Brief On combining statistical and set-theoretic estimation

Authors:
Uwe D. Hanebeck;Joachim Horn;Günther Schmidt
Affiliations:
Institute of Automatic Control Engineering, Technische Universität München, D-80290 München, Germany;Siemens AG, Corporate Technology Information and Communications, D-81730 München, Germany;Institute of Automatic Control Engineering, Technische Universität München, D-80290 München, Germany
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Set-theoretic estimation of hybrid system configurations

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

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Abstract

We consider state estimation based on observations which are simultaneously corrupted by a deterministic amplitude-bounded unknown bias and a possibly unbounded random process. This problem is solved by developing a combined set-theoretic and Bayesian recursive estimator. The new estimator provides a continuous transition between both concepts in that it converges to a set-theoretic estimator when the stochastic error vanishes and to a Bayesian estimator when the deterministic error vanishes. In the mixed noise case, the new estimator supplies solution sets defined by bounds that are uncertain in a statistical sense.