Silvere Bonnabel

Professor

Center · CAOR

Keywords

Awards & distinctions

2024 « 2024 George N. Saridis Best Transactions Paper Award » de la revue IEEE Transactions on Intelligent Vehicles.
2022 IMT-Academy of Sciences Young Scientist Award
2021 2021 European Control Award (the “European Control Award,” a prestigious European control award). “2024 George N. Saridis Best Transactions Paper Award” from the journal *IEEE Transactions on Intelligent Vehicles*.
2015 The 2015 Alain Glavieux Award, presented jointly by the SEE and the IEEE.
2015 Winner of the 2015 SAGEM Innovation Awards.
2009 GDR MACS Thesis Award
2009 EEA Club Thesis Award

Team

CAOR

Biography

Silvère Bonnabel is a researcher whose work focuses on state estimation and filter theory for nonlinear dynamic systems, with particular expertise in the development of advanced filtering and smoothing methods. His research focuses in particular on the Invariant Extended Kalman Filter (IEKF), an approach that leverages the properties of Lie groups to improve the robustness and accuracy of estimators in various contexts, such as robotic navigation, vehicle localization, and extended pose estimation. His contributions include theoretical extensions of the IEKF, such as the Iterated IEKF (IterIEKF) and the adaptation of this framework to two-frame systems, as well as practical applications in sensor fusion (IMU, GNSS, LiDAR) and stochastic optimal control. His work also addresses issues related to dimensionality reduction for large covariance matrices, variational optimization for Bayesian inference, and the integration of constraints into nonlinear estimators.

Publication(s)

