Computes formal covariance (H^T·H)^{-1} via LAPACK dpotrf_/dpotri_
after DC convergence. Returns upper-triangle array (21 elements for
6-state, 28 for 7-state with B*), condition number from SVD, and
nstate count. Covariance is computed even for perfect-seed fits.
Bumps extension to v0.5.0 with full install SQL and migration path.
Eliminates the seed TLE requirement for topocentric fitting by
computing an initial orbit estimate from 3 well-spaced observations
using the Gibbs method. ECI fitting retains the single-observation
r,v approach (exact for two-body) with Gibbs as fallback.
Extend od_observation_t with observer_idx so each observation can
reference a different ground station. Config now holds an array of
observers instead of a single pointer. The existing single-observer
tle_from_topocentric() is unchanged (sets observer_idx=0 for all obs).
New overload: tle_from_topocentric(topo[], ts[], observer[], int4[], ...)
accepts parallel observer_ids array indexing into the observers array.
PG function overloading resolves by argument types.
Tests 9-11: two-station fit converges, single-station via multi-observer
API matches, out-of-range observer_id raises error.
Scale step limits by a trust-region factor that halves on divergence
(RMS increases > 1%) and relaxes toward full step on good convergence
(RMS decreases > 10%). Prevents oscillation with poor initial guesses
without affecting well-seeded fits. Also stores SVD condition number
for diagnostic use in upcoming covariance output.
Existing 8 OD regression tests + 67 standalone math tests unaffected
(adaptive_factor starts at 1.0, round-trip tests never trigger
divergence).
Batch weighted least-squares differential correction using equinoctial
elements, LAPACK dgelss_() for SVD solve, vendored SGP4/SDP4 as the
propagation engine. Per Vallado & Crawford (2008) AIAA 2008-6770.
New SQL functions:
- tle_from_eci(): fit TLE from ECI position/velocity ephemeris
- tle_from_topocentric(): fit TLE from az/el/range observations
- tle_fit_residuals(): per-observation position residuals diagnostic
Solver features: 6-state (orbital) or 7-state (+ B*) fitting,
equinoctial elements for singularity-free optimization, tiered step
limiting, Brouwer/Kozai Newton-Raphson conversion, auto initial guess
from first ECI observation when no seed TLE provided.
Tested: 8 regression tests (LEO/MEO/near-circular round-trips,
B* recovery, topocentric, seedless, error handling, diagnostics),
67 standalone math unit tests, all 14 suites pass.
