/. and *. Re-*-/-s_dot, as = (s->as) * (ins_impl.corr, RE

/. Mvev, +. Mheh, =. Ev, +. , and *. *. _ins->corr, ME.x = (-_ins->gains.mv) * Ev.x + 0.; _ins->corr.ME.y = (-_ins->gains.mv) * Ev.y + 0.; _ins->corr, ME.z = ((-_ins->gains.mvz) * Ev.z) + ((-_ins->gains.mh) * Eh)

/. Nxex, +. Nheh, =. Ex, +. , and *. *. _ins->corr, NE.x = (-_ins->gains.nx) * Ex.x + 0.; _ins->corr.NE.y = (-_ins->gains.nx) * Ex.y + 0.; _ins->corr, NE.z = ((-_ins->gains.nxz) * Ex.z) + ((-_ins->gains.nh) * Eh)

/. Sheh and *. *. _ins->corr, SE = (_ins->gains.sh) * Eh

N. Aghannan and P. Et-rouchon, 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

M. J. Aldon, Capteurs et Méthodes pour la Localisation des Robots Mobiles, 2001.

D. Allan, Statistics of atomic frequency standards, Proceedings of the IEEE, pp.221-230, 1966.
DOI : 10.1109/PROC.1966.4634

D. W. Allan, Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.34, issue.6, pp.647-654, 1987.
DOI : 10.1109/T-UFFC.1987.26997

D. L. Alpach and H. W. Et-sorenson, Nonlinear Bayesian estimation using Gaussian sum approximations, IEEE Transactions on Automatic Control, vol.17, issue.4, pp.439-448, 1972.
DOI : 10.1109/TAC.1972.1100034

B. K. Alpert, Wavelets and Other Bases for Fast Numerical Linear Algebra, Wavelets : A tutorial in theory and applications, 1992.
DOI : 10.1016/B978-0-12-174590-5.50012-5

I. Y. Bar-itzhack, REQUEST - A recursive QUEST algorithm for sequential attitude determination, Journal of Guidance, Control, and Dynamics, vol.19, issue.5, pp.1034-1038, 1996.
DOI : 10.2514/3.21742

M. Barczyk and A. F. Et-lynch, Invariant Observer Design for a Helicopter UAV Aided Inertial Navigation System, IEEE Transactions on Control Systems Technology, vol.21, issue.3, pp.791-806, 2013.
DOI : 10.1109/TCST.2012.2195495

A. Barrau and S. Et-bonnabel, The Invariant Extended Kalman Filter as a Stable Observer, IEEE Transactions on Automatic Control, vol.62, issue.4, pp.1410-1465, 2014.
DOI : 10.1109/TAC.2016.2594085

B. Bell, The Iterated Kalman Smoother as a Gauss???Newton Method, SIAM Journal on Optimization, vol.4, issue.3, pp.626-636, 1994.
DOI : 10.1137/0804035

M. Berger and B. Et-gostiaux, Géométrie Diérentielle, 1972.

G. Besançon, Q. Zhang, and H. Et-hammouri, High-gain observer based state and parameter estimation in nonlinear systems, Proceedings of NOLCOS, IFAC Symposium on Nonlinear Control Systems, p.227, 2004.

D. Bestle and M. Et-zeitz, Canonical form observer design for non-linear time-variable systems, International Journal of Control, vol.27, issue.2, pp.419-431, 1983.
DOI : 10.1080/00207178308933084

J. Bijker and W. Et-steyn, Kalman filter configurations for a low-cost loosely integrated inertial navigation system on an airship, Control Engineering Practice, vol.16, issue.12, pp.1509-1518, 2008.
DOI : 10.1016/j.conengprac.2008.04.011

J. Birk and M. Et-zeitz, Extended Luenberger observer for non-linear multivariable systems, International Journal of Control, vol.27, issue.6, pp.1823-1836, 1988.
DOI : 10.1080/00207177308932395