2025
Iterated Invariant Extended Kalman Filter (IterIEKF) DOI : 10.1109/TAC.2025.3637661
2025
Invariant Extended Kalman Filter for State Estimation of a Robot With an IMU on an Inclined Plane DOI : 10.1109/LCSYS.2025.3620267
2024
Maximum likelihood estimation of the extended Kalman filter's parameters with natural gradient DOI : 10.1109/CDC56724.2024.10886147
2024
Invariant filtering for wheeled vehicle localization with unknown wheel radius and unknown GNSS lever arm DOI : 10.1109/CDC56724.2024.10886559
2024
LOW-RANK PLUS DIAGONAL APPROXIMATIONS FOR RICCATI-LIKE MATRIX DIFFERENTIAL EQUATIONS DOI : 10.1137/23M1587610
2024
Two-Frame Groups with Scalings DOI : 10.1016/j.ifacol.2024.08.300
2024
Invariant Smoothing for Localization: Including the IMU Biases DOI : 10.1109/CDC56724.2024.10886349
2024
Variational Dynamic Programming for Stochastic Optimal Control DOI : 10.1109/CDC56724.2024.10886246
2024
Backpropagation-Based Analytical Derivatives of EKF Covariance for Active Sensing DOI : 10.1109/IROS58592.2024.10801586
2023
Speeding-Up Backpropagation of Gradients Through the Kalman Filter via Closed-Form Expressions DOI : 10.1109/TAC.2023.3297879
2023
Invariant Kalman Filtering with Noise-Free Pseudo-Measurements DOI : 10.1109/CDC49753.2023.10383262
2023
Real-time Classification of Aircrafts Manoeuvers DOI : 10.1007/s11265-022-01823-x
2023
Optimal Active Sensing Control for Two-Frame Systems DOI : 10.1109/CDC49753.2023.10383744
2023
The Geometry of Navigation Problems DOI : 10.1109/TAC.2022.3144328
2023
A Computationally Efficient Global Indicator to Detect Spurious Measurement Drifts in Kalman Filtering DOI : 10.1109/CDC49753.2023.10384039
2023
The limited-memory recursive variational Gaussian approximation (L-RVGA) DOI : 10.1007/s11222-023-10239-x
2023
Variational Gaussian Approximation of the Kushner Optimal Filter DOI : 10.1007/978-3-031-38271-0_39
2022
Variational inference via Wasserstein gradient flows
2022
Associating Uncertainty to Extended Poses for on Lie Group IMU Preintegration With Rotating Earth DOI : 10.1109/TRO.2021.3100156
2022
Invariant Smoothing with low process noise DOI : 10.1109/CDC51059.2022.9993071
2022
The recursive variational Gaussian approximation (R-VGA) DOI : 10.1007/s11222-021-10068-w
2022
The continuous-discrete variational Kalman filter (CD-VKF) DOI : 10.1109/CDC51059.2022.9992993
2021
The α-minimum convex polygon as a relevant tool for isotopic niche statistics DOI : 10.1016/j.ecolind.2021.108048
2021
Factor Graph-Based Smoothing without Matrix Inversion for Highly Precise Localization DOI : 10.1109/TCST.2020.3001387
2021
Nnakf: A Neural Network Adapted Kalman Filter for Target Tracking DOI : 10.1109/ICASSP39728.2021.9414681
2020
A New Approach to 3D ICP Covariance Estimation DOI : 10.1109/LRA.2020.2965391
2020
The Industrial Control of Tower Cranes: An Operator-in-The-Loop Approach [Applications in Control] DOI : 10.1109/MCS.2020.3005256
2020
Denoising IMU Gyroscopes with Deep Learning for Open-Loop Attitude Estimation DOI : 10.1109/LRA.2020.3003256
2020
AI-IMU Dead-Reckoning DOI : 10.1109/TIV.2020.2980758
2020
A Code for Unscented Kalman Filtering on Manifolds (UKF-M) DOI : 10.1109/ICRA40945.2020.9197489
2020
A Mathematical Framework for IMU Error Propagation with Applications to Preintegration DOI : 10.1109/ICRA40945.2020.9197492
2020
Extended Kalman Filtering with Nonlinear Equality Constraints: A Geometric Approach DOI : 10.1109/TAC.2019.2929112
2020
A real-time unscented Kalman filter on manifolds for challenging AUV navigation DOI : 10.1109/IROS45743.2020.9341216
2020
On stability of a class of filters for nonlinear stochastic systems DOI : 10.1137/19M1285974
2019
Learning wheel odometry and imu errors for localization DOI : 10.1109/ICRA.2019.8794237
2019
