@inproceedings{dfb3408bbaa4400587490038cb5329f7,
title = "Second-order-optimal filters on lie groups",
abstract = "We provide an explicit formula for the secondorder- optimal nonlinear filter for state estimation of systems on general Lie groups with disturbed measurements of inputs and outputs. Optimality is with respect to a deterministic cost measuring the cumulative energy in the unknown system disturbances (minimum-energy filtering). We show that the resulting filter will depend on the choice of affine connection, thus encoding the nonlinear geometry of the state space. For the case of attitude estimation, where we are given a second order (dynamic) mechanical system on the tangent bundle of the special orthogonal group SO(3), and where we choose the symmetric Cartan-Schouten (0)-connection, the resulting filter has the familiar form of a gradient observer combined with a matrix Riccati differential equation that updates the filter gain.",
author = "Alessandro Saccon and Jochen Trumpf and Robert Mahony and Aguiar, {A. Pedro}",
year = "2013",
doi = "10.1109/CDC.2013.6760572",
language = "English",
isbn = "9781467357173",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "4434--4441",
booktitle = "2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013",
address = "United States",
note = "52nd IEEE Conference on Decision and Control, CDC 2013 ; Conference date: 10-12-2013 Through 13-12-2013",
}