Abstract
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.
Highlights
As dynamic systems on Riemannian manifold are common in the robotics and avionics, the development of robust and accurate state estimation algorithms for autonomous navigation system has gained a great interest in robotics and avionics industries, especially when the states of the vehicles are evolving on Lie group
Motivated by the equivariant observer design for an equivariant kinematic system, we propose an equivariant filter framework for the inertial-integrated navigation by leveraging the Lie group structure of SE2(3), which can be regarded as equivariant filter design for the second order kinematic systems on TSE2(3)
In this paper, the left equivariant property of the inertialintegrated kinematics system is exploited for the design of equivariant filtering framework
Summary
As dynamic systems on Riemannian manifold are common in the robotics and avionics, the development of robust and accurate state estimation algorithms for autonomous navigation system has gained a great interest in robotics and avionics industries, especially when the states of the vehicles are evolving on Lie group. We propose an equivariant filter framework for the inertial-integrated navigation system which embeds the attitude, velocity, and position into the matrix Lie group SE2(3). Velocity, and position in ECEF frame are represented as Cbe , veeb , and reeb , their differential equations are given as
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