How the airborne analysis has developed

Local Level Lab compares recorded aircraft motion under competing surface geometries. An IMU (inertial measurement unit) measures turning and acceleration; a GPS receiver records the aircraft's route. This page explains how the analysis was built and checked. The methodology explains the measurement principle, and the findings document the selected tracks and results.

1. Establish the observations and freeze the selection

NASA's ILVIS0 recordings supported airborne lidar surveys. The analysis preserves the original IMU increments and reconstructs positions from the primary receiver's recorded output. The combined IMU/GPS navigation solution is used for decoder checks and motion screening, not as fitted evidence. Receiver coordinates still use geodetic conventions; separate recorded streams do not make the comparison free of coordinate assumptions. The archive guide describes decoding and provenance.

All 232 retained recordings were screened before model comparison. Eligibility requires at least four continuous minutes, every supported receiver speed reading at least 700 km/h, and the frozen motion, timing and completeness rules. This produced 53 stretches totaling 424.3 minutes. The selection record preserves exact intervals, source hashes, speeds and exclusions.

Each complete stretch is fitted jointly under three candidates: globe with a specified background rotation field, globe with zero background field, and the specified stationary flat disc. Two processing cases allow either no upstream field removal or a shared amount removed onboard. Both allow constant gyro offsets of ±1 degree/hour. That is a sensitivity assumption, not a measured drift specification.

Shape is evaluated first, comparing the disc with the better globe fit. A background-field comparison is reported only after all required fits finish and both processing cases favor globe. Shorter residual sections are consistency checks, not additional flights.

2. Complete the first comparison and audit its coverage

The twelve completed comparisons also favor the specified background field over zero. These are substantial empirical preferences. Unfinished calculations do not give the models equal support, and successful numerical completion does not mean equal fit quality. Some recordings overlap or share instruments; these are not automatically twelve independent replications. Statistical significance has not yet been calibrated.

The completed recovery adds twenty-nine complete globe comparisons, including IMU8 stretches: 41 globe preferences, zero flat, 12 unresolved. All forty-one also favor the specified background field. The original table above remains the first-pass result; updated findings and source tracks show the additional evidence and its recording overlap.

The earlier six-recording pilot found two complete globe preferences under its four tested cases, two partial globe-favoring comparisons, and two recordings without complete shape comparisons. It remains a separate preserved study.

The post-run review found that most unfinished fits exhausted their numerical allowance. The calibration and fit-quality audit compared the same twelve resolved stretches under both processing cases: median horizontal mismatch was 0.068 m for the background-field globe, 29.5 m for the zero-field globe and 47.1 m for the disc, using each candidate's declared coordinate metric. These are errors against observations used for fitting, not independent predictions. The audit also found frequent calibration parameters at their permitted limits.

3. Separate integration timing from calibration readjustment

The epoch-level diagnostic reproduced individual saved track errors on two recordings without refitting. Replacing nominal 200 Hz intervals with elapsed packet-header time at the same parameters increased vertical error from roughly 0.6–0.7 m to 9.2–9.4 m. A timestamp need not describe exactly the integration interval represented by an increment.

The subsequent matched clock comparison refitted all three models under both processing cases on the completed control. All six fits converged and retained the globe and background-field preference; calibration readjustment restored vertical error to about 0.70 m. The clock/calibration audit showed gravity correction moving away from its limit while Z-axis gyro gain and offset stayed at theirs. This demonstrates sensitivity and readjustment, not independent proof of the correct clock.

A separate within-interval integration comparison finished four of six fits and retained the Z-axis limits. It did not qualify a replacement for the original method.

4. Check whether extreme Z-axis corrections create the preference

The twelve-fit calibration comparison finished eleven fits. Fixing Z gain to zero preserved globe and background-field preferences under both processing cases. Fixing Z offset to zero left one required fit unfinished, so that comparison remained unresolved.

