  In the past few decades, the localization literature has seen many models
attempting to characterize the non-line-of-sight (NLOS) bias error commonly
experienced in range measurements. These models have either been based on
specific measurement data or chosen due to attractive features of a particular
distribution, yet to date, none have been backed by rigorous analysis.
Leveraging tools from stochastic geometry, this paper attempts to fill this
void by providing the first analytical backing for an NLOS bias error model.
Using a Boolean model to statistically characterize the random locations,
orientations, and sizes of reflectors, and assuming first-order (i.e.,
single-bounce) reflections, the distance traversed by the first-arriving NLOS
path is characterized. Under these assumptions, this analysis reveals that NLOS
bias exhibits an exponential form and can in fact be well approximated by an
exponential distribution -- a result consistent with previous NLOS bias error
models in the literature. This analytically derived distribution is then
compared to a common exponential model from the literature, revealing this
distribution to be a close match in some cases and a lower bound in others.
Lastly, the assumptions under which these results were derived suggest this
model is aptly suited to characterize NLOS bias in 5G millimeter wave systems
as well.
