Angular velocity nonlinear observer from vector measurements

Abstract

International audienceThis paper proposes a technique to estimate the angular velocity of a rigid body from vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector measurements are directly filtered through a nonlinear observer estimating the angular velocity. Convergence is established using a detailed analysis of the linear-time varying dynamics appearing in the estimation error equation. This equation stems from the classic Euler equations and measurement equations. A high gain design allows to establish local uniform exponential convergence. Simulation results are provided to illustrate the method

Angular Velocity Nonlinear Observer From Single Vector Measurements

“…Figure 5 shows the convergence of the observer for various values of k. Interestingly, large values of k produce undesirable effects. This is a structural difference with the two reference vectors based observer previously introduced by the authors [15]. The reason is that the convergence is guaranteed by a PE argument and not by a uniformly negative bound on eigenvalues.…”

“…Theorem 2 (main result). We suppose that Assumptions 1-2 are satisfied and that d < d * where d * is defined in (15). The observer (6) defines an error dynamics (8) for which the equilibrium 0 is locally uniformly exponentially stable.…”

“…This is the contribution of this article. In a related philosophy, MINES we have recently proposed an observer using the measurements from two linearly independent vectors as input [15]. The present paper studies a similarly structured observer.…”

Estimation of air velocity for a high velocity spinning projectile using transerse accelerometers

“…For this, the task of estimating the angular velocity of the rigid body can be solved using the embedded magnetometers which serve here as direction sensors, through a state observer. 29,30 Alternatively, a frequency analysis of the magnetometers signal can also be used.…”

Analysis and Compensation of Modulation Angular Rate Error Based on Missile-Borne Rotation Semi-Strapdown Inertial Navigation System

“…Magnis et al considered a nonlinear observer that directly uses the vector measurements to reconstruct the angular velocity. A nonlinear observer with extended state and output injection is defined and its convergence is proved by identifying the error equation as a linear time-varying (LTV) system perturbed by a linear-quadratic term [ 10 ]. However, sensors producing vector measurements, such as Sun sensors, magnetometers and star sensors, are susceptible to the external environment which makes it difficult to employ them in all terrains and at all times.…”