Noise-Zero Crossing Algorithm

NZC is based on the inverted pendulum model of gait, which states that the leg alternates between advancing as a pendulum during swing phase (pivot at the hip) and as an inverted pendulum during the stance phase (pivot at the foot).  Under this mode, heel-strike is identified by the noise spike in the trough following mid-stance swing, and toe-off is identified by the moment of zero velocity following the trough before mid-stance swing.


The trough after MSw has been associated with a region of increased noise that has been observed across studies involving healthy and pathologic populations (Aminian et al., 2002Bötzel et al., 2016Greene et al., 2010 ;  Salarian et al., 2004) in which wavelet transforms and filtering techniques were used to reduce noise to reliably identify the trough. NZC proposes that the universality of this noise can be exploited to identify HS without filtering.


Bötzel et al. note that TO occurs after the second trough in the shank angular velocity signal, but prior to forward velocity. They explain their findings with the physiologic argument that the minimum of the second trough physically represents the point at which the shank begins to decelerate. They argue that TO should occur sometime after that deceleration begins, but before the limb begins to advance about the opposite pivot, represented by the inception of positive angular velocity. We posit that TO can thus be estimated as the zero-crossing after MSt, which is the precise moment of zero shank angular velocity.

NZC algorithm implementation

The NZC algorithm is outlined in the figure above.  NZC waits for the first zero-crossing after the onset of walking. If the slope is negative, the algorithm waits for the onset of noise, defined as the first sample where the slope of the signal becomes positive, checks whether that sample is the minimum swing period from the last transition point (τST), and stores that point as a swing-to-stance heel-strike event (SWtoST). If the slope is positive, the algorithm checks whether the current sample is at least the minimum stance period from the last transition point (τSW) and stores this point as a stance to swing toe-off event (STtoSW). Transition points consist of STtoSW and SWtoST events. Minimum swing and stance periods were defined a priori using knowledge of gait phase knowledge and manually verified for accuracy. For each sample, gait phase is assigned as stance if the most recent transition point was SWtoST or swing if it was STtoSW. GCT, SLS, and DLS time intervals are computed using the gait phase from both limbs.

Missing Sample Algorithm

This paper presents a novel, practical, and effective routine to reconstruct missing samples from a time-domain sequence of wirelessly transmitted IMU data during high-level mobility activities. Our work extends previous approaches involving empirical mode decomposition (EMD)-based and auto-regressive (AR) model-based interpolation algorithms in two aspects: 1) we utilized a modified sifting process for signal decomposition into a set of intrinsic mode functions with missing samples, and 2) we expand previous AR modeling for recovery of audio signals to exploit the quasi-periodic characteristics of lower-limb movement during the modified Edgren side step test. To verify the improvements provided by the proposed extensions, a comparison study of traditional interpolation methods, such as cubic spline interpolation, AR model-based interpolations, and EMD-based interpolation is also made via simulation with real inertial signals recorded during high-speed movement. The evaluation was based on two performance criteria: Euclidian distance and Pearson correlation coefficient between the original signal and the reconstructed signal. The experimental results show that the proposed method improves upon traditional interpolation methods used in recovering missing samples. Read more here