The Impact of Road Configuration on V2V-based Cooperative Localization

Cooperative localization with map matching has been shown to reduce Global Navigation Satellite System (GNSS) localization error from several meters to sub-meter level by fusing the GNSS measurements of four vehicles in our previous work. While further error reduction is expected to be achievable by increasing the number of vehicles, the quantitative relationship between the estimation error and the number of connected vehicles has neither been systematically investigated nor analytically proved. In this work, a theoretical study is presented that analytically proves the correlation between the localization error and the number of connected vehicles in two cases of practical interest. More specifically, it is shown that, under the assumption of small non-common error, the expected square error of the GNSS common error correction is inversely proportional to the number of vehicles, if the road directions obey a uniform distribution, or inversely proportional to logarithm of the number of vehicles, if the road directions obey a Bernoulli distribution. Numerical simulations are conducted to justify these analytic results. Moreover, the simulation results show that the aforementioned error decrement rates hold even when the assumption of small non-common error is violated.