# A Novel AHRS Inertial Sensor-Based Algorithm for Wheelchair Propulsion Performance Analysis
## 1 Introduction  
The rapid development of microelectromechanical systems (MEMS) technology has afforded the use of small, ubiquitous sensors for performance tracking across a variety of sporting domains. Within the field of wheelchair court sports, inertial measurement unit (IMU) MEMS technologies are the most obvious way of tracking wheelchair performance in the field [1]. IMU sensors predominately contain accelerometers and gyroscopes, allowing for biomechanical data to be both captured and analysed in the natural performance environment at low cost [2]. The efficacy of IMUs for wheelchair propulsion metrics has been evidenced by researchers [3; 4]; however, the reliability of these metrics (most commonly velocity, distance, and trajectory) are highly dependent on processing algorithms [5]. Researchers who have investigated wheelchair propulsion using inertial sensors have adopted a few different algorithmic approaches. [PERSON] et al. [3] used a one IMU sensor approach to find push cycle duration and frequency from the forward component of acceleration using a sensor placed on the backrest of the wheelchair. A pitch-roll-yaw 5 s static hold and rotate calibration sequence was employed to ensure all the forward power was in the forward direction of the IMU. This approach is effective, although it only gives accurate information for purely linear acceleration. The vast majority of wheelchair sports--with the exception of the 100 m sprint--contains non-linear propulsivecomponents, rendering this method inappropriate for in-game propulsion measures. Two additional wrist IMU sensors were used to provide further propulsion performance information, including bilateral acceleration synchronicity for a 20 m sprint task. Wrist-based auxiliary algorithms [3], when linked with trajectory information, could be an aid to inform tactics and coaching instruction, or, when linked with player load information, could aid in monitoring fatigue and reducing the risk of injury. Reducing the number IMUs is an obvious advantage, as it reduces costs, reduces algorithmic complexity, and improves ease of implementation. [PERSON] [6] also used a single accelerometer sensor to track velocity and trajectory; however, manual syncing was required using additional technologies--from video and stopwatches--in order to calculate the propulsion performance features. [PERSON] et al. [7] also adopted a single accelerometer approach utilising a fractional dimension algorithmic approach to classify in-game activities in a wheelchair rugby game. Augmented with accurate contextual information, including positioning, velocity, and travelled distance, the activity classification algorithm of [PERSON] et al. [7] has the potential to provide the coach with heightened performance understanding. [PERSON] et al. [5, 8], [PERSON] et al. [9], [PERSON] et al. [4, 10], [PERSON] et al. [11], and [PERSON] et al. [12] utilised wheel-based rigidly mounted gyroscopes to calculate wheelchair propulsion characteristics. These rate gyroscope algorithms have been used to detect angular velocity [2, 4, 8, 9, 10, 11, 12], linear ground velocity [7, 8, 10, 11, 12], distance [2, 4, 8, 11, 12], and trajectory [7, 8, 11], and when combined with Bluetooth [12] or radio-frequency (RF) modules [9, 11] have been used to display this information in real-time. The authors all concluded that measuring performance-based outcomes in both game and training settings is \"highly feasible\" [4]. The suitability of gyroscopes is highlighted by [PERSON] et al. [12], commenting that a \(\pm 6000^{\circ}/\mathrm{s}\) rate gyroscope on a wheel has the theoretical accuracy to measure speeds of up to 64 km/h on a 24 inch wheelchair wheel--well above the fastest recorded flat land wheelchair speed [12]. Where distance [2, 4, 8, 11, 12] is reported, the authors utilised double integration to approximate distance from acceleration; however, this methodology has an error amplification effect [13].