Second-Order-Optimal Minimum-Energy Filters on Lie Groups

• Tipo: Artigo em Revista Científica Internacional
• Data: 2016

Autores

Saccon, A (Autor) Outra; Trumpf, J (Autor) Outra; Mahony, R (Autor) Outra; Aguiar, AP (Autor) FEUP

Revista

Título: IEEE Transactions on Automatic Control

Vol. 61

Páginas: 2906-2919

ISSN: 0018-9286

Editora: IEEE

Indexação

ISI Web of Knowledge - 10 Citações

Scopus - 15 Citações

Outras Informações

ID Authenticus: P-00M-57F

DOI: 10.1109/tac.2015.2506662

Abstract (EN): Systems on Lie groups naturally appear as models for physical systems with full symmetry. We consider the state estimation problem for such systems where both input and output measurements are corrupted by unknown disturbances. We provide an explicit formula for the second-order-optimal nonlinear filter on a general Lie group where optimality is with respect to a deterministic cost measuring the cumulative energy in the unknown system disturbances (minimum-energy filtering). The resulting filter depends on the choice of affine connection which encodes the nonlinear geometry of the state space. As an example, we look at attitude estimation, where we are given a second order mechanical system on the tangent bundle of the special orthogonal group SO(3), namely the rigid body kinematics together with the Euler equation. When we choose the symmetric Cartan-Schouten (0)-connection, the resulting filter has the familiar form of a gradient observer combined with a perturbed matrix Riccati differential equation that updates the filter gain. This example demonstrates how to construct a matrix representation of the abstract general filter formula.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 14