PBN / RNP Accuracy Visualizer
RNP values, accuracy and containment with an animated route and aircraft, keeping precise distinctions from the simplified visualisation.
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RNAV x and RNP x name a lateral accuracy in nautical miles: the total system error (TSE) must stay within ±x for at least 95 % of the flight time (AIM 1-2-1 b 2 (e)). The green band on the stage is that accuracy; the histogram beside it, on the same lateral scale, shows where this flight has actually been, against the bell curve of the model.
The TSE has three parts. Path definition error (PDE): the path the navigator has built versus the desired path — negligible with a valid database. Flight technical error (FTE): how far the aircraft is from the navigator's path — this is the only part the CDI shows. Navigation system error (NSE): how far the true position is from the position the navigator computes. Independent errors add as a root-sum-square of their 95 % values (the bars below the route).
RNP is RNAV with on-board performance monitoring and alerting (AIM 1-2-2 a). RNP specifications also protect twice the accuracy value (the red dashed lines): the chance of being beyond it without an alert must be below 1 in 100,000. That condition is tighter than the 95 % one, so the monitor alerts as soon as the navigator can no longer assure either — compare the RNP 1 and RNAV 1 scenarios with the same degradation.
The monitor checks the navigation system, not your flying: drag the aircraft (or use Drift) and no alert appears, however far off you are (ICAO Doc 9613 Vol II Part A 2.3.10.5). Keep the cross-track error within half the RNP value; brief deviations up to the full value are acceptable only during and right after turns (AC 90-105A 6.2). Fly 1 hour fills the statistics at once; New flight draws new random errors.
Assumption: a simplified visualization. Each error is a zero-mean Gaussian described by its 95 % value (the assumption of ICAO Doc 9613 Vol II Part A 2.2.1); FTE and NSE wander over time with illustrative correlation times (20 s and 120 s); the PDE is one constant per flight; a straight segment only (no turns); the conceptual monitor knows the NSE exactly and assumes the specification's FTE allowance. The default NSE (0.05 NM), the drift and degradation rates and the RNP AR FTE allowance (half the value) are illustrative, not FAA figures. Real equipment computes and annunciates its performance in its own way and with its own wording — use the AFM and the avionics guide.
Budget: TSE95 = √(PDE95² + FTE95² + NSE95²); σ = TSE95 ÷ 1.95996. Model share of the time within ±accuracy = 1 − erfc(accuracy ÷ (σ√2)); probability beyond 2 × accuracy = erfc(2 × accuracy ÷ (σ√2)). Accuracy condition: TSE95 ≤ accuracy (σ ≤ accuracy ÷ 1.96). Containment condition: probability ≤ 10⁻⁵, i.e. σ ≤ 2 × accuracy ÷ 4.417 = accuracy ÷ 2.21 (ICAO Doc 9613 Vol II Part A 2.3.10.2 rounds this to accuracy ÷ 2.23) — the tighter of the two.
Conceptual monitor (RNP specifications only): with negligible PDE and the specification's FTE allowance, it alerts when the NSE estimate exceeds √(T² − FTE²), where T = the smaller of the two TSE95 limits above. Allowances: RNAV 2 1.0 NM, RNAV 1 0.5 NM (AC 90-100A 8 a); RNP 2 1 NM (AC 90-105A E.4.1); RNP 1 0.5 NM with autopilot or flight director, 0.8 NM hand-flown (C.3.1); RNP APCH 0.5 NM initial / intermediate / missed, 0.25 NM final (A.3.1.2); RNP 0.3 0.25 NM (D.4.1). Example: RNP APCH final, FTE 0.25 NM → the NSE may not exceed 0.092 NM.
Simulation: FTE and NSE are first-order Gauss-Markov processes with unit stationary variance scaled by σ (their long-run distribution is exactly the Gaussian of the budget — checked by tests); the PDE is drawn once per flight; the pilot's offset is added to the FTE. The CDI needle = −FTE ÷ full-scale deflection (RNAV 2 and RNP 2 ±2 NM, RNAV 1, RNP 1 and RNP APCH ±1 NM, final approach and RNP 0.3 ±0.3 NM: AC 90-100A 10 b (9), AC 90-105A). One sample per second feeds the histogram (bins of 1/10 of the accuracy value).
- ICAO Doc 9613, Performance-based Navigation (PBN) Manual, 4th ed. 2013, Vol. II Part A ch. 2: 2.2.1 — path definition, flight technical and navigation system errors, assumed independent, zero-mean and Gaussian, the total system error with the root-sum-square standard deviation; 2.3.10.1–2.3.10.2 — accuracy for 95 % of the flight time and the 10⁻⁵ probability of exceeding twice the accuracy value without annunciation (standard deviation at most accuracy ÷ 2.23 versus accuracy ÷ 1.96); 2.3.10.5 — on-board performance monitoring is not error monitoring (no alert when the FTE grows); Table II-A-2-1 — RNAV: TSE distribution not bounded
- FAA Advisory Circular 90-105A (2016), 4.2–4.3 (PDE considered negligible; TSE = vector sum of FTE, PDE and NSE), 6.2 and C.7.4.5 (cross-track error limited to half the RNP value, brief deviations in turns up to the RNP value); FTE allowances A.3.1.2 (RNP APCH 0.5 NM, final 0.25 NM), C.3.1 (RNP 1 0.5 NM with autopilot or flight director, 0.8 NM manual), D.4.1 (RNP 0.3 0.25 NM), E.4.1 (RNP 2 1 NM); alerting A.3.4 (2 NM / 0.6 NM with 10⁻⁵), C.3.4, E.4.2; A.7.1.8 and D.9.10 (notify ATC of any loss of the RNP capability); full-scale deflections ±1 NM / ±0.3 NM (A.3), ±0.3 NM (RNP 0.3)
- FAA Advisory Circular 90-100A Change 2, para. 8 a (1)–(2) (RNAV 2 FTE 1.0 NM, RNAV 1 FTE 0.5 NM) and 10 b (9) (full scale ±1 NM for RNAV 1, ±2 NM for RNAV 2)
- Aeronautical Information Manual 1-2-1 b 2 (e) — the RNAV x / RNP x number is the lateral accuracy in NM achieved at least 95 percent of the flight time; RNAV 1 and RNAV 2 uses
- Aeronautical Information Manual 1-2-2 a — RNP is RNAV with on-board performance monitoring and alerting (OBPMA); b 1 — RNP applications account for errors at a multiple of the accuracy value (for example twice); b 1 (a) (1)–(9) — RNP APCH, RNP AR APCH, RNP 1, RNP 2, RNP 0.3; d NOTE — estimated position uncertainty (EPU), also called ANP or EPE; TBL 1-2-2 — RNP AR approach segments 0.1 to 1.0
- Model choices of this tool (stated on the page): Gaussian errors described by their 95 % values; FTE and NSE varying over time with illustrative correlation times (20 s and 120 s); a straight route segment; a conceptual monitor that knows the NSE and assumes the specification's FTE allowance; an illustrative default NSE of 0.05 NM, illustrative drift and degradation rates and an illustrative RNP AR FTE allowance (half the value)
- Garmin G1000 Pilot’s Guide for Cessna Nav III, 190-00498-08 Rev. A (system software 0563.30 or later), pp. 56-68 — the glass HSI option (Indicator: HSI (glass)): heading-up compass card, course pointer with a two-dot deviation scale (full scale as on a mechanical CDI for VOR and LOC), green for VOR / LOC and magenta for GPS, flight-phase and OBS / SUSP annunciations, glideslope / glidepath indicator; an equipment example, not a statement about every glass display