On the Accuracy Limit of Time-delay Estimation with a Band-limited Signal DOI : 10.1109/ICASSP.2019.8682948
2019
Invariant Extended Kalman Filter Applied to Tracking for Air Traffic Control DOI : 10.1109/RADAR41533.2019.171239
2019
RINS-W: Robust Inertial Navigation System on Wheels DOI : 10.1109/IROS40897.2019.8968593
2019
Linear observed systems on groups DOI : 10.1016/j.sysconle.2019.05.005
2019
A novel nonlinear least-squares approach to highly maneuvering target tracking; [Une nouvelle méthode de moindres carrés non linéaires pour le pistage de cibles hyper-manœuvrantes] DOI : 10.1016/j.crhy.2019.05.019
2019
Exploiting symmetries to design EKFs with consistency properties for navigation and SLAM DOI : 10.1109/JSEN.2018.2882714
2018
Invariant smoothing on Lie Groups DOI : 10.1109/IROS.2018.8594068
2018
Fully adaptive update rate for non-linear trackers DOI : 10.1049/iet-rsn.2018.5252
2018
Unscented Kalman Filter on Lie Groups for Visual Inertial Odometry DOI : 10.1109/IROS.2018.8593627
2018
Maneuver detector for active tracking update rate adaptation DOI : 10.23919/IRS.2018.8447950
2018
Invariant Kalman Filtering for Visual Inertial SLAM DOI : 10.23919/ICIF.2018.8455807
2018
Symmetry reduction for dynamic programming DOI : 10.1016/j.automatica.2018.08.024
2018
Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics DOI : 10.1109/CDC.2018.8619726
2018
Tightly coupled navigation and wind estimation for mini UAVs DOI : 10.2514/6.2018-1843
2018
Invariant Kalman Filtering DOI : 10.1146/annurev-control-060117-105010
2018
Stochastic observers on Lie groups: A tutorial DOI : 10.1109/CDC.2018.8618988
2018
Particle observers for state estimation and adaptation in deterministic systems with random piecewise constant inputs DOI : 10.1109/CDC.2018.8619296
2017
Unscented Kalman filtering on Lie groups DOI : 10.1109/IROS.2017.8206066
2017
Symmetry reduction for dynamic programming and application to MRI DOI : 10.23919/ACC.2017.7963669
2017
Towards realistic covariance estimation of ICP-based Kinect V1 scan matching: The 1D case DOI : 10.23919/ACC.2017.7963703
2017
Tracking the Frenet-Serret frame associated to a highly maneuvering target in 3D DOI : 10.1109/CDC.2017.8263937
2017
Kalman filtering with a class of geometric state equality constraints DOI : 10.1109/CDC.2017.8264033
2017
Three examples of the stability properties of the invariant extended Kalman filter DOI : 10.1016/j.ifacol.2017.08.061
2017
Particle observers for contracting dynamical systems DOI : 10.1007/978-3-319-68445-1_36
2017
Drone tracking using an innovative UKF DOI : 10.1007/978-3-319-68445-1_35
2017
The invariant extended Kalman filter as a stable observer DOI : 10.1109/TAC.2016.2594085
2017
An innovative nonlinear filter for radar kinematic estimation of maneuvering targets in 2D DOI : 10.23919/IRS.2017.8008156
2016
On the covariance of ICP-based scan-matching techniques DOI : 10.1109/ACC.2016.7526532
2016
Navigating with highly precise odometry and noisy GPS: a case study DOI : 10.1016/j.ifacol.2016.10.234
2015
An invariant Linear Quadratic Gaussian controller for a simplified car DOI : 10.1109/ICRA.2015.7139037
2015
Intrinsic filtering on Lie groups with applications to attitude estimation DOI : 10.1109/TAC.2014.2342911
2015
An intrinsic Cramér-Rao bound on SO(3) for (dynamic) attitude filtering DOI : 10.1109/CDC.2015.7402526
2015
Invariant EKF Design for Scan Matching-Aided Localization DOI : 10.1109/TCST.2015.2413933
2015
An intrinsic Cramér-Rao bound on lie groups DOI : 10.1007/978-3-319-25040-3_71
2015
Invariant filtering for Pose EKF-SLAM aided by an IMU DOI : 10.1109/CDC.2015.7402522
2015
A contraction theory-based analysis of the stability of the deterministic extended kalman filter DOI : 10.1109/TAC.2014.2336991
2014
Invariant particle filtering with application to localization DOI : 10.1109/CDC.2014.7040265
