A Complementary Filter for Tracking Bicycle Crank Angles Using Inertial Sensors, Kinematic Constraints, and Vertical Acceleration Updates

In-field tracking of crank angles is important for analyzing outdoor cycling biomechanics, but current encoder-based methods are expensive and time-consuming. Inertial and magnetic measurement systems (IMMSs) have the potential for minimally invasive crank angle tracking, although errors due to magnetic interference and static calibration hinder performance. This paper presents a nonlinear complimentary filter, called the constrained rotational acceleration and kinematics (CRANK) filter, which estimates crank angles without magnetometer measurements or a static calibration for the crank arm IMMS. The CRANK filter removes drift errors by exploiting constraints on the kinematics of the crank arm relative to the bicycle frame. Three 5 min cycling tests were conducted using stereophotogrammetry and two IMMSs; a slow ( $\sim 80$ r/min) and medium (90 r/min) cadence test on a level surface and a fast cadence test (100 r/min) with the bicycle inclined at 20° to the ground. A novel two-segment methodology for collecting ground truth data with an optical motion capture system is presented. We also provide analysis of CRANK filter performance for simulated outdoor dynamics (lateral tilt and roll). The CRANK filter achieved absolute errors (AEs) of 0.9 ± 0.6°, 1.7 ± 1.4°, and 1.8 ± 1.2° for the slow, medium, and fast tests, outperforming a commercial Kalman filter that produced AEs of $\sim 10^{\circ }$ . Under simulated outdoor conditions the CRANK filter was only slightly less accurate ( ${\rm AEs}\approx 3 {^{\circ }}$ ). The CRANK filter is shown to be accurate, drift-free, easy to implement and robust against magnetic disturbances, sensor positioning, bicycle inclination, and bicycle frame dynamics.