Riccati observers for position and velocity bias estimation from either direction or range measurements

This paper revisits the problems of estimating the position of an object moving in n (≥ 2)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global exponential stability of zero estimation errors, even in the case where the measured velocity is biased by an unknown constant perturbation. These results are obtained under persistent excitation (p.e.) conditions depending on the number of source points and body motion that ensure both uniform observability and good conditioning of the CRE solutions. With respect to prior contributions on these subjects some of the proposed solutions are entirely novel while others are adapted from existing ones with the preoccupation of stating simpler and more explicit conditions under which uniform exponential stability is achieved. A complementary contribution, related to the delicate tuning of the observers gains, is the derivation of a lower-bound of the exponential rate of convergence specified as a function of the amount of persistent excitation. Simulation results illustrate the performance of the proposed observers

Riccati observers for position and velocity bias estimation from either direction or range measurements

This paper revisits the problems of estimating the position of an object moving in n (≥ 2)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global exponential stability of zero estimation errors, even in the case where the measured velocity is biased by an unknown constant perturbation. These results are obtained under persistent excitation (p.e.) conditions depending on the number of source points and body motion that ensure both uniform observability and good conditioning of the CRE solutions. With respect to prior contributions on these subjects some of the proposed solutions are entirely novel while others are adapted from existing ones with the preoccupation of stating simpler and more explicit conditions under which uniform exponential stability is achieved. A complementary contribution, related to the delicate tuning of the observers gains, is the derivation of a lower-bound of the exponential rate of convergence specified as a function of the amount of persistent excitation. Simulation results illustrate the performance of the proposed observers

Position estimation from direction or range measurements

International audienceThis paper revisits the problems of estimating the position of an object moving in n (≥ 2)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponential stability of zero estimation errors, also when the measured velocity is biased by an unknown constant vector or when direction measurements are corrupted by an unknown constant bias. With respect to prior contributions on these subjects they provide a coherent generalization of existing solutions with the preoccupation of pointing out general and explicit persistent excitation (p.e.) conditions whose satisfaction ensures uniform exponential stability of the observers

Riccati observers for position and velocity bias estimation from direction measurements

International audienceThis paper addresses the problem of estimating the position of a body moving in n (≥ 2)-dimensional Euclidean space using body velocity measurements and the measurements of direction(s) between the body and one (or several) source point(s) whose location(s) is (are) known. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponential stability of zero estimation errors, even when the measured body velocity is biased by an unknown constant perturbation. These results are obtained under persistent excitation (p.e.) conditions depending on the number of source points and body motion that ensure both uniform observability and good conditioning of the CRE solutions. With respect to previous contributions on the subject the proposed framework encompasses the static case, when the body is motionless and at least two source points are needed to recover its position, and the non-static case, when body motion and a single source are sufficient. Simple and explicit observability conditions under which uniform exponential stability is achieved are also worked out for each case. Simulation results illustrate the performance of the proposed observers

On sensor fusion for airborne wind energy systems

A study on filtering aspects of airborne wind energy generators is presented. This class of renewable energy systems aims to convert the aerodynamic forces generated by tethered wings, flying in closed paths transverse to the wind flow, into electricity. The accurate reconstruction of the wing's position, velocity and heading is of fundamental importance for the automatic control of these kinds of systems. The difficulty of the estimation problem arises from the nonlinear dynamics, wide speed range, large accelerations and fast changes of direction that the wing experiences during operation. It is shown that the overall nonlinear system has a specific structure allowing its partitioning into sub-systems, hence leading to a series of simpler filtering problems. Different sensor setups are then considered, and the related sensor fusion algorithms are presented. The results of experimental tests carried out with a small-scale prototype and wings of different sizes are discussed. The designed filtering algorithms rely purely on kinematic laws, hence they are independent from features like wing area, aerodynamic efficiency, mass, etc. Therefore, the presented results are representative also of systems with larger size and different wing design, different number of tethers and/or rigid wings.Comment: This manuscript is a preprint of a paper accepted for publication on the IEEE Transactions on Control Systems Technology and is subject to IEEE Copyright. The copy of record is available at IEEEXplore library: http://ieeexplore.ieee.org

Accurate 3D maps from depth images and motion sensors via nonlinear Kalman filtering

