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

Authors: S. Bonnabel, Ph. Martin, P. Rouchon , 2008 IFAC World Congress, July 2008, Seoul, Korea, pp. 8594-8598

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.

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BibTeX:

@Proceedings{,

author = {S. Bonnabel, Ph. Martin, P. Rouchon},

editor = {},

title = {Non-linear observer on Lie Groups for left-invariant dynamics with right-equivariant output},

booktitle = {2008 IFAC World Congress},

volume = {},

publisher = {},

address = {Seoul},

pages = {8594-8598},

year = {2008},

abstract = {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.},

keywords = {Lie group, symmetries, invariance, nonlinear asymptotic observers, inertial navigation}}

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.

Download PDF

BibTeX:

@Proceedings{,

author = {S. Bonnabel, Ph. Martin, P. Rouchon},

editor = {},

title = {Non-linear observer on Lie Groups for left-invariant dynamics with right-equivariant output},

booktitle = {2008 IFAC World Congress},

volume = {},

publisher = {},

address = {Seoul},

pages = {8594-8598},

year = {2008},

abstract = {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.},

keywords = {Lie group, symmetries, invariance, nonlinear asymptotic observers, inertial navigation}}