# A Novel AHRS Inertial Sensor-Based Algorithm for Wheelchair Propulsion Performance Analysis
## 1 Introduction
Although feasible, this methodology requires the accurate measurement of wheel camber and then computational adjustment to rotate the sensor's local frame of reference in order to ensure that the rotational measurement from the inertial sensor is completely in the rotational axis of interest. [PERSON] et al. [11] describes the importance of this rotation due to wheel camber, to \"_couple_\" or align the angular velocity of the individual wheel and the wheelchair itself. This then also places large importance on camber measurement, which can be difficult to measure in practice. Furthermore, it also adds complexity to algorithmic development and data analytics. Utilising sensor fusion algorithms, it is possible to create camber agnostic algorithms, ensuring sensor alignment against a global reference and mitigating against computational and mismeasurement errors due to wheel camber rotations. One sensor fusion method that achieves a global reference is the Attitude and Heading Reference System (AHRS) [14]. It provides a complete orientation relative to the direction of gravity and the Earth's magnetic field. [PERSON]'s open-sourced AHRS implementation [14] is designed for either a six degree of freedom (DOF) IMU using accelerometers and gyroscopes to provide attitude, which is relative to the direction of gravity; or, with the addition of magnetometers, a nine DOF IMU package termed Magnetic, Angular Rate, Gravity (MARG) sensors which can provide a complete orientation with respect to the Earth's magnetic field. Traditionally, a Kalman Filter (KF), or an Extended Kalman Filter (EKF) has become the accepted practice for the majority of orientation filter algorithms. Standard KF are limited by complex implementations, the requirement of high sampling rates (which can exceed typical IMU sensors), and can be computationally expensive [14]. The [PERSON] AHRS implementation is a computationally inexpensive, accurate, and tuneable filter. The filter achieved a static RMS error of \(<0.8^{\circ}\) and a dynamic RMS error of \(<1.7^{\circ}\)[14], indicating suitability for wheelchair orientation. The algorithm also has embedded compensation for gyroscopic drift, a common occurrence due to temperature or motion artefact and magnetic distortion compensation. Additionally, due to its low processing power, it is suitable for real-time and embedded applications, rendering it an ideal filter for wheelchair propulsion analysis. With any technology and accompanying algorithm used for elite sports monitoring, the accuracy, validity, and reliably of measurements is paramount. [PERSON] et al. (2015) investigated the reliability and validity of inertial sensors on wheelchair court sports in comparison to high speed video. In terms of speed, the sensor and his algorithmic implementation was found to be reliable, never exceeding a coefficient of variation of 0.9% at any speed. Peak speed was also proven valid using an IMU device with a coefficient of variation of 1.6%, concluding that IMUs are a capable and valuable tool for assessing aspects of linear wheelchair performance. To evidence the validity of spatial tracking in non-linear propulsion, [PERSON] et al. (2015) used 20 participants to compare IMU-based kinematic estimations to a gold standard 24-camera optimal motion analysis system across 21 tasks encompassing typical wheelchair basketball movements. The researchers used intraclass correlation (ICC) to assess IMU-based test outcomes for linear speed (ICC > 0.9), rotational speed (ICC > 0.99), and instantaneous rotation center (ICC > 0.90), showing very high correlations to the gold standard motion capture. This evidences that IMU technology has the potential to accurately and reliably measure in-game propulsive elements. The desire to measure fundamental contextual propulsion characteristics, including distance, velocity, and trajectory in a camber agnostic and sensor-minimal system has led to the development of a new algorithm based on the computationally efficient open-sourced [PERSON]'s AHRS algorithm.