Rnp Anp Containment

RNP / ANP Containment (avionics/flight-management/rnp-anp-containment)

Use when the task is the navigation performance containment check of a flight management system: compare the actual navigation performance (ANP) of the position solution with the required navigation performance (RNP) of the airspace or route segment and decide whether the aircraft stays inside the containment bound. ANP is the 95th percentile lateral position error, taken as two times the supplied 1-sigma lateral position error or read directly from the navigation system, and a required margin fraction of RNP can be applied before the comparison. This leaf implements the standard RNP containment rule in pure Python, stdlib only. It pairs with gnc-autonomy/navigation/dilution-of-precision and gnc-autonomy/navigation/gnss-pseudorange-positioning, which produce the position error inputs, and with lateral-navigation, the FMS lateral function that consumes the containment verdict.

Domain quick reference

• RNP is a 95 percent containment bound: the position must stay within the RNP distance for at least 95 percent of the flight time. RNP values are distances: RNP 0.3 NM equals 0.3 * 1852 = 555.6 m.
• ANP from sigma: anp = 2 * sigma_lateral_m, the 95th percentile lateral position error from a 1-sigma lateral position error (anp_from_sigma).
• Required margin: margin = rnp_m * margin_fraction, zero by default, set by operator or procedure policy (margin_m).
• Containment rule: pass when anp + margin <= rnp, boundary inclusive (containment_pass).
• Available margin: margin_available = rnp - margin - anp, the reserve left over after the required margin (margin_available_m).
• analyze() bundles the check: it takes sigma_lateral_m or anp_m, rnp_m and margin_fraction, and returns the anp_m, rnp_m, pass bool, margin_m and the PASS or FAIL verdict.
• The 1-sigma lateral position error is an input from the navigation error analysis; deriving it from geometry or ranging residuals is out of scope, as are obstacle clearance and route geometry.
• Units are meters for distances and fractions (0.05 means 5 percent) for the margin.

Workflow

1. Fix the segment: read the RNP for the airspace or route segment and convert NM to meters (multiply by 1852) when the procedure gives NM.
2. Get the position error input: the 1-sigma lateral position error sigma_lateral_m from the navigation error estimate, or the ANP value reported by the navigation system.
3. Compute the ANP with anp_from_sigma when only sigma is available, or pass the reported ANP directly as anp_m.
4. Set the required margin fraction (default 0.0) and compute the margin in meters with margin_m when the operator demands a reserve.
5. Run containment_pass for the verdict and margin_available_m for the remaining reserve.
6. For the full record call analyze(sigma_lateral_m=..., anp_m=..., rnp_m=..., margin_fraction=...) and use the returned dict with the verdict.
7. Confirm the deterministic checks with the contract test scripts/test_rnp_anp_containment.py.

Worked example

RNP 0.3 NM = 555.6 m on the approach with a 1-sigma lateral position error of 120 m.

• ANP: anp_from_sigma(120) = 2 * 120 = 240 m (95 percent bound).
• Default margin: margin_m(555.6, 0.0) = 0 m.
• Verdict: containment_pass(240, 555.6) is True because 240 <= 555.6.
• Available margin: margin_available_m(240, 555.6) = 555.6 - 240 = 315.6 m.
• Degraded case: sigma 300 m gives ANP 600 m; 600 > 555.6 so containment_pass(600, 555.6) is False and analyze returns verdict FAIL.
• Direct ANP case: analyze(anp_m=500, rnp_m=555.6, margin_fraction=0.05) applies margin_m = 555.6 * 0.05 = 27.78 m, checks 500 + 27.78 = 527.78 <= 555.6, passes with verdict PASS and 27.82 m of margin still available.

Verification

• Confirm anp_from_sigma(120) returns 240.0 m.
• Confirm containment_pass(240, 555.6) is True and containment_pass(600, 555.6) is False.
• Confirm margin_available_m(240, 555.6) returns 315.6 m within 0.1.
• Confirm analyze(anp_m=500, rnp_m=555.6, margin_fraction=0.05) returns pass True, margin_m 27.78 and verdict PASS.
• Confirm the boundary is inclusive: containment_pass(240, 240) is True.
• Confirm ValueError rejection of non-physical inputs: both sigma and anp missing, rnp_m <= 0, sigma_lateral_m < 0, anp_m < 0 and margin_fraction < 0.
• Run the contract test offline: python3 scripts/test_rnp_anp_containment.py (32 tests, deterministic).

Related leaves

• avionics/flight-management/lateral-navigation: the FMS lateral guidance function that consumes the containment verdict and the cross-track state.
• gnc-autonomy/navigation/dilution-of-precision: navigation geometry based error analysis that can feed the lateral position error sigma.
• gnc-autonomy/navigation/gnss-pseudorange-positioning: the position fix whose residuals bound the navigation error for the sigma input.

Pitfalls

• Feeding the 1-sigma error as the ANP: the ANP is the 95th percentile bound anp = 2 * sigma_lateral_m, so a 120 m sigma is an ANP of 240 m - comparing the raw sigma against the RNP halves the effective containment and can pass a degraded navigation system.
• Mixing nautical miles into a meters check: RNP values arrive in NM (RNP 0.3 NM = 555.6 m) and every comparison runs in meters - an unconverted 0.3 against a 240 m ANP passes any degraded case.
• Comparing ANP against RNP without the required margin: the rule is anp + margin <= rnp, so at RNP 555.6 m with a 5 percent margin (27.78 m) an ANP of 500 m passes only because 527.78 <= 555.6, and margin_available_m reports the reserve after the margin is reserved, not the raw rnp - anp.
• Treating the boundary as exclusive: containment is inclusive - anp + margin equal to rnp passes (containment_pass(240, 240) is True), so an equality case must not be flagged as a violation.
• Reading RNP as an absolute limit: RNP is the 95 percent containment bound that the position must satisfy for at least 95 percent of flight time, and the ANP is the 95th percentile error - momentary excursions beyond the bound are not automatically a containment failure, and neither is the mean error the quantity to compare.
• Deriving the sigma inside this leaf: the 1-sigma lateral position error is an input from the navigation error analysis (dilution-of- precision and gnss-pseudorange-positioning leaves feed it); geometry and ranging-residual estimation are out of scope here, and analyze raises ValueError when both sigma and anp are missing.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_rnp_anp_containment.py

The test covers the worked-example contract (ANP 240 m from a 120 m sigma, pass verdict and 315.6 m available margin at RNP 555.6 m; fail verdict at a 300 m sigma; direct ANP 500 m pass with the 5 percent margin), the margin helper, the inclusive boundary, sigma and ANP input agreement round trip, verdict typing, and ValueError rejection of both missing inputs, non-positive RNP, negative sigma, negative ANP and negative margin fraction.

Compliance

• Standards referenced, not reproduced: DO-178C frames the flight management software context for this containment function; the RNP containment relations above are standard navigation methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.