Optimization algorithms on matrix manifolds, 2009. ,
DOI : 10.1515/9781400830244
Riemannian Lp center of mass: existence, uniqueness, and convexity, Proceedings of the, pp.655-673, 2011. ,
On invariant asymptotic observers, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., pp.1479-1484, 2002. ,
DOI : 10.1109/CDC.2002.1184728
On invariant asymptotic observers, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., pp.1479-1484, 2002. ,
DOI : 10.1109/CDC.2002.1184728
An intrinsic observer for a class of lagrangian systems, IEEE Transactions on Automatic Control, vol.48, issue.6, pp.936-945, 2003. ,
DOI : 10.1109/TAC.2003.812778
Axioms and fundamental equations of image processing. Archive for rational mechanics and analysis, pp.199-257, 1993. ,
Geometric means. Linear algebra and its applications, pp.305-334, 2004. ,
Information-geometric optimization algorithms: a unifying picture via invariance principles. arXiv preprint arXiv:1106, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00601503
Mathematical Methods of Classical Mechanics, 1976. ,
Log-euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic resonance in medicine, pp.411-421, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00502678
Symmetry-based observers for some water-tank problems Automatic Control Dissipation in many-body systems: a geometric approach based on information theory, IEEE Transactions on, vol.5613, issue.131, pp.1046-10581, 1986. ,
Intrinsic filtering on Lie groups with discrete-time observations, 2013. ,
Intrinsic filtering on SO(3) with discrete-time observations, 52nd IEEE Conference on Decision and Control, 2013. ,
DOI : 10.1109/CDC.2013.6760380
A note on the intrisic Cramer-Rao bound, Geometric Science of Information, 2013. ,
MR diffusion tensor spectroscopy and imaging, Biophysical Journal, vol.66, issue.1, pp.259-267, 1994. ,
DOI : 10.1016/S0006-3495(94)80775-1
URL : https://hal.archives-ouvertes.fr/hal-00349721
Statistical decision theory and Bayesian analysis, 1985. ,
DOI : 10.1007/978-1-4757-4286-2
Monotonicity of the matrix geometric mean, Mathematische Annalen, vol.8, issue.4, pp.1453-1467, 2012. ,
DOI : 10.1007/s00208-011-0721-9
Left-invariant extended Kalman filter and attitude estimation, 2007 46th IEEE Conference on Decision and Control, pp.1027-1032, 2007. ,
DOI : 10.1109/CDC.2007.4434662
Observateurs asymptotiques invariants: théorie et exemples, 2007. ,
A simple intrinsic reduced-observer for geodesic flow. Automatic Control, IEEE Transactions on, vol.55, issue.9, pp.2186-2191, 2010. ,
Symmetries in Observer Design: Review of Some Recent Results and Applications to EKF-based SLAM, Robot Motion and Control 2011, pp.3-15 ,
DOI : 10.1007/978-1-4471-2343-9_1
Stochastic Gradient Descent on Riemannian Manifolds, IEEE Transactions on Automatic Control, vol.58, issue.9, p.2013 ,
DOI : 10.1109/TAC.2013.2254619
Contraction and observer design on cones, IEEE Conference on Decision and Control and European Control Conference, pp.7147-7151, 2011. ,
DOI : 10.1109/CDC.2011.6161268
Rank-preserving geometric means of positive semi-definite matrices, Linear Algebra and its Applications, vol.438, issue.8, pp.3202-3216, 2013. ,
DOI : 10.1016/j.laa.2012.12.009
A simple nonlinear filter for low-cost ground vehicle localization system, IEEE Conference on Decision and Control and European Control Conference, pp.3270-3275, 2011. ,
DOI : 10.1109/CDC.2011.6161262
Symmetry-preserving observers. Automatic Control, IEEE Transactions on, vol.53, issue.11, pp.2514-2526, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00449206
Non-Linear Symmetry-Preserving Observers on Lie Groups, IEEE Transactions on Automatic Control, vol.54, issue.7, pp.1709-1713, 2009. ,
DOI : 10.1109/TAC.2009.2020646
A Separation Principle on Lie Groups, 18th IFAC world congress 2011, pp.8004-8009, 2011. ,
DOI : 10.3182/20110828-6-IT-1002.03353
URL : https://hal.archives-ouvertes.fr/hal-00639006
Invariant Extended Kalman Filter: theory and application to a velocity-aided attitude estimation problem, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp.1297-1304, 2009. ,
DOI : 10.1109/CDC.2009.5400372
