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State estimation with partially observed inputs: a unified Kalman filtering approach
For linear stochastic time-varying state space models with Gaussian noises, this paper investigates state estimation for the
scenario where the input variables of the state equation are not fully observed but rather the input data is available only at an
aggregate level. Unlike the existing filters for unknown inputs that are based on the approach of minimum-variance unbiased
estimation, this paper does not impose the unbiasedness condition for state estimation; instead it incorporates a Bayesian
approach to derive a modified Kalman filter by pooling the prior knowledge about the state vector at the aggregate level
with the measurements on the output variables at the original level of interest. The estimated state vector is shown to be a
minimum-mean-square-error estimator. The developed filter provides a unified approach to state estimation: it includes the
existing filters obtained under two extreme scenarios as its special cases, i.e., the classical Kalman filter where all the inputs
are observed and the filter for unknown inputs.
History
School
- Business and Economics
Department
- Business
Citation
LI, B., 2013. State estimation with partially observed inputs: a unified Kalman filtering approach. Automatica, 49 (3), pp. 816-820.Version
- AM (Accepted Manuscript)
Publication date
2013Notes
This is the author’s version of a work that was accepted for publication in the journal Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://dx.doi.org/10.1016/j.automatica.2012.12.007ISSN
0005-1098Publisher version
Language
- en