期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 59, 期 10, 页码 2772-2777出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2014.2310331
关键词
Exponential stability; linear lie groups; state estimation
资金
- Natural Sciences and Engineering Research Council of Canada (NSERC)
This technical note proposes local exponential observers for systems on linear Lie groups. We study two classes of systems. In the first class, the full state of the system evolves on a linear Lie group and is available for measurement. In the second class, only part of the system's state evolves on a linear Lie group and this portion of the state is available for measurement. In each case, we propose two different observer designs. We show that, depending on the observer chosen, local exponential stability of one of the two observation error dynamics, left- or right-invariant error dynamics, is obtained. For the first class of systems these results are developed by showing that the estimation error dynamics are differentially equivalent to a stable linear differential equation on a vector space. For the second class of system, the estimation error dynamics are almost linear. We illustrate these observer designs on an attitude estimation problem.
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