Road Slope Estimation in Bicycles without Torque Measurements

Electrically Power Assisted Cycles (EPACs) have been gaining increasing attention worldwide during the past few years. The delivery of a good assistance during inclines makes or destroys an EPAC. This paper addresses the low-cost estimation of road slope on bicycle without pedaling torque measurement. Two estimation algorithms are discussed. A full 6 Degrees of Freedom kinematic Extended Kalman Filter and a simpler, more cost-effective 2 DoF Kalman filter based on the longitudinal kinematic model. The proposed reduced-sensor algorithm is shown to be very accurate during straight running; however it is affected by errors during cornering. This issue is addressed by augmenting the filter with a curve correction algorithm. The curve correction algorithm, based on a time-varying low pass filter is detailed and validated on experimental data, comparing the estimated road slope against cartographic data.