Geodesic
Comparison of Minimax Filter and Kalman Filter Estimations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 182-186

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The article describes using Kalman filter and minimax filter for estimation of dynamic system state vector under condition of uncertainty. Kalman filter is used when disturbances and noises affecting the system are considered to be stochastic variables with a certain distribution curves. Minimax filter is used when statistic information about disturbances and noises is absent but sets of their possible values are available. The comparison of set and point estimations received by using this filters for process with different disturbances and noises is performed. The article also describes the idea of improvement of information sets received by minimax filter by confidence ellipsoid received by Kalman filter. The example of effective joint using of minimax filter and Kalman filter is given in the article.
Keywords: guaranteed estimation, Kalman filter, minimax filter. 
@article{VYURU_2012_14_a19,
     author = {E. O. Podivilova and V. I. Shiryaev},
     title = {Comparison of {Minimax} {Filter} and {Kalman} {Filter} {Estimations}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {182--186},
     publisher = {mathdoc},
     number = {14},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2012_14_a19/}
}
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E. O. Podivilova; V. I. Shiryaev. Comparison of Minimax Filter and Kalman Filter Estimations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 14 (2012), pp. 182-186. http://geodesic.mathdoc.fr/item/VYURU_2012_14_a19/