Saved prediction errors: scope and safeguards
Question
How do the saved errors grow after training, and what temporal and cross-axis structure do they contain? Do the two working error cases leave materially different patterns that should be examined before broader prediction tests?
This is a descriptive error-model assessment. It does not estimate raw GPS or gyro noise separately, calibrate confidence, change a fit or select a model. Prediction errors combine receiver, IMU, calibration and physical-model effects.
Inputs
Use the verified, closed wider-precision ESA development comparison. Preserve its source and input hashes, all 24 outcomes, the 22 completed error curves, the 800/400 training/prediction boundary and its training-only primary choices. The two deadline-limited starts remain unavailable. Analyze all completed starts; show selected primaries separately rather than counting starts as independent observations.
No original aircraft file, new position observation or protected confirmation group is an input. No IMU propagation, parameter search, refit or new forecast is permitted. Source records and numerical/accuracy labels remain unchanged.
Calculation
Use shared residual-distribution and autocorrelation helpers. Report each physical axis separately in training and prediction: mean, RMS, centred spread, absolute quantiles, cross-axis covariance/correlation, and epoch-lag correlation at 1, 5, 10, 30 and 60 samples with the actual lag times.
Also describe first differences divided by their actual time intervals. For uniformly sampled sections, report centred Fourier variance in periods longer than 60 seconds, 10–60 seconds and shorter than 10 seconds. If cadence is not uniform, flag the spectral calculation as unsupported; do not interpolate or drop measurements. Constant channels have undefined correlations, not invented zeros. These statistics do not establish stationarity or independent sample counts.
Reuse fixed sixty-second error blocks without crossing the training boundary. Report the saved weighted training RMS as a descriptive fitted statistic, not a chi-squared test or a complete prediction-uncertainty estimate. Plots use the original saved errors; no trend is removed from a prediction or score.
Qualification
Before execution, test independent constructed constant, ramp, alternating and sinusoidal series, known cross-axis relationships and Parseval variance. Check irregular timing, invalid/nonfinite input, unchanged arrays and the absence of influence from later errors on training summaries. Test preservation of missing predictions and primary selections in the study/report interfaces.
Bind the complete source list and environment before the qualification report is produced. Freeze the closed parent report and exact curve artifacts before the diagnostic starts. Reuse the shared study lifecycle and append-only work journal, without copying a worker or numerical library tree.
Separate finite allowance
One diagnostic start, one numerical thread, at most 24 saved curves and 28,800 saved error epochs; each curve is capped at 1,200 epochs with 800 training rows. There are at most 24 section-pair summaries and five declared correlation lags. Each complete curve has two position-error sections and two first-difference sections, each with three axis spectra. The cooperative ceiling is five minutes. Native integration calls, optimizer starts, new propagations and original/protected reads are all zero. There are no retries.
Charge saved-curve and epoch processing before the calculation. Record actual work and preserve failures. Audit and package the saved statistics without any fit or propagation. No remaining allowance from the observed run is reused.
Interpretation
Fitted training errors and their correlations are not independent validation. Later positions were excluded from fitting, but this recording has informed method development. Estimated correlations and ranges are descriptive, not calibrated coverage or a total receiver/IMU noise law. Do not alter an error policy merely to favour a physical candidate.
Results guide the next error-law qualification and broader predictive tests. The 53-stretch findings and seven protected ESA groups remain unchanged.