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

Abstract

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.

MSCEqF: A Multi State Constraint Equivariant Filter for Vision-Aided Inertial Navigation

“…A people's visual-inertial odometry, that is, an algorithm whose operation requires minimal knowledge, little to no tuning, and yet still functions in many different real-world scenarios, would enable a whole new tranch of real-world applications without the requirement of having highly trained engineers available. The present letter builds upon the recent results in [21,22,23] and is a step towards enabling this goal.…”

“…In very recent research, van Goor et al introduced the EqF [14,15] as a general filter design for systems on homogeneous spaces, and proposed a symmetry for fixed landmark measurements in the context of VI-SLAM [16,17,18,19,20]. Later, Fornasier et al proposed a novel symmetry for INS that couples navigation states and IMU bias and developed an EqF design for INS [21,22] that proved superior to state-of-the-art in terms of robustness to wrong initialization, transient behavior, and consistency properties. In a very recent research study [23], the same authors analyzed the theoretical properties of different symmetry groups when employed in designing filters for inertial navigation systems, and provided a discussion of the relative strengths and weaknesses of different filter algorithms.…”

“…Apart from the different metric evaluation, this work differentiates itself from state-of-the-art by extending insights on symmetries and EqF design for fixed landmark VINS [19,20] and INS including IMU bias into the symmetry [21,22,23] to the idea of a multi state constraint but equivariant VINS. To the best of our knowledge, the resulting algorithm is the first ever, equivariant multi state constraint filter for VIO.…”

A rapid alignment method for high-precision rotational INS within group affine

“…Furthermore, the nonlinear method cannot achieve the accuracy of the conventional two-phases method due to the shortcomings of the nonlinear error state model. Another idea is an alignment method based on Lie group theory [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. It has been noted that some dynamical models satisfy a particular 'group affine' property if their states are defined in Lie group [20].…”

“…The corresponding linear error state model can accurately reflect the nonlinear group error propagation process by utilizing the 'group affine' property. There have been many studies on inertial navigation based on Lie group theory [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. In [21], a framework for an INS algorithm design by using Lie group and Lie algebra is introduced, and an INS algorithm based on the Special Euclidean group SE(3) is presented under the guidelines of the Lie group method.…”