Running Speed Estimation Using Shoe-Worn Inertial Sensors: Direct Integration, Linear, and Personalized Model

The overground speed is a key component of running analysis. Today, most speed estimation wearable systems are based on GNSS technology. However, these devices can suffer from sparse communication with the satellites and have a high-power consumption. In this study, we propose three different approaches to estimate the overground speed in running based on foot-worn inertial sensors and compare the results against a reference GNSS system. First, a method is proposed by direct strapdown integration of the foot acceleration. Second, a feature-based linear model and finally a personalized online-model based on the recursive least squares' method were devised. We also evaluated the performance differences between two sets of features; one automatically selected set (i.e., optimized) and a set of features based on the existing literature. The data set of this study was recorded in a real-world setting, with 33 healthy individuals running at low, preferred, and high speed. The direct estimation of the running speed achieved an inter-subject mean ± STD accuracy of 0.08 ± 0.1 m/s and a precision of 0.16 ± 0.04 m/s. In comparison, the best feature-based linear model achieved 0.00 ± 0.11 m/s accuracy and 0.11 ± 0.05 m/s precision, while the personalized model obtained a 0.00 ± 0.01 m/s accuracy and 0.09 ± 0.06 m/s precision. The results of this study suggest that (1) the direct estimation of the velocity of the foot are biased, and the error is affected by the overground velocity and the slope; (2) the main limitation of a general linear model is the relatively high inter-subject variance of the bias, which reflects the intrinsic differences in gait patterns among individuals; (3) this inter-subject variance can be nulled using a personalized model.