S. Bonnabel, 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

S. Bonnabel, P. Martin, and P. Et-rouchon, Symmetry-Preserving Observers, IEEE Transactions on Automatic Control, vol.53, issue.11, pp.532514-2526, 2008.
DOI : 10.1109/TAC.2008.2006929
URL : https://hal.archives-ouvertes.fr/hal-00449206

S. Bonnabel, P. Martin, and P. Et-rouchon, 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

S. Bonnabel, P. Martin, and E. Et-salaün, 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

J. V. Breakwell, Estimation with slight non-linearity, 1967.

M. Bronz, J. P. Condomines, and G. Et-hattenberger, Development of an 18 cm micro air vehicle, International Micro Air Vehicle Conference and Filght Competition (IMAV), 2013.
URL : https://hal.archives-ouvertes.fr/hal-00936133

J. P. Condomines, S. Cédric, and G. Et-hattenberger, Nonlinear state estimation using an invariant unscented Kalman filter, AIAA Guidance, Navigation, and Control (GNC) Conference, pp.1-15, 2013.
DOI : 10.2514/6.2013-4869
URL : https://hal.archives-ouvertes.fr/hal-00933568

J. P. Condomines, S. Cédric, and G. Et-hattenberger, Pi-Invariant Unscented Kalman Filter for sensor fusion, 53rd IEEE Conference on Decision and Control, pp.1035-1040, 2014.
DOI : 10.1109/CDC.2014.7039518
URL : https://hal.archives-ouvertes.fr/hal-01109001

J. L. Crassidis and F. L. Et-markley, Unscented Filtering for Spacecraft Attitude Estimation, Journal of Guidance, Control, and Dynamics, vol.26, issue.4, pp.536-542, 2003.
DOI : 10.2514/2.5102

B. Cyganek and J. P. Et-siebert, An Invitation to 3-D Vision Vision Techniques and Algorithms, 2009.

J. E. Darling, S. N. Balakrishnan, and C. Souza, Sigma point modified state observer for nonlinear unscented estimation, AIAA Guidance, Navigation and Control Confe- rence, 2013.

D. Agostino, M. Manzino, A. M. Et-piras, and M. , Performance comparison of dierent mems-based imus, Position Location and Navigation Symposium (PLANS) IEEE, 2013.

D. Laubier and A. , Etalonnage et mise en oeuvre d'une centrale inertielle pour la localisation 6D d'un robot mobile, Thèse de doctorat, Conservatoire National des Arts et Métiers, 2008.

S. Diop, On a dierential algebric approach of control observation problems. archives- ouvertes, 2013.

S. Diop and M. Et-fliess, Nonlinear observability, identifiability, and persistent trajectories, [1991] Proceedings of the 30th IEEE Conference on Decision and Control, pp.714-710, 1991.
DOI : 10.1109/CDC.1991.261405

S. Diop and I. Et-simeonov, On the biomass specific growth rates estimation for anaerobic digestion using dierential algebraic techniques, Bioautomation, vol.13, issue.3, pp.47-56, 2009.

J. A. Farrell, Aided Navigation GPS with High Rate Sensors, 2008.

J. A. Farrell and M. Barth, The Global Positioning System and Inertial Navigation, 1998.

F. Faruqi and K. Et-turner, Extended Kalman filter synthesis for integrated global positioning/inertial navigation systems, Applied Mathematics and Computation, vol.115, issue.2-3, pp.2-3213, 2000.
DOI : 10.1016/S0096-3003(98)10068-1

M. Farza, M. Saad, and L. Et-rossigno, Observer design for a class of MIMO nonlinear systems, Automatica, vol.40, issue.1, pp.135-143, 2004.
DOI : 10.1016/j.automatica.2003.08.008

R. A. Fisher, On the Mathematical Foundations of Theoretical Statics, Philosophical Transactions of the Royal Society-London, 1922.

J. P. Gauthier, H. Hammouri, and S. Et-othman, A simple observer for nonlinear systems applications to bioreactors, IEEE Transactions on Automatic Control, vol.37, issue.6, pp.875-880, 1992.
DOI : 10.1109/9.256352

N. J. Gordon, D. J. Salmond, and A. F. Smith, Novel approach to nonlinear/nongaussian bayesian state estimation, IEEE Proceedings on Radar and Signal Processing, pp.107-113, 1993.

