  Mobile sensing enabled by GPS or smart phones has become an increasingly
important source of traffic data. For sufficient coverage of the traffic
stream, it is important to maintain a reasonable penetration rate of probe
vehicles. From the standpoint of capturing higher-order traffic quantities such
as acceleration/deceleration, emission and fuel consumption rates, it is
desirable to examine the impact on the estimation accuracy of sampling
frequency on vehicle position. Of the two issues raised above, the latter is
rarely studied in the literature. This paper addresses the impact of both
sampling frequency and penetration rate on mobile sensing of highway traffic.
To capture inhomogeneous driving conditions and deviation of traffic from the
equilibrium state, we employ the second-order phase transition model (PTM).
Several data fusion schemes that incorporate vehicle trajectory data into the
PTM are proposed. And, a case study of the NGSIM dataset is presented which
shows the estimation results of various Eulerian and Lagrangian traffic
quantities. The findings show that while first-order traffic quantities can be
accurately estimated even with a low sampling frequency, higher-order traffic
quantities, such as acceleration, deviation, and emission rate, tend to be
misinterpreted due to insufficiently sampled vehicle locations. We also show
that a correction factor approach has the potential to reduce the sensing error
arising from low sampling frequency and penetration rate, making the estimation
of higher-order quantities more robust against insufficient data coverage of
the highway traffic.
