Non-linear observer on Lie Groups for left-invariant dynamics with right-equivariant output

Silvère Bonnabel (1) , Philippe Martin (2) , Pierre Rouchon (2)

1 Institut Montefiore - Department of Electrical Engineering and Computer Science
2 CAS - Centre Automatique et Systèmes

We consider a left-invariant dynamics on an arbitrary Lie group. We show that it is possible, when the output map is right-left equivariant, to build non-linear observers such that the error equation is autonomous. The theory is illustrated by an inertial navigation example.

Mots clés: symmetries; invariance; nonlinear asymptotic observers; inertial navigation; Lie group

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Silvère Bonnabel, Philippe Martin, Pierre Rouchon. Non-linear observer on Lie Groups for left-invariant dynamics with right-equivariant output. 2008 IFAC World Congress, Jul 2008, Seoul, South Korea. pp.8594-8598. ⟨hal-00485749⟩