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Maximum likelihood estimates of linear dynamic systems
Abstract
This paper considers the problem of estimating the states of linear dynamic systems in the presence of additive Gaussian noise. Difference equations relating the estimates for the problems of filtering and smoothing are derived as well as a similar set of equations relating the covariance of the errors. The derivation is based on the method of maximum likelihood and depends primarily on the simple manipulation of the probability density functions. The solutions are in a form easily mechanized on a digital computer. A numerical example is included to show the advantage of smoothing in reducing the errors in estimation. In the Appendix the results for discrete systems are formally extended to continuous systems.
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Citations
Cited by
(2003) · Cited by 1,680
Approximate non-Gaussian filtering with linear state and observation relations
Masreliez, C. (1975) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1975.1100882 · Cited by 369
Computational multiheterodyne spectroscopy
Burghoff, D., Yang, Y., & Hu, Q. (2016) · Science Advances · doi:10.1126/sciadv.1601227 · Cited by 114
Havlicek, M., Jan, J., Brazdil, M., & Calhoun, V. D. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2010.05.063 · Cited by 106
A spatiotemporal dynamic distributed solution to the MEG inverse problem
Lamus, C., Hämäläinen, M. S., Temereanca, S., Brown, E. N., & Purdon, P. L. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2011.11.020 · Cited by 71
Metadata
- Authors
- RAUCH, H. E., TUNG, F., & STRIEBEL, C. T.
- Venue
- AIAA Journal
- Published
- 1965-08
- Volume
- 3
- Issue
- 8
- Pages
- 1445-1450
- ISSN
- 0001-1452 (ISSN-L)
- 1533-385X
- OpenAlex
- W2094227853
- Cited by
- 1,943
- References
- 0
- FWCI
- 18.53
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Maximum likelihood estimates of linear dynamic systems. https://app.cochat.ai/papers/10.2514/3.3166
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- RAUCH, H. E., TUNG, F., & STRIEBEL, C. T. (1965). Maximum likelihood estimates of linear dynamic systems. AIAA Journal. https://doi.org/10.2514/3.3166
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