Field Sensor Bias Calibration With Angular-Rate Sensors: Theory and Experimental Evaluation With Application to Magnetometer Calibration

Abstract

Field sensors, such as magnetometers and accelerometers, are widely used sensors for attitude estimation, yet their accuracy is limited by sensor measurement bias. This paper reports a novel methodology for estimating the sensor bias of three-axis field sensors. Our approach employs three-axis angular velocity measurements from an angular-rate gyroscope to estimate the three-axis field sensor measurement bias that, when properly calibrated, can significantly improve attitude estimation. We report three methods implementing this approach based on batch linear least squares, real-time Kalman filter, and real-time adaptive identification. Assuming the field is constant, our methods impose less restrictive conditions for the movements of the instrument required for calibration than previously reported methods, do not require a priori knowledge of the field (e.g., the magnitude of the local magnetic field) or the attitude of the instrument, and also ensure convergence for the estimated parameters. The proposed methods are evaluated and compared with the previously reported methods with numerical simulation and in a comparative laboratory and field experimental evaluation with the sensors onboard an underwater robot vehicle. Finally, as an application example of the magnetometer bias calibration, the proposed methods are used to improve the estimation of the position of an underwater vehicle in Monterey Bay at 2800 m depth.

Online 3-Axis Magnetometer Hard-Iron and Soft-Iron Bias and Angular Velocity Sensor Bias Estimation Using Angular Velocity Sensors for Improved Dynamic Heading Accuracy

“…• Two papers by Spielvogel and Whitcomb (Spielvogel and Whitcomb, 2018b;Spielvogel and Whitcomb, 2019) do not address magnetometer calibration and instead focus on the calibration of high-end 6-axis IMUs (IMUs with a 3-axis accelerometer and a 3-axis optical angular rate sensor) used in gyrocompass systems. • Spielvogel and Whitcomb (Spielvogel and Whitcomb, 2018a) extends the work by Troni and Whitcomb (Troni and Whitcomb, 2019) to 9-axis IMUs. However, the work estimates magnetometer hard-iron bias only, neglecting soft-iron calibration.…”

“…Note that the present study does not address accelerometer bias estimation, which has been addressed in previously reported studies, e.g. (Batista et al, 2011;Troni and Whitcomb, 2019).…”

“…Sensor biases change over time due to changes in the configuration and payloads of the host vehicle, temperature, etc., which make it imperative to estimate sensor biases in real time. Troni and Whitcomb (Troni and Whitcomb, 2019) report a novel method utilizing angular velocity measurements for estimating magnetometer hard-iron sensor biases, but this approach does not address soft-iron calibration and it assumes that the angular velocity sensor signal is already bias-compensated. Spielvogel and Whitcomb (Spielvogel and Whitcomb, 2018a) extend the work by Troni and Whitcomb (Troni and Whitcomb, 2019) to include estimation of angular-rate gyroscope and accelerometer measurement biases, but this approach again does not address soft-iron magnetometer bias calibration.…”

Magnetometer Calibration Using Genetic Algorithms

“…The calibration algorithm was implemented in C programming language and firstly tested on simulated dataset using consumer grade PC. It became apparent that GA is computationally demanding and requires optimization in order to execute on microcontroller [6], [7]. The following performance improvements were implemented:  mutation step reduction was changed from linear (ℎ ℎ ⋅ ) to hyperbolic; (ℎ ℎ ℎ ⋅ ⋅ ),  solution evaluation was performed on a random subset of original dataset allowing to reduce evaluation dataset for each step.…”

Adaptive bias and attitude observer on the special orthogonal group for true-north gyrocompass systems: Theory and preliminary results

“…Several methods for IMU measurement bias estimation have been reported in recent years. Much of this literature, though, focuses on magnetometer bias estimation (Alonso and Shuster, 2002a,b; Crassidis et al, 2005; Gambhir, 1975; Guo et al, 2008; Kok et al, 2012; Li and Li, 2012; Spielvogel and Whitcomb, 2018; Troni and Whitcomb, 2013; Troni and Whitcomb, 2019).…”