The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
New Results in Linear Filtering and Prediction Theory
Abstract
A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this “variance equation” completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.
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Citations
Cites
A New Approach to Linear Filtering and Prediction Problems
Kalman, R. E. (1960) · Journal of Basic Engineering · doi:10.1115/1.3662552 · Cited by 31,751
Self-citationInformation theory and statistical mechanics
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.106.620 · Cited by 12,931
Cited by
Adaptive noise cancelling: Principles and applications
Widrow, B., Glover, J. R., McCool, J. M., Kaunitz, J., Williams, C. S., Hearn, R. H., Zeidler, J. R., Eugene Dong, Jr., & Goodlin, R. C. (1975) · Proceedings of the IEEE · doi:10.1109/proc.1975.10036 · Cited by 3,939
An internal model for sensorimotor integration
Wolpert, D. M., Ghahramani, Z., & Jordan, M. I. (1995) · Science · doi:10.1126/science.7569931 · Cited by 3,553
Atmospheric Modeling, Data Assimilation and Predictability
Kalnay, E. (2002) · doi:10.1017/cbo9780511802270 · Cited by 3,391
Forward Models for Physiological Motor Control
Miall, R. C., & Wolpert, D. M. (1996) · Neural Networks · doi:10.1016/s0893-6080(96)00035-4 · Cited by 2,260
Merging the senses into a robust percept
Ernst, M. O., & Bülthoff, H. H. (2004) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2004.02.002 · Cited by 1,906
Metadata
- Authors
- Kalman, R. E., & Bucy, R. S.
- Venue
- Journal of Basic Engineering
- Publisher
- ASME International
- Published
- 1961-03-01
- Volume
- 83
- Issue
- 1
- Pages
- 95-108
- ISSN
- 0021-9223 (ISSN-L)
- OpenAlex
- W2083402998
- Cited by
- 6,387
- References
- 2
- FWCI
- 11.84
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
