A satellite-positioning twin with white range noise certifies an error radius the real receiver does not meet: how wrong is it once multipath is correlated, and does averaging fix it?

research/gnss-twin

A white-noise satellite-positioning twin vs a receiver with correlated multipath: exact HDOP √(4/n) and bias map 2b/n, averaging loses the 1/√T gain (95% radius covers 33% at T=10, 5% at T=100), and a residual integrity test tuned on the twin false-alarms 21% at equal multipath. Stylised.

9 tests

What it found

Real receiver: 2-D position and clock from n pseudoranges with multipath; twin: white noise σ only. For an evenly spread constellation HDOP is exactly √(4/n) (simulated to 0.3%) and collapses to 4.25 over a 90° arc; one biased satellite of size b moves the fix by exactly 2b/n toward that satellite, which no amount of averaging removes. With AR(1) multipath (ρ = 0.99) the twin predicts a 1/√T gain but the simulated error only falls from 1.58 to 0.80 m over 500 epochs (exact 0.80), and a 95% radius calibrated on single epochs covers 33% of fixes at T = 10 and 5% at T = 100 (exact 31% and 5%). A residual integrity test tuned to 1% false alarms on the twin alarms 21% of the time when multipath equals the noise (exact closed form), and the statistic rises by only b²(1−3/n) while the position bias is 2b/n. Stylised: 2-D, linearised, evenly spread or arc constellations, stationary AR(1) multipath.

A figure from its own output

Figure produced by research/gnss-twin: rms_vs_T — gnss-twin/experiments/rms_vs_T.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.