Include uncertainty from estimating calibration

The native and receiver components propagate a declared error law at fixed calibration. A fitted calibration is uncertain too. Its effect must not vanish from a prediction simply because the optimizer returned one parameter point.

First qualify the linear, fixed-design calculation. Use earlier observations only for generalized least-squares estimation, preserving their temporal covariance. Predict later observations using both the estimated mean and the error information carried from earlier observations. Add the calibration uncertainty without counting that earlier information twice.

Keep every supplied calibration column. Require explicit parameter units and numerical rank/estimability tolerances. If training leaves a direction unknown and that direction changes the later prediction, return unidentifiable with no finite prediction covariance. A rank-deficient calibration may still make an estimable prediction if every unknown direction cancels there. Do not add an unstated prior, drop nuisance columns or repair variance to obtain an answer.

Compare with independently formed dense generalized least-squares prediction weights and their complete error covariance. Cover all 27 columns, correlated errors, several training cutoffs, parameter rescaling, identifiable predictions with redundant parameters and genuinely unidentifiable later predictions. Accept only training residuals; no later measured residual is an input.

Use at most sixteen deterministic generated cases, sixteen epochs, 27 parameter columns, one numerical thread and a cooperative two-minute allowance. No random draws, native calls, optimizer starts, original reads or protected reads occur. Bind a fresh formal request to the exact sources and numerical environment.

This first step assumes an unrestricted linear mean and a supplied Gaussian error law. It does not cover nonlinear calibration, parameters constrained at bounds, estimation of the error law or simultaneous confidence over a flight. Those require their own qualification before applying uncertainty statements to the aircraft fits. Existing physical accuracy limits and failed controls remain unchanged.

Covariance overview · Combined native/receiver gate · Prediction assumptions · Roadmap.