What approach speed can a lidar twin that returns every beam certify?
research/beam-twin
Approach speed certified by a lidar twin with independent beam dropout vs real whole-scan fades: exact scan-product miss law, real miss ~100× the level at the twin's speed, speed off 10–30% (probabilities off by orders of magnitude), sign reverses when several returns are needed, repaired by a few hundred calibration scans.
What it found
Scanning-lidar detection of a thin obstacle has an exact random-phase beam-count law and a product-over-scans miss probability (matched to a beam-pattern Monte Carlo). A twin calibrated on the mean return rate but with independent beams has no whole-scan fades; the real miss probability cannot fall below sn for n scans. At level 10−3 the twin certifies 13.3 and 12.9 m/s against the real 12.0 and 10.9 (fade rates 0.3, 0.5), with real miss probability 0.09–0.125, about 100× the level; the gap vanishes for early-visible obstacles and reverses sign when several returns are required. The probabilities are off by orders of magnitude but the speed by only 10–30%, because miss probability is a cliff in speed. A few hundred calibration scans repair it. Stylised.
A figure from its own output
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.