How many cheap gyros, fused, match one better gyro at the same cost?

What it found

Single-axis gyro model with angle random walk and rate random walk (Allan-variance terms) and a fraction ρ of each shared between units. With independent errors an array of n cheap units ties a unit k times quieter only when the price ratio exceeds k² (9 for k = 3, 100 for k = 10); shared error above 1/k² means no array size ties (k = 10, ρ ≥ 0.01). If the better unit improves white noise 10× but bias walk only 3×, the number of units needed falls from 100 at 1 s to 10 beyond 300 s, so the answer depends on integration time. Monte Carlo matches the closed form within 0.03. Stylised: illustrative grades, not datasheets; no real IMU data; no prices claimed.

A figure from its own output

Paper, code and results

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

More in Sensing, imaging and 3D

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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.