The Quaternion Based Error Model Based on SE(3) of the INS

Zhu, Tiangao; Li, An; Li, Kailong; Qin, Fangjun

doi:10.1109/jsen.2022.3174596

Cited by 5 publications

(4 citation statements)

References 28 publications

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“…The results are compared with those calculated by the traditional

group model and the conventional

group model. Zhu et al pointed out the equivalence between the left- and right-invariant error models [ 14 ], so only the right-invariant error model on the

group are compared. In the experiment, the proposed left- and right-invariant error models on the

group in the ECI frame and the two models mentioned before are named as ECI-

-L model, ECI-

-R model,

model, and

model, respectively.…”

Section: Methodsmentioning

confidence: 99%

“…Chang et al constructed left- and right-invariant error models of the transformed INS mechanization on the

group in the Earth-Centered Earth-Fixed (ECEF) coordinate system (denoted as e -frame) to address the problem of the group affine property not being met when the n -frame is selected as the reference navigation coordinate system and the Earth’s rotation and the Coriolis effect cannot be neglected, and analyzed their performance in the SINS/GNSS and SINS/Odometer integrated systems [ 13 ]. Zhu et al derived the quaternion-based error model on the

group and compared it to the Euler angle error model and its counterpart on the

group [ 14 ]. Qian et al examined the necessity of the Lie group error model from three perspectives: the stability of variance, estimation accuracy, and observability, and proved its superiority to traditional error models [ 15 ].…”

Section: Introductionmentioning

confidence: 99%

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The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System

Fang,

Cai,

Wang

2024

Sensors

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In this paper, the kinematic models of the Strapdown Inertial Navigation System (SINS) and its errors on the SE(3) group in the Earth-Centered Inertial frame (ECI) are established. On the one hand, with the ECI frame being regarded as the reference, based on the joint representation of attitude and velocity on the SE(3) group, the dynamic of the local geographic coordinate system (n-frame) and the body coordinate system (b-frame) evolve on the differentiable manifold, respectively, and the high-order expansion of the Baker–Campbell–Haussdorff equation compensates for the non-commutative motion errors stimulated by strong maneuverability. On the other hand, the kinematics of the left- and right-invariant errors of the n-frame and the b-frame on the SE(3) group are separately derived, where the errors of the b-frame completely depend on inertial sensor errors, while the errors of the n-frame rely on position errors and velocity errors. In this way, the errors brought by the inconsistency of the reference coordinate system are tackled, and a novel attitude error definition is introduced to separate and decouple the factors affecting the dynamic of the n-frame errors and the b-frame errors for better attitude estimation. Through a turntable experiment and a car-mounted field experiment, the effectiveness of the proposed kinematic models in estimating attitude has been verified, with a remarkable improvement in yaw angle accuracy in the case of large initial misalignment angles, and the models developed have better robustness compared to the traditional SE(3) group-based model.

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“…The results are compared with those calculated by the traditional

group model and the conventional

group model. Zhu et al pointed out the equivalence between the left- and right-invariant error models [ 14 ], so only the right-invariant error model on the

group are compared. In the experiment, the proposed left- and right-invariant error models on the

group in the ECI frame and the two models mentioned before are named as ECI-

-L model, ECI-

-R model,

model, and

model, respectively.…”

Section: Methodsmentioning

confidence: 99%

“…Chang et al constructed left- and right-invariant error models of the transformed INS mechanization on the

group and compared it to the Euler angle error model and its counterpart on the

Section: Introductionmentioning

confidence: 99%

The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System

Fang,

Cai,

Wang

2024

Sensors

View full text Add to dashboard Cite

show abstract

“…Another way to analyze and compensate for an INS error is by building an error propagation model based on navigation principles [ 17 , 18 , 19 , 20 , 21 ]. There are two basic approaches to the deviation in INS error models in the literature: the phi-angle approach (or the true frame approach) and the psi-angle approach (or the computer frame approach) [ 17 , 18 ].…”

Section: Introductionmentioning

confidence: 99%

“…The attitude calculation in INS has three approaches: Euler angle, direction cosine matrix and quaternion. The quaternion method has received extensive attention for the advantages of less computation, higher accuracy and avoiding singularities [ 20 , 21 ]. Nevertheless, most of the error propagation models were established based on the geographic frame and relied on latitude and longitude to provide location information.…”

Section: Introductionmentioning

confidence: 99%

Performance Enhancement of INS and UWB Fusion Positioning Method Based on Two-Level Error Model

Zhang

Shi

et al. 2023

Sensors

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In GNSS-denied environments, especially when losing measurement sensor data, inertial navigation system (INS) accuracy is critical to the precise positioning of vehicles, and an accurate INS error compensation model is the most effective way to improve INS accuracy. To this end, a two-level error model is proposed, which comprehensively utilizes the mechanism error model and propagation error model. Based on this model, the INS and ultra-wideband (UWB) fusion positioning method is derived relying on the extended Kalman filter (EKF) method. To further improve accuracy, the data prefiltering algorithm of the wavelet shrinkage method based on Stein’s unbiased risk estimate–Shrink (SURE-Shrink) threshold is summarized for raw inertial measurement unit (IMU) data. The experimental results show that by employing the SURE-Shrink wavelet denoising method, positioning accuracy is improved by 76.6%; by applying the two-level error model, the accuracy is further improved by 84.3%. More importantly, at the point when the vehicle motion state changes, adopting the two-level error model can provide higher computational stability and less fluctuation in trajectory curves.

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The quaternion based error model based on SE2(3) without singularity and approximation for the integrated navigation

Qian,

Qin,

et al. 2025

Measurement

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The Quaternion Based Error Model Based on SE(3) of the INS

Cited by 5 publications

References 28 publications

The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System

The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System

Performance Enhancement of INS and UWB Fusion Positioning Method Based on Two-Level Error Model

The quaternion based error model based on SE2(3) without singularity and approximation for the integrated navigation

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