URL : https://hal.archives-ouvertes.fr/hal-00494342
Observer-based Hamiltonian identification for quantum systems, Automatica, vol.45, issue.5, pp.1144-1155, 2009. ,
DOI : 10.1016/j.automatica.2008.12.007
URL : https://hal.archives-ouvertes.fr/hal-00447800
Design and prototyping of a low-cost vehicle localization system with guaranteed convergence properties, Control Engineering Practice, vol.19, issue.6, pp.591-601, 2011. ,
DOI : 10.1016/j.conengprac.2011.02.003
Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank, SIAM Journal on Matrix Analysis and Applications, vol.31, issue.3, p.31, 2009. ,
DOI : 10.1137/080731347
The Geometry of Low-Rank Kalman Filters, Arxiv preprint, 2012. ,
DOI : 10.1007/978-3-642-30232-9_3
The Geometry of Low-Rank Kalman Filters, Matrix Information Geometry, pp.53-68, 2013. ,
DOI : 10.1007/978-3-642-30232-9_3
Online Algorithms and Stochastic Approximations. Online Learning and Neural Networks, 1998. ,
The trade-offs of large scale learning, Advances in Neural Information Processing Systems, 2008. ,
Kalman Filtering with Random Coefficients and Contractions, SIAM Journal on Control and Optimization, vol.31, issue.4, pp.942-959, 1993. ,
DOI : 10.1137/0331041
Convex optimization [41] P. Brasseur and J. Verron. The seek filter method for data assimilation in oceanography: a synthesis, Ocean Dynamics, vol.56, pp.5-6650, 2004. ,
Hilbert's metric and positive contraction mappings in a banacb space. Archive for Rational Mechanics and Analysis, 1973. ,
Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements, IEEE Transactions on Information Theory, vol.57, issue.4, pp.2342-2359, 2009. ,
DOI : 10.1109/TIT.2011.2111771
La méthode du repère mobile, la théorie des groupes continus, et les espaces généralisés, 1935. ,
An anisotropy preserving metric for dti processing, Journal of Computer Vision, 2012. ,
Simplification of the kalman filter for meteorological data assimilation, Quarterly Journal of the Royal Meteorological Society, vol.117, issue.498, pp.365-384, 1991. ,
Contraction and observer design on cones, Decision and Control and European Control Conference (CDC-ECC), 2013 52nd IEEE Conference on, 2013. ,
Analysis on symmetric cones, 1994. ,
Riemannian geometry for the statistical analysis of diffusion tensor data, Signal Processing, vol.87, issue.2, 2007. ,
DOI : 10.1016/j.sigpro.2005.12.018
Optimal cooperative motion planning for vehicles at intersections, IEEE Intelligent Vehicles Symposium, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00877765
Priority-based coordination of robots, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00828976
Accurate 3D maps from depth images and motion sensors via nonlinear Kalman filtering, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.5291-5297, 2012. ,
DOI : 10.1109/IROS.2012.6385597
URL : https://hal.archives-ouvertes.fr/hal-01259335
No dice: a deterministic approach to the cartan centroid, J. Ramanujan Math. Soc, vol.27, issue.4, pp.509-521, 2011. ,
Tracking Nonlinear Solutions with Simulated Altimetric Data in a Shallow-Water Model*, Journal of Physical Oceanography, vol.27, issue.1, pp.72-95, 1997. ,
DOI : 10.1175/1520-0485(1997)027<0072:TNSWSA>2.0.CO;2
New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-108, 1961. ,
DOI : 10.1115/1.3658902
Gradient-Like Observers for Invariant Dynamics on a Lie Group, IEEE Transactions on Automatic Control, vol.55, issue.2, pp.367-377, 2010. ,
DOI : 10.1109/TAC.2009.2034937
Sur la théorie du mouvement brownien, CR Acad. Sci. Paris, vol.146, pp.530-533, 1908. ,
Monotonic properties of the least squares mean, Mathematische Annalen, vol.37, issue.2, pp.267-279, 2011. ,
DOI : 10.1007/s00208-010-0603-6
Diffusion tensor imaging: Concepts and applications, Journal of Magnetic Resonance Imaging, vol.44, issue.4, pp.534-546, 2001. ,
DOI : 10.1002/jmri.1076
URL : https://hal.archives-ouvertes.fr/hal-00349820
Low rank approximation for the numerical simulation of high dimensional lindblad and riccati equations, 2012. ,
Low-rank numerical approximations for high-dimensional Lindblad equations, Physical Review A, vol.87, issue.2, p.22125, 2013. ,
