Why a fit can remain numerically unresolved
In the prediction pilots, a fit reconstructs an aircraft path from the IMU measurements while estimating calibration. Before its model comparison is accepted, a fresh calculation checks that the solver has settled. For an ordinary nonzero-cost fit, several checks must pass together. Near-zero generated controls have a separate, tested repeat rule.
| Check | What it asks |
|---|---|
| Stationarity | Would a permitted small calibration change still substantially improve the fit? |
| Cost stability | Does a fresh correction leave the weighted mismatch effectively unchanged? |
| Position stability | Does that correction leave the calculated positions unchanged to within the declared numerical tolerances? |
The position-stability limits are 1 mm RMS and 1 cm maximum on each axis. These compare two calculated paths. They are not accuracy limits against the receiver, sensor specifications or confidence intervals. A numerically settled fit can still predict the unused receiver observations badly.
The separate cost check can fail even when the position change is very small. That calls for diagnosing the numerical calculation; it does not count as evidence for or against a physical model. The original fit label stays unchanged.
For the first ESA pilot, a saved-results audit finds 15 fits satisfying all these checks, eight failing the RMS position check, and one failing both RMS and maximum position checks. This agrees with its original 15 numerical passes and nine unresolved fits.
The shared diagnostic verifies saved fit hashes and reads thresholds from the study's frozen source. It performs no fit or trajectory integration and does not apply a revised stopping rule. The completed gravity revision has eight numerical passes, nine position-stability failures and seven cost-stability failures. All eight specified-field forecasts meet the physical accuracy limits, but only one passes the numerical gate. The other seven remain ineligible for model comparisons. The completed fixed-point diagnostic reproduces every saved cost and numerical outcome. Repeated calculations are identical, while very small calibration changes still upset cost stability. For the field-globe cases, local position changes remain below 4 micrometres. The completed precision comparison reproduces both original residual vectors exactly in binary64. Wider integration precision brings all eight field-globe cost changes below the same limit. Changing only longitude wrapping is insufficient. No threshold or original fit label changes; all 48 long known-motion derivative controls now pass, and the 24-case training study qualifies every case under the unchanged stopping and accuracy checks. The matched observed revision now returns 22 numerically qualified forecasts after 56 source-bound adapter/audit checks. All eight earlier passes are retained and fourteen more starts qualify. Two disc starts reach the cooperative runtime ceiling; those are incomplete calculations, not model ties. Original failed fits keep their historical labels.