AC 20-191 Appendix C Figure C-9 Explicit Calculation of PUL for the Land Short Example Above.
C.2 Alternative Method for Calculating and Using NSE Model Scale Factors.
C.2.1 Estimation of 10-pt piecewise linear interpolation of GBAS NSE autoland simulator histograms – GAST D.
An alternative method to use the NSE model is to compute, before launching any run of the Monte-Carlo autoland simulations, the distributions of the scale factors, Kvert and Kxtrk = Katrk. For these two last quantities, we conservatively allocate the worst horizontal sigma. These distributions have been computed using assumptions described in [11] and [12]. Then for each run of the Monte-Carlo simulations, we draw, from these two distributions, a Sigma_vert= Kvert and a worst horizontal sigma for Kxtrk and Katrk, at the beginning of the approach which are kept constant during the approach.
In order to facilitate the use of these distributions, the 10 point piecewise linear interpolation of Kvert and Kworst_horizontal_sigma are provided on the histograms and using a dual entry table X-axis corresponding to sigma_vert or worst_sigma_horizontal in meters.
C-15
AC 20-191 Appendix C C.2.2 Sigma Vert.
Figure C-10 Sigma Vertical Samples Table C-8 Sigma_vert Values and Number of Occurrences Sigma_vert Number of occurrences
0.485000000000000 0.000429191837945
0.543326533206011 0.002257116788039
0.655055242735278 0.045229563598357
0.699018742036146 0.043376936959747
0.731326218889690 0.035448466874264
0.860858976217526 0.008926572687034
1.070145122860493 0.001211926592757
1.409975954322260 0.000073333137778
1.573104102697827 0.000010035060959
1.735000000000000 0.000008491205427 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05 nb of occurrences sigma vert (meters)
bins width = 0.01 m C-16
AC 20-191 A ppendix C C.2.3 Worst Horizontal Sigma.
As with the NSE noise scale factors, an alternative way of using the step function is to derive scale factors sigma_step_vert and worst_sigma_step horizontal to take into account steps induced by loss of tracking of satellites by the receiver due to geometry (rise/set of satellites) or due to satellite failures. The distributions and the 10 point piecewise linear interpolations are provided below for these two cases for the two dimensions.
Figure C-11 Worst Horizontal Sigma Samples 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.02
0.04
0.06
0.08
0.1
0.12nb of occurrences worst horizontal sigma (meters)
bins width = 0.01 m C-17
AC 20-191 Appendix C Table C-9 Sigma_Worst_Horizontal Values and Number of Occurrences Sigma_worst_horizontal Number of occurrences
0.005000000000000 0
0.257665870406134 0.001235856353506
0.293780182441118 0.021311381766140
0.341769349550846 0.107172907188037
0.398519584681962 0.038574002399152
0.489966724012817 0.005669037514146
0.501954763905412 0.003652762189125
0.733255508608094 0.000223859052165
1.294724573608414 0.000000771927766
1.705000000000000 0.000000771927766 C.2.4 Rise/set Sigma Step Vertical.
Figure C-12 Rise/set Sigma Step Vert. Error Samples 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.005
0.01
0.015
0.02
0.025
0.03
0.035nb of occurrences Rise/set - sigma step vert (meters)
bins width = 0.01 m C-18
AC 20-191 Appendix C Table C-10 Rise/Set Sigma_step_vert and Number of Occurrences Rise/Set Sigma_step_vert Number of occurrences
0.005000000000000 0.000102160167567
0.072435248412769 0.000251314012215
0.173069321361968 0.007640899466239
0.183661728498818 0.014862132304962
0.266851710720950 0.032471159430220
0.360116883106780 0.022183880145120
0.560386526870370 0.010022935263488
0.707103250848933 0.002542678888367
1.168108921989317 0.000590218235325
1.605000000000000 0 C.2.5 Rise/set Worst Sigma Step Horizontal.
Figure C-13 Rise/set Worst Sigma Step-horizontal Error Samples 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.01
0.02
0.03
0.04
0.05
0.06nb of occurrences Rise/set - worst sigma step hor (meters)
bins width = 0.01 m C-19
AC 20-191 Appendix C Table C-11 Rise/Set Worst Sigma_Step_Hor and Number of Occurrences Rise/Set Worst Sigma_Step_Hor Number of occurrences
0.005000000000000 0.000002897188944
0.041875996448845 0.004326488398194
0.054920944044943 0.005392271389607
0.109250543156205 0.058667264538146
0.163832898257929 0.050878995869548
0.205763067528231 0.030017730600579
0.339826367851692 0.005884118967452
0.481495931510671 0.001622467406624
0.537593983881708 0.001038030498786
1.425000000000000 0.000000090537154 C.2.6 Signal Loss Sigma step vertical.
