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Analytical Formulation of Relationship Between Sensors and Euler Angle Errors for Arbitrary Stationary Alignment

Chang June Lee¹, Jung Keun Lee²

¹Department of Integrated Systems Engineering, Hankyong National University, Anseong 17579, Republic of Korea.

Sensors (Basel, Switzerland)

|April 26, 2025

Summary

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This study introduces a new analytical method to understand Euler angle errors in attitude and heading reference systems (AHRS). The formulation accurately describes how sensor errors impact orientation accuracy, regardless of alignment.

Area of Science:

Navigation Systems
Sensor Fusion
Geophysics

Background:

Attitude and Heading Reference Systems (AHRS) are vital for determining sensor orientation in navigation.
Stationary alignment in AHRS is susceptible to sensor errors, affecting accuracy.
Existing research lacks detailed analysis of Euler angle errors across diverse sensor orientations.

Purpose of the Study:

To develop an analytical formulation for Euler angle errors in AHRS based on accelerometer and magnetometer data.
To investigate the relationship between sensor error factors and Euler angle errors, independent of sensor-navigation frame alignment.
To provide a method for analyzing the impact of individual sensor errors on overall orientation accuracy.

Main Methods:

Utilized the Three-Axis Attitude Determination (TRIAD) method for stationary alignment.

Keywords:

Euler angle error analytical formulation inertial measurement unit sensor error stationary alignment

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Incorporated sensor error factors including scale, installation, offset, noise, and constant bias.

Developed a linear equation to model the relationship between sensor errors and Euler angle errors.

Conducted simulations for both sensor-aligned and sensor-misaligned conditions with varying Euler angles.

Main Results:

The proposed formulation accurately describes total Euler angle errors.
The method successfully quantifies partial errors attributed to individual sensor error factors.
The formulation's validity was confirmed across sensor-aligned and arbitrary Euler angle configurations.

Conclusions:

The developed analytical formulation provides a comprehensive understanding of Euler angle errors in AHRS.
This method enables the analytical investigation of individual sensor error impacts on orientation accuracy.
The findings are applicable to random alignment scenarios in navigation systems.