A non-linear symmetry-preserving observer for velocity-aided inertial navigation

Bonnabel, Silvère; Martin, Philippe; Rouchon, Pierre

doi:10.1109/acc.2006.1657161

Cited by 43 publications

(37 citation statements)

References 12 publications

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“…which, using Γ = Ad R Ω, coincides with the direct filteṙ [8,6] but also extensively studied over the last ten years by a range of authors [4,5,7,9,10].…”

Section: Example: Attitude Estimation On So(3)mentioning

confidence: 99%

Gradient-Like Observers for Invariant Dynamics on a Lie Group

Lageman

Trumpf

Mahony

2010

IEEE Trans. Automat. Contr.

133

163

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This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialised to systems on Lie groups. For invariant systems this leads to a general factorisation theorem of a nonlinear observer into a synchronous (internal model) term and an innovation term. The synchronous term is fully specified by the system model. We propose a design methodology for the innovation term based on gradient-like terms derived from invariant or non-invariant cost functions. The resulting nonlinear observers have strong (almost) global convergence properties and examples are used to demonstrate the relevance of the proposed approach.

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“…which, using Γ = Ad R Ω, coincides with the direct filteṙ [8,6] but also extensively studied over the last ten years by a range of authors [4,5,7,9,10].…”

Section: Example: Attitude Estimation On So(3)mentioning

confidence: 99%

Gradient-Like Observers for Invariant Dynamics on a Lie Group

Lageman

Trumpf

Mahony

2010

IEEE Trans. Automat. Contr.

133

163

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show abstract

“…Specifically, when the output manifold is a reductive homogeneous space of the Lie group, the authors in [14], [15] propose an observer design on the output manifold and then lift the designed observer to obtain a corresponding observer on the Lie group. The approach can be applied to many interesting real world scenarios such as attitude estimator design on the Lie group SO (3) or pose estimation on the Lie group SE(3) [3], [7], [11], [18], [20], [26]. For the specific cases of attitude estimation on SO(3) and pose estimation on SE(3), some methods have been proposed for the concurrent estimation of an unknown constant bias corrupting the velocity measurement [18], [26], [27].…”

Section: Introductionmentioning

confidence: 99%

Bias estimation for invariant systems on Lie groups with homogeneous outputs

Khosravian

Trumpf

Mahony

et al. 2013

52nd IEEE Conference on Decision and Control

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In this paper, we provide a general method of state estimation for a class of invariant systems on connected matrix Lie groups where the group velocity measurement is corrupted by an unknown constant bias. The output measurements are given by a collection of actions of a single Lie group on several homogeneous output spaces, a model that applies to a wide range of practical scenarios. The proposed observer consists of a group estimator part, providing an estimate of a bounded state evolving on the Lie group, and a bias estimator part, providing an estimate of the bias in the associated Lie algebra. We employ the gradient of a suitable invariant cost function on the Lie group as an innovation term in the group estimator. We design the bias estimator such that it guarantees uniform local exponential stability of the estimation error dynamics around the zero error state. We propose a systematic methodology for the design of suitable cost functions on Lie groups by lifting invariant cost functions from the homogeneous output spaces. We show that the resulting observer is implementable based on available sensor measurements if the homogeneous output spaces are reductive. As an example, we derive an observer for rigid body attitude using vector and gyro measurements with unknown constant gyro bias.

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“…Recently, Bonnabel, Martin, and Rouchon (2006), Vik and Fossen (2001), Zhao and Slotine (2005), Benallegue et al (2008), Besnard et al (2007), Boutayeb et al (2008), Benzemrane et al (2007), Benzemrane (2009), Madani and Benallegue (2007) and Pflimlin et al (2007) have proposed observers to be implemented on UAVs. The critical issue in this domain comes from the fact that the translation velocity is classically known as non-observable.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear speed estimation of a GPS-free UAV

Santosuosso¹,

Benzemrane²,

Damm³

2011

International Journal of Control

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International audienceIn this article, the problem of robust state observer design for a class of unmanned aerial vehicles (UAVs) is addressed. A prototype four-rotors helicopter robot for indoors and outdoors applications is considered: the drone is not equipped with GPS related devices, so we describe a strategy to estimate its translational velocity vector based on acceleration, angles and angular speeds measurements only. Since the linearised system is non-observable at the equilibrium point, a nonlinear observability verification is performed for persistently exciting trajectories. A global exponential solution to this open problem is provided in the framework of adaptive observation theory when exact measurements are available. A modified observer is presented to enhance velocity estimation robustness in the realistic case of noisy measurements. The results are compared with a classical estimation strategy based on the extended Kalman filter to test the algorithm's performance

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A non-linear symmetry-preserving observer for velocity-aided inertial navigation

Abstract: To cite this version:Silvère Bonnabel, Philippe Martin, Pierre Rouchon. A non-linear symmetry-preserving observer for velocity-aided inertial navigation.

Cited by 43 publications

References 12 publications

Gradient-Like Observers for Invariant Dynamics on a Lie Group

Gradient-Like Observers for Invariant Dynamics on a Lie Group

Bias estimation for invariant systems on Lie groups with homogeneous outputs

Nonlinear speed estimation of a GPS-free UAV

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