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Title: State estimation with partially observed inputs: a unified Kalman filtering approach
Authors: Li, Baibing
Keywords: Bayesian inference
Data aggregation
Input observability
Kalman filters
State space models
Issue Date: 2013
Citation: LI, B., 2013. State estimation with partially observed inputs: a unified Kalman filtering approach. Automatica, 49 (3), pp. 816-820.
Abstract: 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.
Description: 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.2012.12.007
Version: Accepted for publication
DOI: 10.1016/j.automatica.2012.12.007
URI: https://dspace.lboro.ac.uk/2134/12188
Publisher Link: http://dx.doi.org/10.1016/j.automatica.2012.12.007
ISSN: 0005-1098
Appears in Collections:Published Articles (Business School)

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