Jean-Philippe Condomines

Nonlinear state estimation using an invariant unscented Kalman filter

In this paper, we proposed a novel approach for nonlinear state estimation, named π-IUKF (Invariant Unscented Kalman Filter), which is based on both invariant filter estimation and UKF theoretical principles. Several research works on nonlinear invariant observers have been led and provide a geometrical-based constructive method for designing filters dedicated to nonlinear state estimation problems while preserving the physical properties and system symmetries. The general invariant observer guarantees a straight-forward form of the nonlinear estimation error dynamics whose properties are remarkable. The developed π-IUKF estimator suggests a systematic approach to determine all the symmetry-preserving correction terms, associated with a nonlinear state-space representation used for prediction, without requiring any linearization of the differential equations. The exploitation of the UKF principles within the invariant framework has required the definition of a compatibility condition on the observation equations. As a first result, the estimated covariance matrices of the π-IUKF converge to constant values due to the symmetry-preserving property provided by the nonlinear invariant estimation theory. The designed π-IUKF method has been successfully applied to some relevant practical problems such as the estimation of Attitude and Heading for aerial vehicles using low-cost AH reference systems (i.e., inertial/magnetic sensors characterized by low performances).

Pi-Invariant Unscented Kalman Filter for sensor fusion

A novel approach based on Unscented Kalman Filter (UKF) is proposed for nonlinear state estimation. The Invariant UKF, named π-IUKF, is a recently introduced algorithm dedicated to nonlinear systems possessing symmetries as illustrated by the quaternion-based mini Remotely Piloted Aircraft System (RPAS) kinematics modeling considered in this paper. Within an invariant framework, this algorithm suggests a systematic approach to determine all the symmetry-preserving terms which correct accordingly the nonlinear state-space representation used for prediction, without requiring any linearization. Thus, based on both invariant filters, for which Lie groups have been identified and UKF theoretical principles, the developed π-IUKF has been previously and successfully applied to the mini-RPAS attitude estimation problem, highlighting remarkable invariant properties. We propose in this paper to extend the theoretical background and the applicability of our proposed π-IUKF observer to the case of a mini-RPAS equipped with an aided Inertial Navigation System (INS) which leads to augment the nonlinear state space representation with both velocity and position differential equations. All the measurements are provided on board by a set of low-cost and low-performance sensors (accelerometers, gyrometers, magnetometers, barometer and even Global Positioning System (GPS)). Our designed π-IUKF estimation algorithm is described in this paper and its performances are evaluated by exploiting successfully real flight test data. Indeed, the whole approach has been implemented onboard using a data logger based on the well-known Paparazzi system. The results show promising perspectives and demonstrate that nonlinear state estimation converges on a much bigger set of trajectories than for more traditional approaches

Design of a robust controller/observer for TCP/AQM network: First application to intrusion detection systems for drone fleet

This paper proposes a robust controller/observer for UAVs network anomaly estimation which is based on both Lyapunov Krasovkii functional and dynamic behavior of TCP (Transmission Control Protocol). Several research works on network anomaly estimation have been led using automatic control techniques and provide methods for designing both observer and command laws dedicated to time delay problem while estimating the anomaly or intrusion in the system. The observer design is based on a linearized fluid-flow model of the TCP behavior and must be associated to an AQM (Active Queue Management) to perform its diagnosis. The developed robust controller/observer in this paper has to be tuned by considering the time delay linear state-space representation of TCP model. As a first result, the designed controller/observer system has been successfully applied to some relevant practical problems such as topology network for aerial vehicles and the effectiveness is illustrated by using real traffic traces including Denial of Service attacks. Our first results show promising perspectives for Intrusion Detection System (IDS) in a fleet of UAVs.

Tightly coupled navigation and wind estimation for mini UAVs

A novel nonlinear filter for the state-space model based on aided Inertial Navigation System, 1D Pitot static tube, angle-of-attack and angle-of-sideslip sensors is proposed. The solution, based on Multiplicative Kalman filtering, estimates in real-time the orientation, the velocity and the position of an Unmanned Aerial Vehicle along with sensor bias and 3D wind components. This paper describes and justifies the designed tightly coupled estimation scheme with both theoretical and experimental considerations. We validate then the whole approach for a mini UAV controlled through the well-known Paparazzi autopilot system which we equip with a set of low-cost sensors (accelerometers, gyros, GPS, magnetometer, barometer, 1D Pitot static tube and angular sensors), by successfully comparing the estimates obtained from real flight data with the 3D wind ground truth provided from a 60-m weather measurement tower.

Piece-wise Identification and Analysis of the Aerodynamic Coefficients, Trim Conditions, and Safe Sets of the Generic Transport Model

Aeronautical research has investigated the Generic Transport Model (GTM) in windtunnel studies and provides today an elaborated aerodynamic model for designing methods dedicated to convergence analysis or control problems of aerial vehicles. In this paper, we propose a novel approach for fitting aerodynamic coefficients, namely piece-wise polynomial identification, which is based on measurements in both preand post-stall region. The developed method suggests a systematic approach to determine full envelope better than the purely polynomial models published yet. As a result, an analysis of GTM’s longitudinal trim conditions has been successfully applied on the piece-wise identified model and achieves better results than polynomial models. Based on the trim conditions, safe set computation for linear-quadratic controllers is argued to be a powerful tool for verification of nonlinear control systems. Using common and multiple Lyapunov-functions theory, we are able to present a method for the safe set computation with piece-wise defined systems dynamics.

Optimal Invariant Observers Theory for Nonlinear State Estimation

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Optimal Invariant Observers Theory for Nonlinear State Estimation Jean-Philippe Condomines, Cédric Seren, Gautier Hattenberger