Fig. 4

Steps in the FPA estimation approach. FPA estimation approach using gyroscope (\(\omega _t^X\)) and accelerometer (\(a_t^X\)) data: a sensor angular velocity is corrected using the Zero Angular Velocity Update (ZAVU). Next, it is rotated to the foot frame (\(\psi ^{F}\)) by using the mapping between the sensor and foot frames (\(R^{XF}\)). The orientation of the dynamic foot frame (\(R^{F_i}_t\)) is determined by integrating this angular velocity and initializing it with \(R^{F_i}_{t_0} = I\). b Acceleration information is rotated to the dynamic foot frame (\(\psi ^{F_i}\)), such that the gravitational acceleration can be subtracted to obtain the estimated free acceleration (\(a^{F_i}_{e,t}\)). This is integrated to velocity (\(v^{F_i}_{e,t}\)) by initializing it with \(v^{F_i}_{t_0} = 0\), which in turn is corrected using ZUPT. After another integration step (initialized with \(p^{F_i}_{t_0} = 0\)) the position of the foot is calculated in the dynamic foot frame. c Since everything is calculated in \(\psi ^{F_i}\) the FPA is estimated using a trigonometric relation of the foot position at the end of the step (\(t_{end}\))