A lidar twin without atmospheric loss overstates range in fog: by how much, how sensitive is it to a mis-set extinction, and what does it do to a driving policy?

research/fog-twin

Clear-air lidar twin vs fog: detection range W(αr0)/α overstated by exactly e^{αr}, range error is W/(1+W)<1 times the extinction error, a policy sized on median fog is violated 50% of the time (5%-quantile range: 5%, 43.5% slower), and one extinction calibrated on a bright target fails for dark ones in patchy fog. Stylised.

15 tests

What it found

Detection range solves re^αr = r₀, i.e. r = W(αr₀)/α; the clear-air twin overstates it by exactly e^αr (×2.32 at 200 m visibility) and a relative extinction error moves range by the elasticity W/(1+W) < 1. With lognormal episode-to-episode fog a policy sized on the median fog is violated 50% of the time (mean fog 34%), the 5%-quantile range gives exactly 5% at a 43.5% speed cost, and in patchy fog one extinction calibrated on a bright target underestimates dark targets by up to 29% (calibrated on a dark one, bright targets are overestimated 61–168%). Stylised: hard threshold, Beer–Lambert medium, no lidar data.

A figure from its own output

Figure produced by research/fog-twin: fog_range — fog-twin/experiments/fog_range.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.