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In the past few decades, the localization literature has seen many modelsattempting to characterize the non-line-of-sight (NLOS) bias error commonlyexperienced in range measurements. These models have either been based onspecific measurement data or chosen due to attractive features of a particulardistribution, yet to date, none have been backed by rigorous analysis.Leveraging tools from stochastic geometry, this paper attempts to fill thisvoid 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 NLOSpath is characterized. Under these assumptions, this analysis reveals that NLOSbias exhibits an exponential form and can in fact be well approximated by anexponential distribution -- a result consistent with previous NLOS bias errormodels in the literature. This analytically derived distribution is thencompared to a common exponential model from the literature, revealing thisdistribution to be a close match in some cases and a lower bound in others.Lastly, the assumptions under which these results were derived suggest thismodel is aptly suited to characterize NLOS bias in 5G millimeter wave systemsas well.

A Mathematical Justification for Exponentially Distributed NLOS Bias