Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups

Ng, Yonhon; Goor, Pieter van; Hamel, Tarek; Mahony, Robert

doi:10.1109/cdc42340.2020.9303761

Cited by 8 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The practical applicability of this approach, named "Imperfect-IEKF" by Barrau [5], has been confirmed by several authors [5], [6], [7]. Recent work [8] on second order systems on Lie-groups has demonstrated that there is a natural symmetry that can be used to model both configuration and velocity states in a single geometry. This symmetry draws from advances in the field of equivariant system theory and observer design [9], [10], [8], [11] and provides a framework for stochastic filter design that applies to a broader class of systems than the IEKF while specialising back to the IEKF for groupaffine systems on Lie-groups [12].…”

Section: Introduction and Related Workmentioning

confidence: 93%

“…Recent work [8] on second order systems on Lie-groups has demonstrated that there is a natural symmetry that can be used to model both configuration and velocity states in a single geometry. This symmetry draws from advances in the field of equivariant system theory and observer design [9], [10], [8], [11] and provides a framework for stochastic filter design that applies to a broader class of systems than the IEKF while specialising back to the IEKF for groupaffine systems on Lie-groups [12]. In [13], a new symmetry was introduced to couple the navigation state as well as the accelerometer and gyroscope biases in a single geometric structure.…”

Section: Introduction and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation With Online Calibration

Fornasier

Brommer

et al. 2022

IEEE Robot. Autom. Lett.

Self Cite

View full text Add to dashboard Cite

Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g., for regular operation) and transient response (e.g., for fast initialization and reset) of such filters are of crucial importance in guaranteeing robust operation of autonomous systems.This paper introduces a new generic formulation for a gyroscope aided attitude estimator using N direction measurements including both body-frame and reference-frame direction type measurements. The approach is based on an integrated state formulation that incorporates navigation, extrinsic calibration for all direction sensors, and gyroscope bias states in a single equivariant geometric structure. This newly proposed symmetry allows modular addition of different direction measurements and their extrinsic calibration while maintaining the ability to include bias states in the same symmetry. The subsequently proposed filter-based estimator using this symmetry noticeably improves the transient response, and the asymptotic bias and extrinsic calibration estimation compared to state-of-the-art approaches. The estimator is verified in statistically representative simulations and is tested in real-world experiments.

show abstract

Section: Introduction and Related Workmentioning

confidence: 93%

Section: Introduction and Related Workmentioning

confidence: 99%

Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation With Online Calibration

Fornasier

Brommer

et al. 2022

IEEE Robot. Autom. Lett.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The gauge invariance inherent in the SLAM problem induces a homogeneous space structure that underlies recent work by the authors [vHM20,vMHT20,vMHT19,vM21]. This perspective is critically important for the visual SLAM problem where cameras are the primary exteroceptive sensor and the SLAM problem can no longer be modelled [vGHM20] using the SE n+1 (3) geometry introduced by Barrau et [NvMH19,NvHM20] for second order kinematics, while Phogat et al considered a direct product structure for general second order systems on Matrix Lie groups [PC20].…”

Section: Literature Reviewmentioning

confidence: 99%

Observer Design for Nonlinear Systems with Equivariance

Mahony,

van Goor,

Hamel

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a globally defined intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of the system dynamics for the observer internal model we show that the error dynamics have a particularly nice form. Applying the methodology of Extended Kalman Filtering (EKF) to the equivariant error state yields the Equivariant Filter (EqF). The geometry of the state-space manifold appears naturally as a curvature modification to the classical EKF Riccati equation. The equivariant filter exploits the symmetry and respects the geometry of an equivariant system model and yields high performance robust filters for a wide range of mechatronic and navigation systems.

show abstract

“…Therefore, it is promising to embed the inertial-integrated navigation system into an equivariant system so that an equivariant filter can be designed as a kinematic system on a Lie group. Equivariant system theory has been used for the full second order kinematic systems on TSO(3) (Ng et al 2019) and TSE(3) (Ng et al 2020), where the second order means both the first and second derivatives of position are considered in the kinematic system.…”

Section: Introductionmentioning

confidence: 99%

Equivariant filtering framework for inertial-integrated navigation

2021

View full text Add to dashboard Cite

This paper proposes an Equivariant Filtering (EqF) framework for the inertial-integrated state estimation. As the kinematic system of the inertial-integrated navigation can be naturally modeled on the matrix Lie group SE2(3), the symmetry of the Lie group can be exploited to design an equivariant filter which extends the invariant extended Kalman filtering on the group-affine system and overcomes the inconsitency issue of the traditional extend Kalman filter. We firstly formulate the inertial-integrated dynamics as the group-affine systems. Then, we prove the left equivariant properties of the inertial-integrated dynamics. Finally, we design an equivariant filtering framework on the earth-centered earth-fixed frame and the local geodetic navigation frame. The experiments show the superiority of the proposed filters when confronting large misalignment angles in Global Navigation Satellite Navigation (GNSS)/Inertial Navigation System (INS) loosely integrated navigation experiments.

show abstract

Equivariant Systems Theory and Observer Design for Second Order Kinematic Systems on Matrix Lie Groups

Cited by 8 publications

References 24 publications

Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation With Online Calibration

Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation With Online Calibration

Observer Design for Nonlinear Systems with Equivariance

Equivariant filtering framework for inertial-integrated navigation

Contact Info

Product

Resources

About