When measurement errors persist over time

Averaging reduces independent noise. An error that persists through many samples can survive that averaging and resemble a physical signal. This study asks how much that matters for the experiment, using the same six simulated IMU recordings and saved fitted parameters as the previous shared-error study.

It varies GPS and IMU error persistence separately: independent seconds, or correlation durations of 1, 5, 15, 60 and 300 seconds. Correlation decays exponentially with elapsed time. Each of the six saved cases receives all 36 combinations, giving 216 sensitivity scenarios. Marginal error scales and the same 79 supported minutes stay fixed. No new flights, fits, bootstrap or calibrated decisions ran.

Across this grid, predicted measured-minus-model variation ranges from 11.25 to 42.31°/hour. The corresponding local fit-response estimate ranges from 11.13 to 40.65°/hour. These are predictions under different error assumptions. The recordings themselves still have about 7.1–7.5°/hour of residual variation.

For illustration, the rotating-globe recording with the broad wind description gives the following when GPS and IMU share the same correlation duration:

The largest variation occurs with 15-second GPS and 300-second IMU persistence in every case. Longer persistence does not always increase the residual scale: the acceleration correction contains derivatives, while gyro averaging responds differently to slow errors. Uncertainty in the model coefficients also changes substantially. A single residual noise number cannot describe this behavior.

Shared GPS paths and accelerometer/gyro correlations remain intact. Persistent IMU errors follow physical sensor axes through the recovered mounting rotations. The covariance uses actual elapsed time through gaps; it adds no measurements, filter support or derivative rows in those gaps. These assumed input correlations are distinct from the measured residual correlations, which filtering and fitting can change.

This is a sensitivity study, not evidence that either instrument has a particular correlation duration. Marginal accuracy scales, empirical IMU covariance, missing GPS channel correlations and fixed mounting/calibration references remain provisional. The local fit response uses the old weights and deterministic penalties at saved parameters; no optimum was refitted and no interval coverage or Earth-model significance is established. The grid is not an exhaustive bound on credible error processes. Every scenario is preserved; none becomes a chosen calibration assumption on the basis of these results.

The next step is to implement and verify a research objective that uses the full covariance matrices, including shared GPS errors in the wind constraint, before separately defining further refits. Device characterization and fresh calibration remain necessary before any scientific decisions.

Five new tests and 34 focused checks pass. Independent dense-kernel comparisons, recovery of the previous independent-second result, covariance checks and all 216 response summaries are verified. The six evaluations took about 68 summed seconds on one numerical thread. Production code, eligibility and decisions are unchanged.

The documented corpus contains plan.json, six task-named JSON/NPZ pairs, review.json, verification.json, status.json and run.lock. It binds the scientific sources, inputs, fitted checkpoints, parent results and numerical environment. Completed results are immutable; a resume check skipped all six completed cases. No worker remains active.

To resume an interrupted evaluation with unchanged source/input/environment:

env OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 /home/sweisman/venv/bin/python analysis/tests/review_temporal_measurement_covariance.py docs/observed-pair-replay-20261007/run docs/joint-acceleration-motion-20261007/refits docs/continuous-measurement-motion-20261007 --output docs/temporal-measurement-covariance-20261007