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On-site scale factor linearity calibration of MEMS triaxial gyroscopes

Yaqi Li, Li Wang, Zhitao Wang, Xiangqing Li, Jiaojiao Li, Steven Weidong Su

TL;DR

The paper addresses the challenge of calibrating MEMS triaxial gyroscopes for precise attitude estimation by introducing a field-ready, LS-based method that uses the constant dot product $L = \mathbf{A}^c \cdot \mathbf{G}^r$ between gravity and rotation. It leverages a 6-parameter gyroscope model and stationary accelerometer data to estimate axis scale factors via $\boldsymbol{\beta} = (\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \mathbf{l}$, with a speed constraint $ (G_x^m \hat K_x \alpha)^2 + (G_y^m \hat K_y \alpha)^2 + (G_z^m \hat K_z \alpha)^2 = n^2 $ that links to a known servo speed $n$. The method enables calibration at a single installation to obtain $K$ and then extend to multiple speeds to evaluate scale-factor linearity across a range, validated through simulations and experiments with an LSM9DS1 IMU and a servo motor. The results show high calibration accuracy, robustness to noise, and practical on-site applicability for wearable and edge devices.

Abstract

The calibration of MEMS triaxial gyroscopes is crucial for achieving precise attitude estimation for various wearable health monitoring applications. However, gyroscope calibration poses greater challenges compared to accelerometers and magnetometers. This paper introduces an efficient method for calibrating MEMS triaxial gyroscopes via only a servo motor, making it well-suited for field environments. The core strategy of the method involves utilizing the fact that the dot product of the measured gravity and the rotational speed in a fixed frame remains constant. To eliminate the influence of rotating centrifugal force on the accelerometer, the accelerometer data is measured while stationary. The proposed calibration experiment scheme, which allows gyroscopic measurements when operating each axis at a specific rotation speed, making it easier to evaluate the linearity across a related speed range constituted by a series of rotation speeds. Moreover, solely the classical least squares algorithm proves adequate for estimating the scale factor, notably streamlining the analysis of the calibration process. Extensive numerical simulations were conducted to analyze the proposed method's performance in calibrating a triaxial gyroscope model. Experimental validation was also carried out using a commercially available MEMS inertial measurement unit (LSM9DS1 from Arduino nano 33 BLE SENSE) and a servo motor capable of controlling precise speed. The experimental results effectively demonstrate the efficacy of the proposed calibration approach.

On-site scale factor linearity calibration of MEMS triaxial gyroscopes

TL;DR

The paper addresses the challenge of calibrating MEMS triaxial gyroscopes for precise attitude estimation by introducing a field-ready, LS-based method that uses the constant dot product between gravity and rotation. It leverages a 6-parameter gyroscope model and stationary accelerometer data to estimate axis scale factors via , with a speed constraint that links to a known servo speed . The method enables calibration at a single installation to obtain and then extend to multiple speeds to evaluate scale-factor linearity across a range, validated through simulations and experiments with an LSM9DS1 IMU and a servo motor. The results show high calibration accuracy, robustness to noise, and practical on-site applicability for wearable and edge devices.

Abstract

The calibration of MEMS triaxial gyroscopes is crucial for achieving precise attitude estimation for various wearable health monitoring applications. However, gyroscope calibration poses greater challenges compared to accelerometers and magnetometers. This paper introduces an efficient method for calibrating MEMS triaxial gyroscopes via only a servo motor, making it well-suited for field environments. The core strategy of the method involves utilizing the fact that the dot product of the measured gravity and the rotational speed in a fixed frame remains constant. To eliminate the influence of rotating centrifugal force on the accelerometer, the accelerometer data is measured while stationary. The proposed calibration experiment scheme, which allows gyroscopic measurements when operating each axis at a specific rotation speed, making it easier to evaluate the linearity across a related speed range constituted by a series of rotation speeds. Moreover, solely the classical least squares algorithm proves adequate for estimating the scale factor, notably streamlining the analysis of the calibration process. Extensive numerical simulations were conducted to analyze the proposed method's performance in calibrating a triaxial gyroscope model. Experimental validation was also carried out using a commercially available MEMS inertial measurement unit (LSM9DS1 from Arduino nano 33 BLE SENSE) and a servo motor capable of controlling precise speed. The experimental results effectively demonstrate the efficacy of the proposed calibration approach.
Paper Structure (11 sections, 10 equations, 11 figures)

This paper contains 11 sections, 10 equations, 11 figures.

Table of Contents

  1. Introduction
  2. calibration methodology
  3. Simulation Study
  4. Simulation at a specific speed
  5. Simulation for assessing linearity
  6. Experiment
  7. Experiment Design
  8. Results of Single Speed Point
  9. Experimental results of the linearity of the scale factor
  10. Discussion
  11. Conclusion

Figures (11)

  • Figure 1: The alignment of the IMU, local gravity, and rotational axis during the calibration process.
  • Figure 2: The dot product between the gyroscope and the accelerometer before and after calibration
  • Figure 3: The statistic results of Calibration and Uncalibration
  • Figure 4: The speed before and after calibration
  • Figure 5: The impact of different sizes of Gaussian noise on calibration results at different speeds
  • ...and 6 more figures