How many redundant sensors does a twin with independent errors say a robot needs?
research/fusion-twin
How many redundant sensors a twin with independent errors says a robot needs: exact equicorrelated fused variance, n_eff < 1/ρ and a floor σ√ρ, twin says 16 sensors vs real 30 (ρ=0.03) or none (ρ≥0.0625), 3σ gate false-alarms 8.6× too often, and a plug-in ρ repair that misses the target about half the time.
What it found
Redundant sensors that share an error source have pairwise correlation ρ; the equal-weight fused variance is exactly σ2(1+(n−1)ρ)/n, so a twin with independent errors understates the fused std by √(1+(n−1)ρ), n sensors are worth fewer than 1/ρ independent ones, and no fleet beats σ√ρ. For a target std of 0.25σ the twin says 16 sensors; the real fleet needs 30 at ρ=0.03, 77 at 0.05, 376 at 0.06 and none at 0.0625 or above. A 3-σ gate sized from the twin false-alarms 8.6× too often at ρ=0.05 (n=16). Repair from calibration logs is mixed: the estimated ρ is unbiased, but a plug-in fleet size misses the target in about half of repeats; a 90% bootstrap upper bound misses in 8.5% (T=400) at almost twice the sensors, and short logs cannot support the target. Stylised: equal-variance Gaussian errors with one common factor, simulated fleet, no sensor data.
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.