7,063 research outputs found
Angular velocity nonlinear observer from single vector measurements
The paper proposes a technique to estimate the angular velocity of a rigid
body from single 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 a linear-time varying dynamics appearing in the estimation error
equation. This equation stems from the classic Euler equations and measurement
equations. As is proven, the case of free-rotation allows one to relax the
persistence of excitation assumption. Simulation results are provided to
illustrate the method.Comment: 10 pages, 8 figures. arXiv admin note: substantial text overlap with
arXiv:1503.0287
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
Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs
This paper provides a new observer design methodology for invariant systems
whose state evolves on a Lie group with outputs in a collection of related
homogeneous spaces and where the measurement of system input is corrupted by an
unknown constant bias. The key contribution of the paper is to study the
combined state and input bias estimation problem in the general setting of Lie
groups, a question for which only case studies of specific Lie groups are
currently available. We show that any candidate observer (with the same state
space dimension as the observed system) results in non-autonomous error
dynamics, except in the trivial case where the Lie-group is Abelian. This
precludes the application of the standard non-linear observer design
methodologies available in the literature and leads us to propose a new design
methodology based on employing invariant cost functions and general gain
mappings. We provide a rigorous and general stability analysis for the case
where the underlying Lie group allows a faithful matrix representation. We
demonstrate our theory in the example of rigid body pose estimation and show
that the proposed approach unifies two competing pose observers published in
prior literature.Comment: 11 page
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