M. S. Grewal, L. R. Weill, and A. P. Et-andrews, Global positiong systems, inertial navigation, and intergration, 2001.

G. Hattenberger, M. Bronz, and M. Et-gorraz, Using the paparazzi uav system for scientific research, IMAV 2014 : International Micro Air Vehicle Conference and Competition, pp.12-15, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01059642

W. T. Higgins, A Comparison of Complementary and Kalman Filtering, IEEE Transactions on Aerospace and Electronic Systems, vol.11, issue.3, pp.321-325, 1975.
DOI : 10.1109/TAES.1975.308081

A. H. Jazwinski, Stochastic processes and Filtering theory, 1970.

S. J. Julier, The spherical simplex unscented transformation, Proceedings of the 2003 American Control Conference, 2003., pp.2430-2434, 2003.
DOI : 10.1109/ACC.2003.1243439

S. J. Julier and J. K. Et-uhlmann, Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), pp.887-891, 2002.
DOI : 10.1109/ACC.2002.1023128

S. J. Julier and J. K. Et-uhlmann, Unscented Filtering and Nonlinear Estimation, Proceedings of the IEEE, pp.401-422, 2004.
DOI : 10.1109/JPROC.2003.823141

S. J. Julier, J. K. Uhlmann, and H. F. Et-durrant-whyte, A new approach for filtering nonlinear systems, Proceedings of 1995 American Control Conference, ACC'95, pp.1628-1632, 1995.
DOI : 10.1109/ACC.1995.529783

S. J. Julier, J. K. Uhlmann, and H. F. Et-durrant-whyte, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Transactions on Automatic Control, vol.45, issue.3, pp.45477-482, 2000.
DOI : 10.1109/9.847726

R. E. Kalman, A new approach to linear filtering, Transactions of the ASME Journal of Basic Engineering, 1960.

R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

N. Kazantzis and C. Et-kravaris, Nonlinear observer design using Lyapunov???s auxiliary theorem, Systems & Control Letters, vol.34, issue.5, pp.241-247, 1998.
DOI : 10.1016/S0167-6911(98)00017-6

H. Keller, Non-linear observer design by transformation into a generalized observer canonical form, International Journal of Control, vol.34, issue.6, pp.1915-1930, 1987.
DOI : 10.1080/00207728408926614

A. Kolmogorov, Grundbegrie der Wahrscheilichkeitrechung, 1922.

S. R. Kou, D. L. Elliott, and T. J. Et-tarn, Exponential observers for nonlinear dynamic systems, Information and Control, vol.29, issue.3, pp.204-216, 1975.
DOI : 10.1016/S0019-9958(75)90382-4

A. J. Krener and A. Et-isidori, Linearization by output injection and nonlinear observers, Systems & Control Letters, vol.3, issue.1, pp.47-52, 1983.
DOI : 10.1016/0167-6911(83)90037-3

C. J. Lagemann and R. Et-mahony, Observer design for invariant systems with homogeneous observations, 2008.

J. P. Laumond, La robotique mobile, 2001.

J. J. Laviola, A comparison of unscented and extended Kalman filtering for estimating quaternion motion, Proceedings of the 2003 American Control Conference, 2003., pp.2190-2195, 2004.
DOI : 10.1109/ACC.2003.1243440

. Lawrence, Modern Inertial Technology : Navigation, Guidance, and Control, 1998.

T. Lefebvre, H. Bruyninckx, and J. Et-de-schutter, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Transactions on Automatic Control, pp.1406-1409, 2002.

E. J. Lefferts, F. L. Markley, and M. D. Shuster, Kalman Filtering for Spacecraft Attitude Estimation, Journal of Guidance, Control, and Dynamics, vol.5, issue.5, pp.417-429, 1982.
DOI : 10.2514/3.56190

J. Levine and R. Et-marino, Nonlinear system immersion, observers and finite-dimensional filters, Systems & Control Letters, vol.7, issue.2, pp.133-142, 1986.
DOI : 10.1016/0167-6911(86)90019-8

H. Lim and J. Et-park, Open-source projets on unmanned aerial vehicles, IEEE Robortics and Automation, vol.19, issue.2, pp.1070-9932, 2012.