2014
Experimental implementation of an Invariant Extended Kalman Filter-based scan matching SLAM DOI : 10.1109/ACC.2014.6859291
2014
Fixed-rank matrix factorizations and Riemannian low-rank optimization DOI : 10.1007/s00180-013-0464-z
2014
Priority-based intersection management with kinodynamic constraints DOI : 10.1109/ECC.2014.6862377
2014
Anisotropy preserving DTI processing DOI : 10.1007/s11263-013-0674-4
2014
Humanoid robot navigation: Getting localization information from vision DOI : 10.1515/jisys-2013-0079
2013
Rank-preserving geometric means of positive semi-definite matrices DOI : 10.1016/j.laa.2012.12.009
2013
Contraction-based design of positive observers DOI : 10.1109/CDC.2013.6760929
2013
Humanoid robot navigation: From a visual SLAM to a visual compass DOI : 10.1109/ICNSC.2013.6548820
2013
Stochastic gradient descent on riemannian manifolds DOI : 10.1109/TAC.2013.2254619
2013
A note on the intrinsic Cramer-Rao bound DOI : 10.1007/978-3-642-40020-9_41
2013
Intrinsic filtering on SO(3) with discrete-time observations DOI : 10.1109/CDC.2013.6760380
2012
Accurate 3D maps from depth images and motion sensors via nonlinear Kalman filtering DOI : 10.1109/IROS.2012.6385597
2012
Symmetries in observer design: Review of some recent results and applications to EKF-based SLAM DOI : 10.1007/978-1-4471-2343-9_1
2011
Contraction and observer design on cones DOI : 10.1109/CDC.2011.6161268
2011
A simple nonlinear filter for low-cost ground vehicle localization system DOI : 10.1109/CDC.2011.6161262
2011
Linear regression under fixed-rank constraints: A Riemannian approach
2011
A separation principle on Lie groups DOI : 10.3182/20110828-6-IT-1002.03353
2011
Symmetry-based observers for some water-tank problems DOI : 10.1109/TAC.2010.2067291
2011
Regression on fixed-rank positive semidefinite matrices: A Riemannian approach
2011
Design and prototyping of a low-cost vehicle localization system with guaranteed convergence properties DOI : 10.1016/j.conengprac.2011.02.003
2010
A simple intrinsic reduced-observer for geodesic flow DOI : 10.1109/TAC.2010.2052481
2010
An introduction to symmetry-preserving observers. Application to a multi-sensor data fusion tutorial example DOI : 10.3166/jesa.44.743-770
2010
Coordinated motion design on lie groups DOI : 10.1109/TAC.2010.2042003
2010
Coordinated Motion Design on Lie Groups DOI : 10.1109/TAC.2010.2048152
2009
Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank DOI : 10.1137/080731347
2009
From subspace learning to distance learning: A geometrical optimization approach DOI : 10.1109/SSP.2009.5278557
2009
Observer-based Hamiltonian identification for quantum systems DOI : 10.1016/j.automatica.2008.12.007
2009
Fusion of inertial and visual: a geometrical observer-based approach DOI : 10.1063/1.3106512
2009
Invariant extended Kalman filter: Theory and application to a velocity-aided attitude estimation problem DOI : 10.1109/CDC.2009.5400372
2009
Non-linear symmetry-preserving observers on lie groups DOI : 10.1109/TAC.2009.2020646
2008
Non-linear observer on lie groups for left-invariant dynamics with right-left equivariant output DOI : 10.3182/20080706-5-KR-1001.2525
2008
A simple feedback-loop for a frequency lock on a narrow atomic transition DOI : 10.3182/20080706-5-KR-1001.1456
2008
Symmetry-preserving observers DOI : 10.1109/TAC.2008.2006929
2008
Coordination on Lie groups DOI : 10.1109/CDC.2008.4739201
2008
Qubit Hamiltonian identification: A symmetry-preserving observer-based approach DOI : 10.3182/20080706-5-KR-1001.1455
2007
Left-invariant extended Kalman filter and attitude estimation DOI : 10.1109/CDC.2007.4434662
2006
A non-linear symmetry-preserving observer for velocity-aided inertial navigation DOI : 10.1109/acc.2006.1657161
2005
On invariant observers DOI : 10.1007/11529798_4

