
- 4
- Pages
- 439-448
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2099867508
- Cited by
- 1,239
- References
- 12
- FWCI
- 5.83
- Type
- journal article
- Language
- en
- Open access
- closed
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