D. G. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.596-602, 1971.
DOI : 10.1109/TAC.1971.1099826

Y. Ma, S. Soatto, J. Kosecka, and S. Sastry, An Invitation to 3-D Vision : From Images to Geometric Models, 2004.
DOI : 10.1007/978-0-387-21779-6

R. Mahony, T. Hamel, and J. Et-pflimlin, 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

D. Maithripala, W. P. Dayawansa, and J. M. Et-berg, Intrinsic Observer-Based Stabilization for Simple Mechanical Systems on Lie Groups, SIAM Journal on Control and Optimization, vol.44, issue.5, pp.1691-1711, 2005.
DOI : 10.1137/S0363012904439891

A. Manecy, S. Viollet, and N. Et-marchnad, Bio-inspired hovering control for an aerial robot equipped with a decoupled eye and a rate gyro, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.1110-1117, 2012.
DOI : 10.1109/IROS.2012.6385853
URL : https://hal.archives-ouvertes.fr/hal-00714332

F. L. Markley, N. Berman, and U. Et-shaked, Hinfty-type filter for spacecraft attitude estimation, AAS/GSFC International Symposium on Space Flight Dynamics, 1993.

P. Martin and E. Et-salaün, Invariant observers for attitude and heading estimation from low-cost inertial and magnetic sensors, 2007 46th IEEE Conference on Decision and Control, pp.1039-1045, 2007.
DOI : 10.1109/CDC.2007.4435006
URL : https://hal.archives-ouvertes.fr/hal-00533306

P. Martin and E. Et-salaün, An Invariant Observer for Earth-Velocity-Aided Attitude Heading Reference Systems, IFAC Proceedings Volumes, vol.41, issue.2, 2008.
DOI : 10.3182/20080706-5-KR-1001.01668
URL : https://hal.archives-ouvertes.fr/hal-00495953

P. Martin and E. Et-salaün, Design and implementation of a low-cost observer-based attitude and heading reference system, Control Engineering Practice, vol.18, issue.7, pp.712-722, 2010.
DOI : 10.1016/j.conengprac.2010.01.012
URL : https://hal.archives-ouvertes.fr/hal-00494325

R. K. Mehra, On the identification of variances and adaptive Kalman filtering, IEEE Transactions on Automatic Control, vol.15, issue.2, pp.175-184, 1970.
DOI : 10.1109/TAC.1970.1099422

R. L. Moose, An adaptive state estimation solution to the maneuvering target problem, IEEE Transactions on Automatic Control, vol.20, issue.3, pp.359-362, 1975.
DOI : 10.1109/TAC.1975.1100961

R. L. Moose, M. K. Sistanizadeh, and G. Et-skagfjord, Adaptive State Estimation for a System With Unknown Input and Measurement Bias, IEEE Journal of Oceanic Engineering, vol.12, issue.1, 1987.
DOI : 10.1109/JOE.1987.1145235

J. W. Murrell, Precision attitude determination for multimission spacecraft, Guidance and Control Conference, 1978.
DOI : 10.2514/6.1978-1248

K. M. Nagpal and P. P. Et-khargonekar, Filtering and smoothing in an hinfty setting, IEEE Transactions on Automatic Control, issue.2, pp.36152-166, 1991.

M. Nwogugu, Decision-making, risk and corporate governance: A critique of methodological issues in bankruptcy/recovery prediction models, Applied Mathematics and Computation, vol.185, issue.1, pp.178-196, 2007.
DOI : 10.1016/j.amc.2005.11.178

P. J. Olver, Classical Invariant Theory, 2003.
DOI : 10.1017/CBO9780511623660

P. J. Olver, Equivalence, Invariance and symmetry, 2008.

J. Picard, Eciency of the extended kalman filter for nonlinear systems with small noise, Applied Mathematics ans Computation, vol.51, issue.3, pp.359-410, 1991.

