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Boundedness of the Optimal State Estimator Rejecting Unknown Inputs

Qinghua Zhang 1 Bernard Delyon 2 
1 I4S - Statistical Inference for Structural Health Monitoring
Inria Rennes – Bretagne Atlantique , COSYS - Département Composants et Systèmes
Abstract : The Kitanidis filter is a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs or disturbances. Though the optimality of the Kitanidis filter was founded for general time varying systems more than 30 years ago, its boundedness and stability analysis is still limited to time invariant systems, up to the authors' knowledge. In the framework of general time varying systems, this paper establishes upper and lower bounds of the error covariance of the Kitanidis filter, as well as upper bounds of all the auxiliary variables involved in the filter. By preventing data overflow, upper bounds are crucial for all recursive algorithms in real time applications. The upper and lower bounds of the error covariance will also serve as the basis of the Kitanidis filter stability analysis, like in the case of time varying system Kalman filter.
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https://hal.inria.fr/hal-03850433
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Submitted on : Sunday, November 13, 2022 - 4:52:21 PM
Last modification on : Wednesday, November 16, 2022 - 3:57:20 AM

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Qinghua Zhang, Bernard Delyon. Boundedness of the Optimal State Estimator Rejecting Unknown Inputs. IEEE Transactions on Automatic Control, 2022, pp.1-7. ⟨10.1109/TAC.2022.3174447⟩. ⟨hal-03850433⟩

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