DOI : 10.1103/PhysRevA.87.022125
URL : https://hal.archives-ouvertes.fr/hal-00941530
Lévy processes in Lie groups, 2004. ,
DOI : 10.1017/cbo9780511546624
An introduction to observers, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.596-602, 1971. ,
DOI : 10.1109/TAC.1971.1099826
Nonlinear Complementary Filters on the Special Orthogonal Group, IEEE Transactions on Automatic Control, vol.53, issue.5, pp.1203-1218, 2008. ,
DOI : 10.1109/TAC.2008.923738
URL : https://hal.archives-ouvertes.fr/hal-00488376
Linear regression under fixed-rank constraints: a riemannian approach, Proc. of the 28th International Conference on Machine Learning (ICML), 2011. ,
Regression on fixed-rank positive semidefinite matrices: a riemannian approach, Journal of Machine Learning Reasearch (JMLR), vol.12, pp.593-625, 2011. ,
Fixed-rank matrix factorizations and riemannian low-rank optimization. arXiv preprint, accepted in Computational Statistics On the riemannian geometry defined for selfconcordant barriers and interior point methods, Found. Comput. Math, vol.2, pp.333-361, 2002. ,
DOI : 10.1007/s00180-013-0464-z
URL : http://arxiv.org/abs/1209.0430
Subspace methods of pattern recognition, 1983. ,
Principal components, minor components, and linear neural networks, Neural Networks, vol.5, issue.6, 1992. ,
DOI : 10.1016/S0893-6080(05)80089-9
Moving frames, Journal of Symbolic Computation, vol.36, issue.3-4, pp.501-512, 2003. ,
DOI : 10.1016/S0747-7171(03)00092-0
Filtrage non linéaire etéquationsetéquations aux dérivées partielles stochastiques associées, 1991. ,
DOI : 10.1007/bfb0085168
A Riemannian Framework for Tensor Computing, International Journal of Computer Vision, vol.6, issue.2, pp.41-66, 2006. ,
DOI : 10.1007/s11263-005-3222-z
URL : https://hal.archives-ouvertes.fr/inria-00070743
??tude math??matique du mouvement brownien de rotation, Annales scientifiques de l'??cole normale sup??rieure, vol.45, 1928. ,
DOI : 10.24033/asens.782
URL : http://archive.numdam.org/article/ASENS_1928_3_45__1_0.pdf
A singular evolutive extended Kalman filter for data assimilation in oceanography, Journal of Marine Systems, vol.16, issue.3-4, pp.323-340, 1998. ,
DOI : 10.1016/S0924-7963(97)00109-7
THE ESTIMATION OF THE LOCATION AND SCALE PARAMETERS OF A CONTINUOUS POPULATION OF ANY GIVEN FORM, Biometrika, vol.30, issue.3-4, pp.391-421, 1939. ,
DOI : 10.1093/biomet/30.3-4.391
Acceleration of Stochastic Approximation by Averaging, SIAM Journal on Control and Optimization, vol.30, issue.4, pp.838-855, 1992. ,
DOI : 10.1137/0330046
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization, SIAM Review, vol.52, issue.3, pp.471-501, 2010. ,
DOI : 10.1137/070697835
Coordinated motion design on lie groups. Automatic Control, IEEE Transactions on, vol.55, issue.5, pp.1047-1058, 2010. ,
DOI : 10.1109/tac.2010.2042003
URL : http://arxiv.org/abs/0807.4416
Consensus Optimization on Manifolds, SIAM Journal on Control and Optimization, vol.48, issue.1, pp.56-76, 2009. ,
DOI : 10.1137/060673400
URL : http://arxiv.org/abs/0811.4275
Géomètrie des matrices semi-définies positives de rang fixé: un peu de théorie et beaucoup d'applications, CIFA, 2010. ,
Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds, IEEE Transactions on Signal Processing, vol.53, issue.5, pp.1610-1630, 2005. ,
DOI : 10.1109/TSP.2005.845428
On the gap between deterministic and stochastic ordinary differential equations. The Annals of Probability, pp.19-41, 1978. ,
Probabilistic robotics, Communications of the ACM, vol.45, issue.3, 2006. ,
DOI : 10.1145/504729.504754
Landmark based nonlinear observer for rigid body attitude and position estimation, 2007 46th IEEE Conference on Decision and Control, pp.1033-1038, 2007. ,
DOI : 10.1109/CDC.2007.4434417
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.456.6756
Global analysis of Oja's flow for neural networks, IEEE Transactions on Neural Networks, vol.5, issue.5, pp.674-683, 1994. ,
DOI : 10.1109/72.317720
On the Convergence of Ordinary Integrals to Stochastic Integrals, The Annals of Mathematical Statistics, vol.36, issue.5, pp.1560-1564, 1965. ,
DOI : 10.1214/aoms/1177699916