Figure C-14 Signal Loss- Sigma Step Vert Error Samples 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.005
0.01
0.015
0.02
0.025nb of occurrences Signal Loss - sigma step vert (meters)
bins width = 0.01 m C-20
AC 20-191 Appendix C Table C-12 Signal loss Sigma_Step_Vert and Number of Occurrences Signal loss Sigma_Step_Vert Number of occurrences
0.005000000000000 0
0.175788354389016 0.000006172962943
0.341225896607212 0.001849289916083
0.501345966346395 0.016428884464905
0.509272880272156 0.014817130740563
0.585415172749149 0.024277512141267
0.634728223925139 0.019985074857159
0.971964045257760 0.004855442265040
0.993665191757176 0.004618156897366
1.565000000000000 0 C.2.7 Signal Loss Worst Sigma Step Horizontal.
Figure C-15 Signal loss worst sigma step hor. Samples 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04 nb of occurrences Signal Loss - worst sigma step hor (meters)
bins width = 0.01 m C-21
AC 20-191 Appendix C Table C-13 Signal Loss Worst Sigma_Step_Hor and Number of Occurrences Signal Loss Worst Sigma_Step_Hor Number of occurrences
0.005000000000000 0.000476007789371
0.115610839554299 0.025790440689983
0.180148721789614 0.034439075056633
0.320833114781513 0.015472307517217
0.586810140697307 0.003675003851236
0.880744610706960 0.000358424380494
3.908283843494504 0.000000000123437
3.975118428756177 0.000000000123437
4.601736622281720 0
4.995000000000000 0.000000016910875 C.3 References for GBAS Performance Model.
• ICAO NSP Mar 2009 WGW/WP 30 "SARPS Support for Airworthiness Assessments GLS Signal Modeling", presented by Tim Murphy, Bretigny, 17-27 March 2009.
• ICAO NSP May10 WGW/WP16, "Computation of Maximum Undetected Error for RRFM in Support of Airworthiness Assessments".
• ICAO NSP May 2010 WGW WP 19, " SARPS Support for Airworthiness Assessments - More on GLS Signal Modeling" Prepared by Tim Murphy.
• ICAO Paper GNSSP-WP-8, Validation of GBAS CAT I Accuracy: A GLS Model and Autoland Simulations for Boeing Airplanes, presented at the ICAO Global Navigation Satellite Systems Panel, Working Group B Meeting, Seattle, WA, May 29 - June 9, 2000.
• ICAO Standards and Recommended Practices (SARPs) for the Global Navigation Satellite System (GNSS). Annex 10 to the Chicago Convention, Vol 1.
• M. Harris, T. Murphy, "Geometry Screening for GBAS to Meet CAT III Integrity and Continuity Requirements", Proceedings of the Institute of Navigation International Technical Meeting 2007.
• Neri, P., Macabiau, C., Azoulai, L., "Study of a GBAS Model for CAT II/III Simulations", Proceedings of the 22nd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2009), Savannah, GA, September 2009.
• RTCA / DO-245, Minimum Aviation System Performance Standards (MASPS) for the Local Area Augmentation System (LAAS).
C-22
AC 20-191 Appendix C
• RTCA/DO-253D, "Minimum operational Performance Standards for GPS Local Area Augmentation Airborne Equipment".
• RTCA / DO-253C, Minimum Operational Performance Standards (MOPS) for GPS Local Area Augmentation System (LAAS) Airborne Equipment.
• T. Murphy, M Harris, C. Shively, L. Azoulai , M. Brenner "Fault Modeling for GBAS Airworthiness Assessments", Proceedings of the Institute of Navigation Global Navigation Satellite System Conference, 2010.
• Use of GNSS signals and their augmentations for civil Aviation Navigation during Approaches with Vertical Guidance and Precision Approaches – PhD Thesis P. Neri – 2011.
C.4 Acronyms and Definitions for GBAS Performance Model.
