Invariant observers for attitude and heading estimation from low-cost inertial and magnetic sensors

International audienceIn this paper we propose invariant nonlinear observers for attitude and heading estimation using directly the measurements from low-cost inertial and magnetic sensors. In particular we propose a simple and easy-to-tune observer where moreover the estimated attitude behaves well even in the presence of magnetic disturbances

A global observer for attitude and gyro biases from vector measurements

We consider the classical problem of estimating the attitude and gyro biases of a rigid body from vector measurements and a triaxial rate gyro. We propose a simple "geometry-free" nonlinear observer with guaranteed uniform global asymptotic convergence and local exponential convergence; the stability analysis, which relies on a strict Lyapunov function, is rather simple. The excellent behavior of the observer is illustrated through a detailed numerical simulation

Generalized Multiplicative Extended Kalman Filter for Aided Attitude and Heading Reference System

International audienceIn this paper, we propose a “Generalized Multiplicative Extended Kalman Filter” (GMEKF) to estimate the position and velocity vectors and the orientation of a flying rigid body, using measurements from lowcost Earth-fixed position and velocity, inertial and magnetic sensors. Thanks to well-chosen state and output errors, the gains and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as it is the case for the standard Multiplicative Extended Kalman Filter (MEKF). We recover thus the fundamental properties of the Kalman filter in the linear case, especially the convergence and optimality properties, for a large set of trajectories, and it should result in a better convergence of the estimation. We illustrate the good performance and the nice properties of the GMEKF on simulation and on experimental comparisons with a commercial system

A general symmetry-preserving observer for aided attitude heading reference systems

International audienceWe generalize several recent works on nonlinear observers for aided attitude heading reference systems: we propose a symmetry-preserving nonlinear observer which merges the most common measurements available on an aircraft (altitude, Earth-fixed and body-fixed velocity, inertial and magnetic sensors). It can be seen as an alternative to the Extended Kalman Filter, but easier to tune and computationally much more economic. Moreover it has by design a nice geometrical structure appealing from an engineering viewpoint. We illustrate its good performance on simulation and experimental results

Rigid Body Attitude Estimation: An Overview and Comparative Study

The attitude estimation of rigid body systems has attracted the attention of many researchers over the years. The development of efficient estimation algorithms that can accurately estimate the orientation of a rigid body is a crucial step towards a reliable implementation of control schemes for underwater and flying vehicles. The primary focus of this thesis consists in investigating various attitude estimation techniques and their applications. Two major classes are discussed. The first class consists of the earliest static attitude determination techniques relying solely on a set of body vector measurements of known vectors in the inertial frame. The second class consists of dynamic attitude estimation and filtering techniques, relying on body vector measurements as well other measurements, and using the dynamical equations of the system under consideration. Various attitude estimation algorithms, including the latest nonlinear attitude observers, are presented and discussed, providing a survey that covers the evolution and structural differences of these estimation methods. Simulation results have been carried out for a selected number of such attitude estimators. Their performance in the presence of noisy measurements, as well as their advantages and disadvantages are discussed

Reducing Computational Cost in the Invariant Unscented Kalman Filtering For Attitude Estimation

This article proposes a new formulation to derive the invariant unscented Kalman filter (IUKF) algorithm for attitude estimation problem, where both state and sigma-point are considered as a transformation group parametrization of the filter. The detailed IUKF equations are presented in this article. The filter equations relie on the same ideas as the usual Unscented Kalman Filter (UKF), but it uses a geometrically adapted correction term based on an invariant output error. The specific interest of the proposed formulation is that only the invariant state estimation errors between the predicted state and each sigma point must be known to determine the predicted outputs errors. As we have already computed the set of invariant state errors during the prediction step, the computation cost to find the covariance matrix of the invariant state estimation in the update step is greatly reduced

Velocity-aided Attitude Estimation for Accelerated Rigid Bodies

Two nonlinear observers for velocity-aided attitude estimation, relying on gyrometers, accelerometers, magnetometers, and velocity measured in the body-fixed frame, are proposed. As opposed to state-of-the-art body-fixed velocity-aided attitude observers endowed with local properties, both observers are (almost) globally asymptotically stable, with very simple and flexible tuning. Moreover, the roll and pitch estimates are globally decoupled from magnetometer measurements