This paper investigates the use of depth images as localisation sensors for 3D map building. The localisation information is derived from the 3D data thanks to the ICP (Iterative Closest Point) algorithm. The covariance of the ICP, and thus of the localization error, is analysed, and described by a Fisher Information Matrix. It is advocated this error can be much reduced if the data is fused with measurements from other motion sensors, or even with prior knowledge on the motion. The data fusion is performed by a recently introduced specific extended Kalman filter, the so-called Invariant EKF, and is directly based on the estimated covariance of the ICP. The resulting filter is very natural, and is proved to possess strong properties. Experiments with a Kinect sensor and a three-axis gyroscope prove clear improvement in the accuracy of the localization, and thus in the accuracy of the built 3D map.Comment: Submitted to IROS 2012. 8 page

Riccati Observers for the non-stationary PnP problem

This paper revisits the problem of estimating the pose (position and orientation) of a body in 3D space with respect to (w.r.t.) an inertial frame by using i) the knowledge of source points positions in the inertial frame, ii) the measurements of the body velocity, either in the body frame or in the inertial frame, and iii) source points bearing measurements performed in the body frame. An important difference with the much studied static Perspective-n-Point (PnP) problem addressed with iterative algorithms is that body motion is not only allowed but also used as a source of information that improves the estimation possibilities. With respect to the probabilistic framework commonly used in other studies that develop Extended Kalman filter (EKF) solutions, the deterministic approach here adopted is better suited to point out the observability conditions, that involve the number and disposition of the source points in combination with body motion characteristics, under which the proposed observers ensure robust estimation of the body pose. These observers are here named Riccati observers because of the instrumental role played by the Continuous Riccati equation (CRE) in the design of the observers and in the Lyapunov stability and convergence analysis that we develop independently of the well-known complementary (either deterministic or probabilistic) optimality properties associated with Kalman filtering. The set of these observers also encompasses Extended Kalman filter solutions. Another contribution of the present study is to show the importance of using body motion to improve the observers performance and, when this is possible, of measuring the body translational velocity in the inertial frame rather than in the body frame in order to remove the constraint of knowing the positions of the source points in the inertial frame. This latter issue is the link that connects the problem of body pose estimation with single source point bearing measurements and the Simultaneous Localization and Mapping (SLAM) problem in Robotics

Riccati Observers for the Non-Stationary PnP Problem

International audienceThis paper revisits the problem of estimating the pose (position and orientation) of a body in 3D space with respect to (w.r.t.) an inertial frame by using i) the knowledge of source points positions in the inertial frame, ii) the measurements of the body angular velocity expressed in the body's frame iii) the measurements of the body translational velocity, either in the body frame or in the inertial frame, and iv) source points bearing measurements performed in the body frame. An important difference with the much studied static Perspective-n-Point (PnP) problem addressed with iterative algorithms is that body motion is not only allowed but also used as a source of information that improves the estimation possibilities. With respect to the probabilistic framework commonly used in other studies that develop Extended Kalman filter (EKF) solutions, the deterministic approach here adopted is better suited to point out the observability conditions, that involve the number and disposition of the source points in combination with body motion characteristics, under which the proposed observers ensure robust estimation of the body pose. These observers are here named Riccati observers because of the instrumental role played by the Continuous Riccati equation (CRE) in the design of the observers and in the Lyapunov stability and convergence analysis that we develop independently of the well-known complementary (either deterministic or probabilistic) optimality properties associated with Kalman filtering. The set of these observers also encompasses Extended Kalman filter solutions. Another contribution of the present study is to show the importance of using body motion to improve the observers performance and, when this is possible, of measuring the body translational velocity in the inertial frame rather than in the body frame to allow for the body pose estimation from a single source point taken as the origin of the inertial frame. This latter possibility finds a natural extension in the Simultaneous Localization and Mapping (SLAM) problem in Robotics

Invariant EKF Design for Scan Matching-aided Localization

Localization in indoor environments is a technique which estimates the robot's pose by fusing data from onboard motion sensors with readings of the environment, in our case obtained by scan matching point clouds captured by a low-cost Kinect depth camera. We develop both an Invariant Extended Kalman Filter (IEKF)-based and a Multiplicative Extended Kalman Filter (MEKF)-based solution to this problem. The two designs are successfully validated in experiments and demonstrate the advantage of the IEKF design