Close geographic propagation and endpoint observations
The supplied-context local-step matrix is complete. Preserve its sources and allowance. The next separately identified component must mirror the complete predictor/corrector in the native kernel, not a different integration scheme.
Preserve scalar physical domains
A global norm radius is a symmetric outer relaxation. At a fitted removal fraction of zero, a true physical interval [0,1] needs change radius one; that outer ball also contains negative fractions. Checking the relaxed ball itself as the physical domain would incorrectly reject this legitimate boundary case.
Keep declared scalar intervals separately from their change/remainder radii. Validate the actual interval and center, then propagate the conservative norm bound. Qualify boundary-centered removal and period intervals explicitly. Preserve the completed local component unchanged; revised interfaces need a new source identity.
Geographic predictor/corrector
Represent latitude, longitude and height as separate scalar bounds with their declared units. Do not mix radian and metre uncertainties into an unexplained single coordinate norm. Keep longitude continuous; do not silently wrap it.
- Compute candidate coordinate rates from the old position and velocity.
- Form midpoint coordinates using those rates and half the interval.
- Form transport using midpoint latitude and the old rates, then evaluate the first local step to obtain its velocity estimate.
- Recompute rates at the same midpoint coordinates using the average of the old velocity and that estimate.
- Recompute transport with these rates and midpoint latitude. Evaluate the second local step from the original attitude/velocity, not from the first local step's endpoint.
- Update coordinates with the recomputed rates and the full interval.
Use the kernel's declared globe/disc metrics. Scalar inverse and metric-power bounds must cover the complete state region and reject denominator/domain crossings rather than clip them. Sine/cosine propagation must retain both actual change and first-order approximation error. Report conservatism and unsupported domains; passing a short control need not imply useful long-record precision.
Lever arms and time
For endpoint observations, rotate the body lever arm by the predicted attitude, apply the candidate coordinate metric at the predicted IMU position, and add the offset as the kernel does. Do not substitute fused attitude or receiver truth.
A later extension can propagate a bounded integration period and correspondingly scaled raw increments for observations inside one packet. Preserve their shared fraction and cross terms. A time interval crossing packet boundaries requires separate support/union handling; it is not covered by a single local tangent. Long-record arithmetic and shared observational covariance remain separate gates.
Qualification
First test scalar/domain operations and full predictor/corrector values against independent formulas, including nonzero parameter centers and supported physical boundaries. Then freeze finite end-to-end generated cases and a separate unchanged C-kernel harness. Compare values, directional derivatives and global remainder radii for all candidates, both hemispheres, lever arms and timing scopes. Retain all original nuisance directions; identify fixed timing explicitly.
No observed prediction allowance follows from this plan. The existing archive findings, old failures and protected ESA groups remain unchanged.