2013/10/09 by Mikhail Koldychev, Christopher Nielsen
Computer Science · Engineering · Mathematics · #Adaptive Control of Nonlinear Systems #Applied mathematics #Artificial intelligence #Computer science #Control (management) #Control theory (sociology) #Exponential stability #Inertial Sensor and Navigation #Lie group #Linear system #Mathematical analysis #Mathematics #Nonlinear system #Observer (physics) #Pure mathematics #Target Tracking and Data Fusion in Sensor Networks #math.OC
paper · pdf · doi:10.1109/tac.2014.2310331
published as IEEE Transactions on Automatic Control, vol.59, no.10, pp.2772-2777, Oct. 2014
arxiv created 2013/10/09 · openalex publication_date 2014/03/06 · arxiv updated 2015/04/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.