DO-316 / DO-229E integrity compliance map

This document maps the RTCA DO-229E (SBAS MOPS) and DO-316 (GPS/SBAS 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 + 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/GIVE/airborne/ tropo budget). The position covariance is D = (GᵀWG)⁻¹; its ENU block gives

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$ \text{by} \text{inverting} \text{the} 4 \times 4 \text{normal} \text{matrix} \text{with} \text{the} \text{same} \text{routine} \text{the} \text{RAIM} \text{stack} \text{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

Mode	K_H	K_V	Source
En-route → NPA (horizontal only)	6.18	—	Rayleigh √(−2·ln 5e-9) = 6.1829
Precision Approach	6.0	5.33	DO-229E MOPS

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. 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 IF coefficients against the IS-GPS-705 frequencies, first-order iono cancellation against the independent delay physics, and the WLS protection levels against a numpy inv(GᵀG) reference geometry.
• Founder-gated, external: reproducing a published WAAS/EGNOS protection level from a real RINEX-OBS + augmentation-message epoch (as RTKLIB rtkpos / ESA gLAB do) requires Earthdata-authenticated CDDIS data and is tracked as a roadmap item. DO-229E/DO-316 themselves are RTCA-paywalled; the open derivation source is ESA Navipedia's ICAO/EGNOS SBAS pages.