Teaching

Differential, Integral, and Stochastic Calculus II (Math2)

Lecturer

EC2 consists of two modules: Differential Equations and Probability. The differential equations course aims to introduce students to the study of dynamical systems: existence, uniqueness, and regularity of solutions to a differential equation (Peano–Arzela, Cauchy-Lipschitz, regularity with respect to initial conditions in finite time, chaotic systems), as well as an introduction to the study of the asymptotic behavior of solutions (periodic cycles, asymptotic stability of equilibrium points, etc.) An introduction to the simulation and numerical analysis of differential equations is also provided (discretization schemes, consistency/convergence analysis, differences between explicit and implicit schemes for stiff systems, the role of symplectic schemes for Hamiltonian systems, etc.) The probability course aims to consolidate and supplement the knowledge of probability theory acquired in CPGE, but above all to develop probabilistic reasoning. In CPGE, probability was studied in the context of random phenomena with at most a countable number of possible outcomes. Probabilities defined on the real line, as well as real random variables and vectors, are first introduced within the general formalism of measure theory—covered in EC1—which allows for the inclusion of the discrete case. The concepts of independence and conditioning of random variables, sequences of random variables, and finally stochastic simulation methods are addressed in turn to cover all the prerequisites necessary for the various engineering specializations offered at the school, particularly data science.

Stochastic Processes and Applications

Course Director

The course sessions will cover the following topics: Kolmogorov’s Conditional Expectation Theory, Discrete-Time Martingales and Financial Modeling, Brownian Motion, Stochastic Calculus, Stochastic Differential Equations, Markov Property, Girsanov’s Theorem, the Black–Scholes Model, Numerical Implementation, Various Applications

Regulation

Lecturer

Control – General FC Sensors and Actuators Fundamentals and Principles of Control Open-Loop and Closed-Loop Systems Static and dynamic behavior of systems; concepts of gain and loop complexity Control modes: T/R, P, I, D, cascade control. Technology of control loop components Practical Training – Industrial Control (7 hours) – Common to FC Implementing control loops on a simulator Boyds model Process identification. Proportional control Bode plot Stability.

Applied Mathematics: Robotics, Computer Vision, and Control Systems (MAREVA) track

