Comparison of quaternion-based orientation estimation methods using 9-dof marg sensors

Abstract

Orientation estimation using inertial and magnetic sensors has become a fundamental capability across robotics, autonomous vehicles, and wearable systems. Accurate and low-latency orientation tracking enables balance control, motion planning, and sensor fusion in environments where external references like GNSS or visual markers may be unreliable or unavailable. Among various representation methods, quaternions are widely adopted for their singularity-free, computationally efficient handling of 3D rotations. This thesis presents a comprehensive evaluation of quaternion-based orientation estimation algorithms using a nine-degrees-of-freedom (9-DOF) inertial and magnetic sensor also known as a magnetic, angular rate, and gravity (MARG) sensor, under various motion scenarios. These filters ranging from simple complementary filters to more advanced solutions like Madgwick, ESKF (6-DOF and 9-DOF), XKF3i, and the modular Versatile Quaternion-Based Filter (VQF), were tested for their ability to fuse gyroscope, accelerometer, and magnetometer data into consistent orientation estimates. Quaternions were used to avoid singularities and provide stable performance in dynamic multi-axis movements. Experimental validation was conducted using both free-hand and robot-guided motion. In hand trials, the IMU was manually moved through varied rotational patterns. For robot trials, a UR3 robotic arm followed pre-programmed trajectories, with the IMU rigidly mounted on its end-effector. Reference orientation was derived from an OptiTrack motion capture system and, in robot trials, forward kinematics. Two data acquisition pipelines were used: a manual logging approach for early trials and a ROS-based synchronized recording system for later robot trials, capturing IMU, motion capture, and joint states. Filter performance was assessed by comparing estimated orientations against reference data, using both quaternion-based angular errors and Euler angle deviations. Quantitative evaluation relied on Root Mean Square Error (RMSE) and normalized Integrated Time-weighted Squared Error (ITSE) metrics, which capture both instantaneous accuracy and cumulative drift over time. Results varied across motion types: filters performed similarly in slow or repetitive motion but diverged under fast or complex dynamics. Magnetometer integration generally improved yaw accuracy but introduced sensitivity to environmental disturbances. Simpler filters like Madgwick and the complementary filter offered fast computation and easy deployment, while Kalman-based methods required careful tuning but were more robust. XKF3i provided strong results but lacked transparency. The VQF filter, on the other hand, delivered the most consistent and stable performance on average - though not in all scenarios-, benefiting from its modular correction of tilt, heading, and bias. The findings highlight that no single filter excels universally; instead, trade-offs depend on application needs such as accuracy, computational load, and sensitivity to noise. Future work could include tests in magnetically disturbed environments, improved calibration and tuning automation, and extensions toward translational motion estimation or multi-IMU fusion on articulated platforms. Overall, this thesis offers a practical framework for filter selection and tuning, supporting the development of resilient orientation tracking providing a structured experimental basis for selecting and tuning orientation filters in robotics, wearable sensing, and human–machine systems.