The next tests fixed gain and offset together across a small grid, allowing all other parameters their original bounds:

The grid spans Z gyro gain −2%, zero and +2%, and constant offset −1, zero and +1 degree/hour. On the first recording, background-field horizontal errors remained 0.081–0.093 m, versus 29.0–29.6 m for zero-field globe and 63.6–64.1 m for the disc. The preferred fits needed at most one remaining parameter at its limit. The advantage therefore did not require the original extreme Z corrections. These tests do not identify the instrument's true calibration and are repeated checks, not new flights.

The saved follow-up audit compares all 81 fits and preserves the two unfinished labels despite their small errors and passing saved stationarity checks. The profiled removal fraction on the first recording stayed essentially zero. The second recording's full-grid background-field conclusion remains withheld.

5. Examine uncertainty and predictions beyond fitted observations

Small errors alone do not establish reliable uncertainty. The residual correlation audit found slow vertical correlation on October 5, including errors a minute apart, with less slow correlation on September 24. The original uncertainty adjustment did not remove all dependence. A shared correlated-error alternative is development work, not a calibrated replacement likelihood.

Software uncertainty controls check correlated errors, training-only estimation, nonlinear behavior and calibration limits. Native integration controls check all 27 calibration and processing derivatives against independently constructed paths. These validate calculations rather than certify observational uncertainty.

The retrospective prediction trial finished five of six fits. The later training/prediction covariance comparison finished ten of twelve; its combined comparison remains unresolved. Predictions on reserved times are more informative than fitting those times, but these development tests do not constitute independent-flight confirmation.

6. Qualify numerical recovery before extending it to the unfinished stretches

A solver is the numerical procedure that searches for the best permitted fit. Its completion checks assess both proximity to an optimum and whether another feasible step materially changes the result. A failed check is not evidence for either geometry.

| Paired wider-arithmetic qualification | 16/16 fits passed in 129 sweeps, including both controls and repeats. Two additional stretches resolve, bringing the tally to 32/0/21. Physical assumptions and numerical stopping tolerances unchanged. |

| Completed cost-only precision recovery | 83/86 fits passed in 891 sweeps and about four hours. Both controls and all twelve repeats passed; nine more stretches have complete comparisons. Current tally: 41 globe, zero flat, 12 unresolved. Three primary fits exhausted their small evaluation allowance; all prior failures remain preserved. |

Software controls have known answers and expose numerical failures without choosing favorable flight data. Their success cannot guarantee success on the archive. The completed trial retains the original physical models and bounds, preserves old results, and allowed no retries. It did not qualify a full rerun of the 41 unfinished stretches.

The saved-tangent audit distinguishes ten early gradient failures, three early stability failures and three exhausted fits. A known-answer control reproduces a stall caused by starting one floating-point step inside a parameter bound. Moving such coordinates to their exact limits improves local affine-system completion from 12/24 to 16/24, but does not resolve every failure. These are numerical diagnostics, not recovered flight results.

The separate boundary-aware candidate checks each bounded linear step against the actual nonlinear cost and shortens rejected moves. It passes the predetermined nonlinear controls, including weak and redundant directions. Its final stationarity and fresh stability requirements are unchanged. Its completed observed comparison does not qualify for wider use. Saved results now locate the remaining problem in prediction-stability checks near nearly identical tracks, plus one genuinely nonstationary budget failure. The separate actual-position rule checks the full model's change in predicted receiver coordinates rather than allowing a local residual estimate alone to reject it. Covariance unwhitening is verified against direct native coordinates on independent short controls. Its 1 mm RMS / 1 cm maximum limits describe numerical stability; they do not establish instrument accuracy or calibrated uncertainty. A new finite observed trial is required before wider use.

7. Next milestone and interpretation

The priority is recovering more complete comparisons: qualify a representative subset, check repeatability under a finite budget, then prepare a separately authorized all-stretch recovery. The roadmap also tracks absolute fit adequacy, covariance calibration, receiver-coordinate and measurement-channel controls, and independent prediction. Exact device identification continues at lower priority.

A later rotation-field study will estimate the retained field's direction and magnitude freely. The present fixed-rate comparisons neither identify its ultimate cause nor distinguish solar from sidereal rate. Geometry, a measured field and its causal explanation remain separate questions. Explanations predicting identical observations cannot be distinguished by these recordings alone.