  Cooperative map matching (CMM) uses the Global Navigation Satellite System
(GNSS) positioning of a group of vehicles to improve the standalone
localization accuracy. It has been shown to reduce GNSS error from several
meters to sub-meter level by matching the biased GNSS positioning of four
vehicles to a digital map with road constraints in our previous work. While
further error reduction is expected by increasing the number of participating
vehicles, fundamental questions on how the vehicle membership of the CMM
affects the performance of the GNSS-based localization results need to be
addressed to provide guidelines for design and optimization of the vehicle
network. The quantitative relationship between the estimation error and the
road constraints has to be systematically investigated to provide insights. In
this work, a theoretical study is presented that aims at developing a framework
for quantitatively evaluating effects of the road constraints on the CMM
accuracy and for eventual optimization of the CMM network. More specifically, a
closed form expression of the CMM error in terms of the road angles and GNSS
error is first derived based on a simple CMM rule. Then a Branch and Bound
algorithm and a Cross Entropy method are developed to minimize this error by
selecting the optimal group of vehicles under two different assumptions about
the GNSS error variance.

Systems and Control