How wrong is a twin's localisation error when real ranges have non-line-of-sight bias?

What it found

A twin draws anchor ranges as true distance plus Gaussian noise; real sites also have long-biased NLOS ranges. On a ring of anchors the rms position error is exactly GDOP·√(σ²+p(2−p)m²) (1.105 vs law 1.095 m at p=0.1, n=6), 4.5× and 7.3× the twin's at p=0.1 and 0.3, with zero mean. A blocked side is a bias the linear formula predicts to about 0.02 m per coordinate (0.924 vs 0.930 m) while the twin predicts none. Sized on the twin, a 1 m / 95% corridor needs 4 anchors; the NLOS site needs about 28 (p=0.1) or 46 (p=0.2), and the 4-anchor ring leaves the corridor 34.7% of the time instead of 5%. Dropping the largest-residual anchor cuts rms error 0.947→0.414 m at p=0.1 but costs 24% with no NLOS. Stylised: 2-D ring, iid exponential NLOS, simulated site, no sensor data.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
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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.