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Walking speed is an important determinant of energy expenditure. We present the use of Gaussian Process-based Regression (GPR), a non-linear, non-parametric regression framework to estimate walking speed using data obtained from a single on-body sensor worn on the right hip. We compare the performance of GPR with Bayesian Linear Regression (BLR) and Least Squares Regression (LSR) in estimating treadmill walking speeds. We also examine whether using gyroscopes to augment accelerometry data can improve prediction accuracy. GPR shows a lower average RMS prediction error when compared to BLR and LSR across all subjects. Per subject, GPR has significantly lower RMS prediction error than LSR and BLR (p <; 0.05) with increasing training data. The addition of tri-axial gyroscopes as inputs reduces RMS prediction error (p <; 0.05 per subject) when compared to using only acclerometers. We also study the effect of using treadmill walking data to predict overground walking speeds and that of combining data from more than one person to predict overground walking speed. A strong linear correlation exists (rX,Y = .8861) between overground walking speeds predicted from treadmill data and ground truth walking speed measured. Combining treadmill data from multiple subjects with similar height characteristics improved the prediction capability of GPR for overground walking speeds as measured by correllation between ground truth and GP-predicted values (rX,Y = .8204 with combined data).