M. L. Psiaki, Attitude-Determination Filtering via Extended Quaternion Estimation, Journal of Guidance, Control, and Dynamics, vol.23, issue.2, pp.206-214, 2000.
DOI : 10.2514/2.4540

T. Raïssi, G. Videau, and . Zolghadri, Interval observer design for consistency checks of nonlinear continuous-time systems, Automatica, vol.46, issue.3, pp.518-527, 2010.
DOI : 10.1016/j.automatica.2009.12.005

R. W. Randal, Estimation for micro air vehicles, Studies in Computational Intelligence, vol.70, pp.173-199, 2007.

W. Respondek and A. J. Et-krener, Nonlinear observer with linearizable error dynamics, SIAM Journal on Control and Optimization, vol.23, issue.2, pp.197-216, 1985.

F. Ruffier and N. Et-franceschini, Visually guided micro-aerial vehicle: automatic take off, terrain following, landing and wind reaction, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004, pp.2339-2346, 2004.
DOI : 10.1109/ROBOT.2004.1307411

F. Ruffier, J. Serres, G. Portelli, and N. Et-franceschini, Boucles visuo-motrices biomimétiques pour le pilotage automatique de micro-aéronefs, Proceedings of the 7ème Journées Nationales de la Recherche en Robotique, 2009.

S. Sarkka, On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems, IEEE Transactions on Automatic Control, vol.52, issue.9, pp.1631-1641, 2007.
DOI : 10.1109/TAC.2007.904453

J. Sedlak and D. Chu, Kalman filter estimation of attitude and gyro bias with the quest observation model, AAS/GSFC International Symposium on Space Flight Dynamics, 1993.

M. D. Shuster, A simple kalman filter and smoother for spacecraft attitude, Journal of the Astronautical Sciences, vol.38, issue.3, pp.377-393, 1989.

M. D. Shuster and S. D. Et-oh, Three-axis attitude determination from vector observations, Journal of Guidance, Control, and Dynamics, vol.4, issue.1, 1981.
DOI : 10.2514/3.19717

R. H. Smith, An hinfty-type filter for gps-based attitude estimation, AAS/AIAA Space Flight, Mechanics Conference, 1995.

F. Steimann and K. P. Et-adlassnig, Fuzzy medical diagnosis, 2001.
DOI : 10.1887/0750304278/b438c104

F. E. Thau, Observing the state of non-linear dynamic systems???, International Journal of Control, vol.82, issue.3, pp.471-479, 1973.
DOI : 10.1109/TAC.1966.1098323

D. H. Titterton and J. L. Et-weston, Strapdown Inertial Navigation Technology. The institution of Electrical Engineers, 2004.

E. Trucco and A. Verri, Introductory Technique for 3-D Computer Vision, 1998.

J. Vasconcelos, C. Silvestre, and P. Et-oliveira, A nonlinear observer for rigid body attitude estimation using vector observations. 17th World Congres. The International of Automatic Control, pp.8599-8604, 2008.

A. Viterbi, Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Transations on information Theory, pp.260-269, 1967.

E. Wan and R. Van-der-merwe, The unscented Kalman filter for nonlinear estimation, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), pp.153-158, 2000.
DOI : 10.1109/ASSPCC.2000.882463

E. Wan and R. Van-der-merwe, The Unscented Kalman Filter, Kalman Filtering and NeuralNetworks, 2001.

L. Wenger and D. G. Et-egziabher, Systems concepts and performances analysis of multisensor navigation system for uav applications, 2nd AIAA Unmanned Unlimited Systems Conference, 2003.

J. Xu, S. Wang, G. Dimirovski, and Y. Et-jing, Stochastic stability of the continuous-time unscented kalman filter, IEEE Conference on Decision and Control, pp.5110-5115, 2008.

L. A. Zadeh, Fuzzy sets, Information and Control, vol.8, issue.3, pp.338-353, 1965.
DOI : 10.1016/S0019-9958(65)90241-X

M. Zeitz, Comments on comparative study of nonlinear state observation techniques, International journal of Control, vol.46, issue.5, pp.1823-1836, 1988.