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Estimation and filtering of processes in matrix Lie groups

Abstract : Signals subject to nonlinear constraints are numerous in Physics and Engineering applications. Recent work have pointed the necessity of intrinsic geometrical methods to process such signals. The work presented in this thesis aims at providing new algorithm within this framework. Some problems in wave Physics and motion capture have been formalised and resolved. Signals subject to nonlinear constraints are modelled like processes taking values in matrix Lie groups. The problems considered in this work are filtering and nonparametric estimation problems. In order to propose new solutions, we have proposed new methods based on probability theory and processes dynamics, mainly based on the important property of stability.
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Submitted on : Thursday, January 21, 2010 - 5:29:56 PM
Last modification on : Thursday, November 19, 2020 - 12:59:39 PM
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  • HAL Id : tel-00449473, version 1

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Salem Said. Estimation and filtering of processes in matrix Lie groups. Signal and Image processing. Institut National Polytechnique de Grenoble - INPG, 2009. English. ⟨tel-00449473⟩

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