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Symmetry-Preserving Observers

Abstract : This paper presents the theory of invariant observers, i.e, symmetry-preserving observers. We consider an observer to consist of a copy of the system and a correction term, and we propose a constructive method (based on the Cartan moving-frame method) to find all the symmetry-preserving correction terms. The construction relies on an invariant frame (a classical notion) and on an invariant output-error, a less standard notion precisely defined here. Using the theory we build three non-linear observers for three examples of engineering interest: a non-holonomic car, a chemical reactor, and an inertial navigation system. For each example, the design is based on physical symmetries and the convergence analysis relies on the use of invariant state-errors, a symmetry-preserving way to define the estimation error.
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Silvère Bonnabel, Philippe Martin, Pierre Rouchon. Symmetry-Preserving Observers. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2008, 53 (11), pp.2514-2526. ⟨10.1109/TAC.2008.2006929⟩. ⟨hal-00449206⟩

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