SGP4/SDP4 validation against the community reference

Kshana's orbit propagator is validated against the canonical community reference for SGP4/SDP4: the verification vectors published with Vallado et al., "Revisiting Spacetrack Report #3" (AIAA 2006-6753), distributed as SGP4-VER.TLE (the test TLEs) and tcppver.out (the expected TEME state at each time). This is the same reference the public C++/Python/MATLAB implementations validate against, so agreement here is agreement with the de-facto standard.

Result

Quantity	Value
Reference states compared	666 (all rows in tcppver.out, pinned in the test)
Worst position error	≈ 4 mm (< 2e-5 km tolerance)
Worst velocity error	≈ 1.85e-9 km/s (< 1e-6 km/s tolerance)
Cases covered	near-Earth SGP4, deep-space SDP4 (lunar-solar + 12 h/24 h resonance), and the deliberate error-code cases

The deep-space and resonant cases matter specifically for this project: GNSS satellites sit in ~12 h orbits that are deep-space and resonant, which a two-body + J2-secular model cannot reproduce — SGP4/SDP4 can.

Method

• The implementation (src/sgp4.rs) is a dependency-free Rust port of the public-domain Vallado algorithm; epoch handling is days-since-1950, the improved (not afspc) mode is used, and WGS-72 gravity constants are applied as the reference specifies.
• The test (tests/sgp4_verification.rs) parses the vendored SGP4-VER.TLE and tcppver.out fixtures (tests/fixtures/sgp4/), propagates each test satellite to every reference time, and asserts the TEME position and velocity match within the tolerances above. The compared-row count is pinned at exactly 666 so a fixture or skip-behaviour regression cannot quietly reduce coverage.

Reproduce it

cargo test --test sgp4_verification -- --nocapture

The test prints the number of rows compared and the worst-case position and velocity errors. The fixtures are committed, so the check is fully offline and deterministic.

Independent cross-check against the sgp4 crate

Matching the published reference proves correctness against a table. To also prove correctness against an independent implementation, tests/sgp4_crate_comparison.rs runs the most widely used Rust SGP4 library — the sgp4 crate (neuromorphicsystems/sgp4) — over the same 666 AIAA vectors and compares the two codebases head-to-head. Both are driven with the WGS72 gravity model the vectors are defined in (the crate's default from_elements uses WGS84, which differs from the WGS72 reference by ~km — a modelling choice, surfaced honestly, not an error).

Regime	kshana ↔ reference	crate ↔ reference	kshana ↔ crate
near-earth (LEO/MEO)	7.3e-9 km	7.3e-9 km	4.4e-10 km
deep-space (non-resonant)	4.1e-6 km	2.1e-7 km	4.1e-6 km
deep-space resonance (½-day)	8.1e-9 km	7.7e-9 km	2.2e-9 km
deep-space resonance (1-day)	8.2e-9 km	7.8e-9 km	2.2e-9 km

Two independent implementations agree to sub-micron on near-earth and resonant orbits and to 4.12 mm worst-case across all regimes — the same 4.12 mm that is Kshana's own deviation from the reference, i.e. the disagreement is that one deep-space case, with the crate sitting between Kshana and the table. The full table (with per-regime row counts and the four pathological cases the crate rejects at construction) is committed at tests/fixtures/sgp4_comparison.md and regenerated via KSHANA_REGEN_FIXTURES=1 cargo test --test sgp4_crate_comparison.

Status of "publishing" this result

The cross-validation itself is complete and in-tree. Submitting the result to external venues (a community catalogue, a short note, a DOI-archived record) is a maintainer action tracked separately on the roadmap; this document is the in-repository record those submissions would point to.