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Two-stage Kalman estimator with unknown exogenous inputs

Authors
Journal
Automatica
0005-1098
Publisher
Elsevier
Publication Date
Volume
35
Issue
2
Identifiers
DOI: 10.1016/s0005-1098(98)00194-0
Keywords
  • Minimum Variance
  • Kalman Filter
  • Unknown Disturbance
  • Bias Filtering
Disciplines
  • Mathematics

Abstract

Abstract This paper presents a two-stage estimator for bias and state filtering in discrete-time stochastic linear systems affected by unknown inputs or disturbances. We show that the state estimate can be expressed as X k/k= X ̃ k/k+β k/kb k/k where X ̃ k/k is a bias-free state estimate and b k/ k the optimal estimate of constant bias. The proposed two-stage estimator is based on an alternate derivation of the unbiased minimum variance estimator with unknown exogenous inputs developed by Darouach and Zasadzinski (1997, Automatica 33, 717–719).

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