Channel-diagnostic approximation and error budget

Purpose

Measure the software diagnostic's sensitivity to receiver-trajectory truncation, nonlinear propagation and acceleration averaging before any recorded-data use. Preserve the completed exact-trajectory controls and the main flight results. These deterministic controls do not estimate a false-rejection rate or an observational confidence interval.

Matrix fixed before execution

• Thirty-six trajectory cases: three reference models, degree 2 or 4, half-windows of 4, 8 or 16 seconds, and receiver-noise multipliers 1 or 50. All candidates are evaluated in each case. The same analytic trajectory has small sinusoidal latitude, longitude and height changes. It is deliberately not polynomial.
• Receiver coordinates are sampled every second. The declared fixture covariance has 0.3/0.3/0.7 m north/east/height scales, 60-second exponential correlation plus a 10% independent term, and cross-axis correlations. A common spherical reporting metric converts these assumptions to coordinate units for every candidate. These are known control assumptions, not measured receiver errors.
• Full position/rate/acceleration covariance is retained. Symmetric derivatives at 0.01 and 0.02 standard-normal steps provide a local delta approximation. A separate 18-point spherical-radial cubature probes nonlinear response. The cubature is an approximation check, not exact Gaussian coverage.
• Six one-second rotation controls at 0, 0.1, 1, 5, 20 and 90 degrees compare mean packet magnitudes with the magnitude of summed increments at 200 Hz. Increments are exact integrals of a rotating constant-magnitude force.
• Four isotropic acceleration-noise controls use standard deviations 0.001, 0.01, 0.1 and 0.5 m/s². Independent order-5 and order-9 Gaussian quadrature measure magnitude bias and compare with the small-noise expansion.

Finite allowance

Seal sources, environment, tasks, constants and limits before launch. Reserve each identity's full allowance before evaluation. Preserve failed identities; completed work cannot restart or transfer its unused allowance.

Checks and interpretation

Software correctness requires finite results, independent-reference force agreement within 10⁻⁹ m/s², exact formula-call counts, and rotation-integral agreement within 10⁻¹¹ m/s². Quadrature orders must agree on magnitude bias to within 1% or 10⁻¹¹ m/s², whichever is larger; the small-noise expansion is a separate reported comparison.

For each candidate, flag a local approximation when derivative disagreement exceeds 1%, cubature and linear standard deviations differ by more than 5%, or the nonlinear mean shift exceeds 0.1 linear standard deviation. Also report trajectory-truncation bias relative to linear standard deviation; a ratio above 0.25 fails the control's declared truncation screen. These screens are numerical development rules, not calibrated scientific acceptance thresholds. Stress cases are allowed to fail these screens; no window or model is selected by the outcome.

Show all cases and all candidates. Do not infer real instrument noise from these assumed inputs, qualify a recorded-data likelihood, or change the 53-stretch result.