On Invariant Observers

Abstract

A definition of invariant observer and compatible output function is proposed and motivated. For systems admitting a Lie symmetry-group G of dimension less or equal to the state dimension and with a G-compatible output, an explicit procedure based on the moving frame method is proposed to construct such invariant observers. It relies on an invariant frame and a complete set of invariant estimation errors. Two examples of engineering interest are considered: an exothermic chemical reactor and an inertial navigation problem. For both examples we show how invariance and the proposed construction can be a useful guide to design non-linear convergent observers, although the part of the design procedure which achieves asymptotic stability is not systematic and must take into account the specific nonlinearities of the case under study.

Keywords: Observers, symmetries, invariance, moving frame, chemical reactor, inertial navigation.