Active travel researchers often use satellite navigation data to investigate relationships between behaviour, infrastructure, environmental exposures, and/or health. These studies often employ map-matching algorithms to convert the raw waypoints into trajectories through a transport network. While less common, satellite navigation data can also be used to investigate motion characteristics such as variations in speed and acceleration, which is especially relevant for investigating safety and physical activity. Emerging literature has demonstrated the value in combining map-matching with motion characteristics, but current methods are unreliable on noisy data. We present an open-source framework that integrates state-space modelling and map-matching to produce precise trajectories and consistent motion profiles using satellite navigation data. Our methodology takes advantage of additional information provided the raw waypoints (e.g., speed, accuracy) and knowledge of physical motion to capture plausible active travel behaviour even with noisy and variable-quality data. Through several examples, we demonstrate how the integrated methodology can produce more accurate motion profiles and map-matched trajectories versus existing methods, which is especially beneficial for data from older devices. This framework aims to support active travel research particularly in safety, environmental epidemiology, and physical activity, by enabling investigators to take greater advantage of available satellite navigation and network data.