Calibration can hide an acceleration-only difference
The gyro-removal diagnostic compares acceleration magnitudes without supplying an assumed aircraft orientation. A new known-answer control shows why that comparison also needs a calibration-identifiability check.
On the constructed constant-height eastbound leg, one constant accelerometer gain change of 0.066–0.307% erases every wrong-model magnitude difference. The same gain applies to all three axes and all 21 epochs, including two changing instrument orientations. No per-epoch adjustment, bias or gravity change is needed. All nine truth/candidate combinations pass this mathematical control.
This is a limitation of the scalar diagnostic, not a finding about the airborne measurements. It does not change the completed 53-stretch full-position results.
Why it happens
For constant required force magnitude, let the generated measurement have magnitude \(m\) and a candidate require magnitude \(q\). With the calibration convention \(f_{\rm corrected}=f_{\rm measured}/(1+g)\), setting
makes their magnitudes agree. Rotating the body axes does not change this result. On a changing trajectory, one constant gain need not match every epoch; the part of the difference that varies over time must be assessed separately.
| Generated truth | Comparison candidate | Constant gain change | Largest uncorrected gap (m/s²) |
|---|---|---|---|
| Specified-field globe | Zero-field globe | −0.2406% | 0.0235885 |
| Specified-field globe | Stationary disc | −0.3065% | 0.0300683 |
| Zero-field globe | Specified-field globe | +0.2412% | 0.0235885 |
| Zero-field globe | Stationary disc | −0.0661% | 0.00647984 |
| Stationary disc | Specified-field globe | +0.3074% | 0.0300683 |
| Stationary disc | Zero-field globe | +0.0661% | 0.00647984 |
Every corrected gap is below 4 × 10⁻¹⁵ m/s². The existing exploratory model permits axis gain changes up to ±15%; that is an assumed search bound, not a measured device error. These controls neither estimate actual gains nor justify changing the bound. Same-model controls recover zero gain within numerical rounding.
The nine known-answer tests use the independent Cartesian reference motion and the receiver-force adapter. The complete numerical table retains all nine combinations. No archive file, fused navigation, observed fit or native integration is used. These are ordinary software controls, separate from the completed frozen error-budget matrix.
Consequence for the next comparison
The subsequent 72-case local calibration matrix is complete. Straight-leg differences disappear in its projection; changing motion retains local differences, but all wrong-model changing-motion linear corrections exceed the permitted bounds. A bounded nonlinear check is needed before those differences can be interpreted.
The bounded nonlinear follow-up passes its twelve known-answer starts but only 32/72 complete matched comparisons. It is finished; incomplete repeat comparisons still block observed channel fitting. The roadmap records the remaining qualification and independent measurement-error tasks.
An acceleration-only model ranking with calibration fixed cannot establish which part of the original separation requires gyroscopes. Before recorded-data use, test whether differences remain after the allowed calibration freedoms:
- Start with changing-speed, changing-heading and changing-latitude controls. Compare complete time histories with one shared calibration per constructed recording, rather than matching each epoch separately.
- Include all three acceleration gains, all three offsets and gravity. A surviving difference after only isotropic gain removal is insufficient. Check nonlinear ambiguity as well as local rank; retain unidentifiable nuisance directions.
- Specify the quantization, noise, time association and averaging model equally for every candidate. Select support using receiver motion and completeness, before examining observed model residuals.
- If the remaining information is inadequate, report that limitation and retain the full-vector analysis. Do not tighten bounds or choose favorable windows to create a separation.