  High-resolution location ("heartbeat") data of transit fleet vehicles is a
relatively new data source for many transit agencies. On its surface, the
heartbeat data can provide a wealth of information about all operational
details of a recorded transit vehicle trip, from its location trajectory to its
speed and acceleration profiles. Previous studies have mainly focused on
decomposing the total trip travel time into different components by vehicle
state and then extracting measures of delays to draw conclusions on the
performance of a transit route. This study delves into the task of
reconstructing a complete, continuous and smooth transit vehicle trajectory
from the heartbeat data that allows for the extraction of operational
information of a bus at any point in time into its trip. Using only the
latitude, longitude, and timestamp fields of the heartbeat data, the authors
demonstrate that a continuous, smooth, and monotonic vehicle trajectory can be
reconstructed using local regression in combination with monotonic cubic spline
interpolation. The resultant trajectory can be used to evaluate transit
performance and identify locations of bus delay near infrastructure such as
traffic signals, pedestrian crossings, and bus stops.
