A twin with an ideal magnetometer returns the true heading: how large is the hard-iron and soft-iron error, what does it do to a compass-held path, and how much of a turn does a swing calibration need?

What it found

A hard-iron offset β (relative to the field B) gives a peak heading error of exactly asin(β/B) (11.5° at 0.20, 53.1° at 0.80); soft-iron axis scaling r gives asin(|1−r|/(1+r)) (6.4° at r = 0.8), unchanged by removing the offset. A compass-held 100 m square misses its start by 2Lβ/B (2, 6, 20, 60 m at 0.01–0.3) for every offset direction tried, while the ideal twin closes to 10⁻¹⁴ m; a straight leg stays within 1 m cross-track for only 10–50 m at β/B = 0.02–0.10. A circle-fit swing calibration over a full turn has offset error ≈ 2σ/√n (0.0040 at n = 100), growing ×1.8 at 180°, ×12 at 90° and ×45 at 60° of turn (median heading residual 0.18° → 2.2° → 10.7°). Stylised: level 2-D sensor, simulated data, no gyro fusion, no ellipse fit; the 2Lβ/B closure law is verified numerically, not proved beyond first order.

A figure from its own output

Paper, code and results

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

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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.