What the prediction error ranges assume
The current development tests check whether the software can bound a prediction while calibration is uncertain. Those ranges are not yet confidence intervals for the aircraft recordings. Several different sources of error must remain separate.
An IMU (inertial measurement unit) supplies the gyroscope and accelerometer records used to reconstruct motion.
| Source | What is currently checked | What still needs establishing |
|---|---|---|
| Calibration | Keep one set of physical calibration parameters shared across the whole generated history. Preserve the full declared domain. | Whether that domain and its time behavior adequately describe a particular recording. |
| IMU noise and quantization | Preserve the recorded increments as inputs to the generated calculation. | Their contribution to prediction uncertainty; constant calibration bounds do not automatically cover random sensor errors. |
| Approximation | Bound the error introduced by simplifying the nonlinear calculation. Check complete coverage of the permitted domain. | Useful widths over complete recording lengths. A short-example success is insufficient. |
| Numerical arithmetic | Use exact rational checks and outward-rounded primitive operations in the qualified components. Preserve reference-transfer errors. | A whole-program floating-execution bound; sampled agreement does not prove one. |
| Receiver observations | Check supplied error assumptions without consulting future observations. | An adequate error distribution and temporal covariance for the real receiver stream. |
| Physical model | Preserve the candidate's stated motion, gravity and processing assumptions. | Whether predicted unused positions, including height, adequately match observations. This is the later prediction test. |
The short generated example
The present complete-cover comparison predicts a position at 7.2 seconds from six earlier generated observation epochs. It keeps 27 physical parameters and 78 enclosing coordinates. The extra coordinates represent shared error terms and products; they are not additional independent instruments or observations.
Its training constraints allow 1 mm per observed coordinate, plus a separate 0.00001 m arithmetic allowance. These are frozen software-test assumptions, not measured receiver precision or survey-IMU specifications. The saved outputs explicitly leave whole-program floating enclosure and observational coverage unqualified. Neither allowance can be carried into an aircraft study merely because the example retains its known truth.
The width target is also a software-development target: halve the earlier complete range without changing the problem. It is not a significance level or an absolute adequacy criterion for a flight.
Shared observation uncertainty
The shared-scale calculation assumes a stated covariance shape and Gaussian errors. Its reference projection must be fixed independently of those errors, with positive residual degrees of freedom. All physical candidates use the same scale source. A poorly fitting candidate cannot give itself a larger measurement-error budget.
The software controls establish results under these supplied assumptions. They do not show that receiver errors are Gaussian, that their covariance is correct, or that the same law applies to another instrument or archive. A mismatched reference can make a conservative range wide; that is not proof of large measurement noise.
Receiver error and accumulated IMU error are different contributions. An aircraft prediction error model must include both, or justify why an omitted contribution is negligible for its declared test. A receiver-only covariance does not become a complete error model merely because its software tests pass. This assessment can use observations and stated sensitivity assumptions; exact proprietary device documentation is not a prerequisite.
The accumulated inertial-error component passes 28 software checks against an independent continuous-time reference. It preserves correlation between training and future observations under a supplied linear Gaussian model. Its noise inputs have no hardware defaults, and its constant-coupling approximation is not yet an adequate error law for a flight. Noise settings, coupling matrices and reference projections must not use withheld positions. Estimating them from noisy IMU inputs also introduces dependence that must be accounted for before applying an independence-based coverage calculation.
The longer-study training interface requires an explicit allowance for each observation coordinate. Its 15 focused checks prevent the short example's 1 mm allowance from becoming a silent default. Supplying an allowance remains an assumption that needs justification.
Before applying the method to aircraft predictions
Freeze the calibration domain, observation-error family, numerical treatment, prediction horizon and adequacy criteria before examining withheld positions. Demonstrate useful bounds over the intended recording length. Missing or unsupported regions must remain unsupported, rather than disappear from the reported range. Keep every covariance alternative required by the frozen plan.
The archival prediction tests will be retrospective development validation. Independent confirmation and confidence for the complete two-stage model decision require their own reserved data and dependence-aware calibration.
Current diagnostic · Technical backlog · Training-only interface.