• Bj,vert Estimate of the vertical error due to a fault of the jth reference receiver
• ECEF Earth-Centered, Earth Fixed coordinate system
• EL Lateral Error
• EMAX Peak error magnitude
• EV Vertical error
• GERP GBAS Elevation Reference Point
• GRP GLS Reference Point
• GW Lateral distance between the main landing gear
• GWN Gaussian White Noise
• Gx Compensation gain
• H(s) Second order Butterworth filter that is implemented in the GBAS NSE generator
• Katrk NSE geometry scale factor – along track
• Kvert NSE geometry scale factor – vertical track
• Kxtrk NSE geometry scale factor – cross-track
• LAL Lateral Alert Limit
• LLC Land Long Criteria
• LP Lateral Protection Level
• LSC Land Short Criteria
• LTP Landing Threshold Point
• M Number of GNSS reference receivers C-23
AC 20-191 Appendix C
• maxEL User specified maximum allowable lateral position error
• maxEV User specified maximum allowable vertical position error
• Pmd Probability of missed detection
• pTSE_LATE(x,E) P robability density function for the lateral touchdown given a bias of magnitude E
• pTSE_LONE(x,E) Probability density function for the longitudinal touchdown given a bias of magnitude E
• Pmd (E) Probability of an error not being detected as a function of E
• PU (E) Probability of an unsuccessful landing given an error
• PULE (E) Probability of an unsuccessful landing given a particular size of error
• RMS Root Mean Square
• RR Ramp Rate
• RRFM Reference Receiver Fault Monitor
• RWE Lateral landing criteria
• SAprvert.i Projection of the vertical component and translation of the alongtrack components into the vertical for ith ranging source
• Slat Largest lateral coefficient magnitude for any single satellite
• Slat2 Largest sum of lateral coefficient magnitudes for any two satellites
• Svert Largest vertical coefficient magnitude for any single satellite
• Svert_max Maximum vertical projection for any satellite allowed by geometry screening
• Svert2 Largest sum of vertical coefficient magnitudes for any two satellites
• TBAC Maximum threshold for the RRFM monitor
• TTD Time To Detect
• VAL Vertical Alert Limit
• VPL Vertical Protection Level
• ω n Natural frequency in radians/second C-24
AC 20-191 Appendix D APPENDIX D. AFM PROVISIONS AND EXAMPLE AFM WORDING D.1 Example Provision: AFM "Certificate Limitation" Section.
(With "Type Specific" Example Information and Notes) (List Aircraft Type)
AIRPLANE FLIGHT MANUAL Section 1 - CERTIFICATE LIMITATIONS
ELECTRONIC SYSTEMS
AUTOPILOT/FLIGHT DIRECTOR SYSTEM Automatic Landing Maximum wind component speeds when landing weather minima are predicated on autoland operations:
Headwind: 25 knots Tailwind: 15 knots Crosswind: 5 knots The maximum and minimum glideslope angles are 3.25 degrees and 2.5 degrees respectively.
The autoland capability may be used with flaps 20 or 30, with both engines operative or with one engine inoperative. The Autopilot Flight Director System (AFDS) status annunciation must have LAND 2 or LAND 3 displayed and the SLATS DRIVE message must not be present.
Automatic Approach with Flaps 25 Autoland is not approved with flaps 25.
FAA APPROVED (Date) Section 3 Page D-1
AC 20-191 Appendix D D.2 Example Provision - AFM “Normal Procedures” or “Normal Operation” Section.
[Typical Aircraft Type with Fail Operational and Fail Passive FGS Capability] (List Aircraft Type)
AIRPLANE FLIGHT MANUAL Section 3 - NORMAL PROCEDURES AUTOPILOT - FLIGHT DIRECTOR SYSTEM (AFDS)
LOW WEATHER MINIMA - AUTOMATIC LANDING - FAIL-OPERATIONAL The autopilot system has been shown to meet the applicable airworthiness, performance, and integrity criteria applicable to Category III as specified in FAA Advisory Circular AC 20-191 for a fail- operational automatic landing system, with the following functions operative and LAND 3 annunciated:
Autoland status annunciation on both PFD’s Autothrottle/autothrust Independent ILS and radio altitude sources on the PFD for each pilot, i.e., the following alerting messages are not displayed:
SGL SOURCE DISPLAYS
SGL SOURCE RAD ALT
SINGLE SOURCE ILS
LOW WEATHER MINIMA - AUTOMATIC LANDING - FAIL-PASSIVE The autopilot system has been shown to meet the applicable airworthiness, performance, and integrity criteria applicable to Category III as specified in FAA AC 20-191 for a fail-passive automatic landing system, with the following functions operative and LAND 2 annunciated:
Autoland status annunciation on both PFD’s Independent ILS and radio altitude sources on the PFD for each pilot, i.e., the following alerting messages are not displayed:
SGL SOURCE DISPLAYS
SGL SOURCE RAD ALT
SINGLE SOURCE ILS The demonstration for fail-passive autoland operations with LAND 2 annunciated included a provision for a go-around if a subsequent autopilot system failure were to be detected on approach, if operational credit for use of autoland is required.
CAUTION: If the autopilot disconnects during an engine-out go-around, loss of autopilot rudder control can result in large yaw and roll excursions.
FAA APPROVED (Date) Section 3 Page D-2