  Cooperative map matching (CMM) uses the Global Navigation Satellite System
(GNSS) position information of a group of vehicles to improve the standalone
localization accuracy. It has been shown, in our previous work, that the GNSS
error can be reduced from several meters to sub-meter level by matching the
biased GNSS positioning to a digital map with road constraints. While further
error reduction is expected by increasing the number of participating vehicles,
fundamental questions on how the vehicle membership within CMM affects the
performance of the CMM results need to be addressed to provide guidelines for
design and optimization of the vehicle network. This work presents a
theoretical study that establishes a framework for quantitative evaluation of
the impact of the road constraints on the CMM accuracy. More specifically, a
closed-form expression of the CMM error in terms of the road constraints and
GNSS error is derived based on a simple CMM rule. The asymptotic decay of the
CMM error as the number of vehicles increases is established and justified
through numerical simulations. Moreover, it is proved that the CMM error can be
minimized if the directions of the roads on which the connected vehicles travel
obey a uniform distribution. Finally, the localization accuracy of CMM is
evaluated based on the Safety Pilot Model Deployment and Pillar dataset of Ann
Arbor traffic flow collected over three years period. The contributions of this
work include establishing a theoretical foundation for CMM as well as providing
insight and motivation for applications of CMM.