Course Director

Second-Year Curriculum The courses and educational activities offered in the second year are the same for all students who have chosen the MAREVA program and take place in Paris. The second-year curriculum focuses on the study of Complex Systems: discrete-time dynamic systems, filtering and identification, embedded sensors and data fusion, image processing, and medical imaging. This module is supplemented by introductory lectures on robotics and ITS, virtual reality and augmented reality, C++ programming and graphical programming sessions, as well as mini-project sessions conducted in pairs, supervised by researchers from the centers, and applying the concepts covered in class. Here are a few examples of mini-projects completed in recent years: lateral control (Lane Keeping, ESP) and longitudinal control of a vehicle (ACC); color-sensor-based control of a small car on a white line; evaluation of a consumer motion-capture system (the Wiimote); 3D point cloud registration for digital mapping; modeling and stabilization of a diver; image editing based on hierarchical segmentation; modeling and control of construction cranes; estimation and control algorithms for a mobile robot developed by SAGEM; development of parking algorithms, validation, and testing using 3D graphics software; implementation of human-environment interactions in a virtual kitchen. Third-Year Curriculum In the third year, the activities for the month of October remain the same for all students. The first two weeks in Paris are devoted to courses, notably on computer vision and image processing in the automotive context, on nonlinear control and its applications in robotics, on humanoid robots, on discrete-event systems, and on systems with delays.... A one-week intensive course in computer vision and mathematical morphology held in November rounds out the training for the Computer Vision and Robotics specializations. The last two weeks of October are dedicated to mini-projects (at a more advanced level than those in the second year), as well as to the optional field trip during which students visit laboratories and companies. Over the past four years, the trip has been organized to Italy and the Rhône-Alpes region (STMicroelectronics, ISPRA, INRIA Rhône-Alpes, LAG ...), in the Nice and Monaco region (INRIA Sophia-Antipolis, Thalès Alénia Space, the Automata Museum ...), in Germany in Stuttgart and Munich (Bosch, Mercedes, German Aerospace ...), and in Toulouse (CNES, LAAS, Pierre Fabre Laboratories...), and in Bordeaux (LABRI, LAPS, Laser MégaJoule, Thales, EvTronic, BeTomorrow...). These trips provide excellent opportunities to establish valuable contacts for elective internships in the third year. Internship topics for the third year are pooled and proposed by faculty members from the school’s various applied mathematics centers (CAOR, CAS, CMA, CMM), often in connection with their collaborative work with industry partners. It should be noted that each year, the number of internships offered far exceeds the number of students taking the elective! Some representative elective topics covered in recent years: Control Systems: Exo-atmospheric guidance of Ariane V – EADS (Control Systems); Signal processing using filter banks (IFP); Development of a method for analyzing ECG signals using inverse scattering (INRIA); Simulation and control of humanoid robots (ATR Computational Neuroscience Laboratory, Kyoto); Synthesis of flight control correctors for a supersonic aerobatic vehicle (ONERA); Validation of vehicle models for control and command (PSA) Quantification of maximum allowable disturbances on the control surfaces of a winged vehicle during atmospheric reentry (EADS) Parameter estimation for quantum systems (Princeton University) Optimization of electricity generation (EDF, Clamart) Sizing of natural gas transmission networks, (GdF Suez, Saint-Denis) Robotics: Computer Vision-Assisted Driving (INRIA/CAOR) Improving Road Safety and Comfort via Global Chassis Control (PSA) Identification of Available Traction for a Vehicle (NEXYAD, ARCOS project) Configuration of a force-feedback system in virtual reality (CEA/CAOR) Vehicle-to-infrastructure communication on highways (ASFA) Virtual vehicle coupling for convoy driving (INRIA) Development of a humanoid robot behavior editor (Aldebaran Robotics) Motion planning for humanoid robots (Joint Research Laboratory Tsukuba) Development of a social robot (Advanced Telecommunications Research, Kyoto) The Cybercars Olympics: a competition featuring smart vehicles on the “road of the future” in Saint-Brieuc (Côtes d’Armor General Council) Simulation and position estimation of a quadcopter drone (Parrot, Paris) Preparation of the French pavilion at the Shanghai World Expo on ITS Road traffic modeling, Millennium project (University of Berkeley) Neural algorithms for perception (MIT, Cambridge) Spherical vision sensor for autonomous mobile robotics (INRIA Sophia-Antipolis) Vision: Automatic image annotation (LTU, Paris) Indexing of medical images (CEA, Fontenay-aux-Roses) Environmental sensor for a telematics service (PSA, Vélizy) Segmentation of medical images for radiation therapy (Gustave Roussy Institute, Villejuif) Fingerprint image analysis (SAGEM, Eragny-sur-Oise) Analysis of sports video sequences (Thomson Broadcast, Breda, Netherlands) Compression/deconvolution optimization (Alcatel Space Industries, Cannes) Quantitative cytology and drug discovery (CSIRO, Sydney, Australia) 3D morphogenesis of the mouse kidney (Monash University, Clayton, Australia) Video scene interpretation (Bosch, Hildesheim, Germany) Geolocation of a landscape (Google Earth, USA) Quality control of photovoltaic glass (Saint-Gobain, China) Image analysis for studying the mechanical properties of bone (University of Adelaide, Australia) Special features of the track: Students greatly appreciate working on these mini-projects. It is an excellent way to deepen their understanding of and apply the concepts covered in class, as well as a great opportunity to meet researchers from the school’s various laboratories and gain their first—albeit limited—experience in the research environment.

PhD supervision

2026 Collaborative navigation of a fleet of agents MARIE-ANNE Julien
2025 Simultaneous Localization and Mapping with Traversability Information in Unstructured Environments CALZAS Julien
2022 Optimal control regularized by covariance using extended Kalman filter backpropagation BENHAMOU Jonas
2020 Backpropagation in a Kalman Filter with applications to fault detection and navigation PARELLIER Colin
2019 Using machine learning methods for radar tracking and aircraft classification tasks. JOUABER Sami
2017 Smoothing algorithms for navigation, localization, and mapping, based on high-quality inertial sensors CHAUCHAT Paul
2017 Modern techniques for multi-sensor navigation prototyping BROSSARD Martin
2015 Dynamic resource management for tracking highly maneuverable targets PILTÉ Marion