DO-316 / DO-229E integrity compliance map

This document maps the RTCA (formerly the Radio Technical Commission for Aeronautics) DO-229E (SBAS (satellite-based augmentation system) MOPS (minimum operational performance standards)) and DO-316 (GPS/SBAS (GPS: Global Positioning System) airborne equipment) protection-level and integrity-monitoring requirements to the Kshana functions that implement them. It is an engineering traceability aid, not a certified conformance statement — Kshana implements the published algorithms; it is not certified avionics.

The machine-readable form is sbas::do316_compliance_map; this prose is its companion (mirroring docs/ARAIM_REFERENCE.md).

Weighted-least-squares protection levels (DO-229E Appendix J)#

For each satellite i with elevation Elᵢ and azimuth Azᵢ at the user, the local-level (ENU (east-north-up) + clock) observation row is

Gᵢ = [ −cos Elᵢ·sin Azᵢ,  −cos Elᵢ·cos Azᵢ,  −sin Elᵢ,  1 ]

with weight wᵢ = 1/σᵢ², σᵢ² = σ_flt² + σ_uire² + σ_air² + σ_tropo² (the UDRE (user differential range error) / GIVE (grid ionospheric vertical error) / airborne / troposphere budget). The position covariance is D = (GᵀWG)⁻¹; its ENU block gives the horizontal and vertical protection levels (HPL, VPL):

d_major = √( (d_E² + d_N²)/2 + √( ((d_E² − d_N²)/2)² + d_EN² ) )
d_U     = √(d_U²)
HPL = K_H · d_major        VPL = K_V · d_U

Kshana computes D by inverting the 4×4 normal matrix with the same routine the RAIM (receiver autonomous integrity monitoring) stack uses (orbit::invert4), and validates the result two ways (the covariance route D[2][2] and the projection route Σᵢ S_{U,i}²·σᵢ² must agree) plus against an independent numpy inv(GᵀG) reference geometry.

K-factors#

Honesty note: the MOPS uses the rounded horizontal constant 6.0; the exact two-sided normal quantile Φ⁻¹(1 − 1e-9/2) is 6.109. Kshana uses the published 6.0 in code and derives K_V = Φ⁻¹(1 − 1e-7/2) = 5.327 from the same raim::normal_quantile the RAIM stack uses, a non-circular cross-check (the value rounds to the MOPS 5.33).

L1/L5 dual-frequency ionosphere-free combination (IS-GPS-705)#

With f₁ = 1575.42 MHz, f₅ = 1176.45 MHz, γ₁₅ = (f₁/f₅)² = 1.79327:

ρ_IF = (f₁²·ρ₁ − f₅²·ρ₅) / (f₁² − f₅²) = c₁·ρ₁ + c₅·ρ₅
c₁ = +2.260604,  c₅ = −1.260604   (c₁ + c₅ = 1, unit gain)

The first-order ionospheric delay (40.3·10¹⁶·TEC/f²) cancels exactly — verified against the engine's independent timetransfer_adv::iono_delay_m physics for a range of TEC (total electron content). The noise amplification for equal-variance inputs is √(c₁² + c₅²) = 2.588.

Validation status#

• In-repo, automated (every commit): the K-factors against their distributional definitions, γ₁₅ and the ionosphere-free (IF) coefficients against the IS-GPS-705 (IS: Interface Specification) frequencies, first-order iono cancellation against the independent delay physics, and the weighted-least-squares (WLS) protection levels against a numpy inv(GᵀG) reference geometry (sbas::tests::wls_pl_matches_numpy_on_five_satellite_geometry).
• External oracle, automated (tests/sbas_reference.rs): given each satellite's elevation, azimuth and total 1-σ, sbas_protection_level reproduces the HPL of an independent implementation, waasprotlevels() in the RTKLIB (an open-source real-time kinematic positioning library) SBAS protection-level fork zsiki/rtklib_ws (Siki & Takács 2017), on six epochs that tool computed from real EGNOS (European Geostationary Navigation Overlay Service) broadcast messages (geostationary PRN (pseudo-random noise code number) 120) and real RINEX (Receiver Independent Exchange Format) observations from the BUTE station in Budapest (2017-02-19), to < 2e-3 m. The oracle rounds K_V to 5.33, so the vertical is compared K-factor-free, as d_U against its VPL / 5.33. ESA (European Space Agency) gLAB v6.0.0 (core/filter.c) uses the same formula.
• Not done: the per-satellite σ is the oracle's own; modelling σ from raw UDRE/GIVE messages is out of scope, and no official published WAAS (Wide Area Augmentation System) or EGNOS protection-level product has been reproduced end to end. DO-229E/DO-316 themselves are RTCA-paywalled; the open derivation source is ESA Navipedia's ICAO/EGNOS (ICAO: International Civil Aviation Organization) SBAS pages.