Shankar Ramakrishnan, Jiyun Lee, Sam Pullen and Per Enge Stanford University

1. Targeted Ephemeris Decorrelation Parameter Inflation for Improved LAAS Availability during Severe Ionosphere Anomalies Shankar Ramakrishnan, Jiyun Lee, Sam Pullen and Per Enge Stanford University ION National Technical Meeting -2008San Diego,California Session A2: Algorithms & Methods 1 January 28, 2008

2. Ice Breaker • Flight Delayed or Cancelled due to Bad Weather? • Flight Diverted due to Poor Runway Visibility? • What is it like to land without Runway Visibility? Video Courtesy: http://youtube.com/watch?v=uigpqpDWIwE Image Courtesy: www.images.google.com

3. Overview • Current Autoland systems based on Instrument Landing Systems • ILS based systems have inherent limitations • Next-Gen Air Traffic Systems to extensively leverage GNSS technology • Local Area Augmentation System (LAAS) to eventually provide autoland capability • LAAS systems must meet stringent requirements on four key system parameters: • Accuracy • Integrity • Continuity • Availability

4. Integrity Requirement Federal Aviation Administration (FAA) places strict requirements on risk of missing touchdown box: 10-9 per approach • Flight Technical Error (FTE) • Navigation Sensor Error (NSE)

5. Integrity Requirement Federal Aviation Administration (FAA) places strict requirements on risk of missing touchdown box: 10-9 per approach • Flight Technical Error (FTE) • Navigation Sensor Error (NSE) Alert Limit

6. GPS Error Sources GPS clock error Ephemeris error Ionospheric delay Tropospheric delay Multipath error Receiver noise

7. Error Mitigation: Differential GPS (DGPS) GPS clock error Ephemeris error Ionospheric delay Tropospheric delay Differential Corrections Receiver noise Multipath error

8. Failure Local Area Augmentation System (LAAS) Space Segment Ranging Signal Orbit parameters LAAS Ground Facility (LGF) Airborne User 1) Differential corrections 2) Detect failure and Alarm user 3) Integrity parameters VHF Data Broadcast Multiple Receivers

9. User Error Bound LAAS Provides Protection Level that Bound Residual User Errors out to Integrity Requirement • Measurement Noise (air, ground) • Nominal Ionosphere Decorrelation • Multipath • Undetected Faults Protection Level Alert Limit

10. Ionosphere – Something to Fear About • Ionosphere Anomalies poses the biggest integrity threat to LAAS • Periods of Solar High results in anomalous ionospheric conditions. • Users can suffer errors as high as 50m just due to the ionosphere! • Efficient algorithms required at the LAAS ground facility to detect and mitigate such risks Image Courtesy: http://sohowww.nascom.nasa.gov/gallery/SolarCorona/combo001.html

11. Modeling an Ionosphere Front Simplified Ionosphere Wave Front Model: a wave front ramp defined by the “slope”. “width” and the front “speed” Front Speed Front Slope LGF IPP Speed Front Width Airplane Speed LAAS Ground Facility Data from Past Solar Storms analyzed to determine upper and lower bounds for the three parameters.

12. Ionosphere Induced Range Error • Ionosphere Threat Model: Basis for Worst-case airborne differential range errors • Use of a Code-Carrier Divergence Rate (CCD) Monitor limits impact. • Closed Form Range Error Tables derived which leverage front velocity as key parameter • Slow Front Speed: 10m/s < Δv < 40m/s • No CCD Detection • Largest Error: • Moderate Speed : Monitor Starts to Trip, Errors Drop • Fast Speed: Monitor Trips for sure • Obtain Maximum Ionosphere Induced Error in Range (MIER)

13. Meeting LAAS Integrity Under Faulted Conditions; Position Error < Total Error Limit Total Error Limit Position Error Under Nominal Conditions; Protection Level < Alert Limit Alert Limit Protection Level

14. Position-Domain Geometry Screening • Worst Case: Any two satellites in a geometry can be impacted simultaneously. • Require Error In Vertical! • Position domain verification is needed to establish the safety of a given geometry • Max. Iono. Error Vertical (MIEV) is compared to Obstacle Clearance Surface (OCS) limit to determine if a given user subset geometry is “safe” • If MIEV falls below OCS, no hazard would occur • If MIEV exceeds OCS, geometry is potentially hazardous Need an Efficient Algorithm to Eliminate Unsafe Subsets

15. Sigma of Vertical Ionosphere Gradient (vig) ; Protection Level and Sigmas Vertical navigation error bound evaluated by aircraft Standard deviation of differentially corrected pseudorange error Vertical Protection Level (VPL) Broadcast Integrity Parameters LGF

16. Real-Time P-Value Inflation: Step 1 Increase P-value by a small amount DP on all approved satellites and re-evaluate availability of remaining unsafe subsets at all separations from DH. Continue until no unsafe subsets remain or until PA is reached. PA Many small steps DP Pnom 1 2 3 4 N # unsafe subsets Satellites Approved by LGF

17. Real-Time P-Value Inflation: Step 2 Increase P-value of one approved satellite by DP and re-evaluate availability. Continue until no unsafe subsets remain or until PB is reached. If PB is reached first, repeat as needed with 2nd satellite, then 3rd satellite, etc. until all satellites reach PB. PB Current heuristic to select SV to inflate: Maxi { Sverti(worst subset) / Sverti (all usable) } DP PA Pnom 1 2 3 4 N # unsafe subsets Satellites Approved by LGF Pnorm =135e-6 PA = 170e6 PB = 270e-6

18. Real-Time P-Value Inflation: Step 3 If PB is reached for all satellites while unsafe subsets remain, revert to increasing P-values on all satellites until no unsafe subsets remain available (at any separation from DH). DP PB PA Pnom # unsafe subsets 1 2 3 4 N Satellites Approved by LGF

19. Pseudocode for Targeted “P-value” Inflation • Begin Execution • Compute Inflated σpr_gnd to protect DH = 2km. Input for subsequent DH distances. • For DH = 3:6 km { • For Distance = [DH,DH+1,DH+2,DH+3,DH+7]{ • Determine Unsafe Subsets • While Exists(Unsafe Subsets) • P-value = PvalueInflation(DH,Distance,P-value) • } • } • Broadcast Inflated P-values, σpr_gnd for N “all-in-view” satellites LGF can track • End Execution

20. Results – Memphis Intl. Airport

21. Results – Memphis Intl. Airport

22. Results – Memphis Intl. Airport

23. Results – Memphis Intl. Airport

24. Results – Memphis Intl. Airport

25. Results – Memphis Intl. Airport

26. Results – Memphis Intl. Airport

27. Results – Memphis Intl. Airport

28. Results – Major US Airports

29. Summary • Targeted Ephemeris Decorrelation Parameter Inflation Algorithm helps meet integrity. • Achieves guaranteed LAAS Cat – I availability for major US airports • Computationally robust: • Average Computation Time : 30 seconds per epoch • Worst Case Computation Time: 73 seconds per epoch • Computations performed on Matlab running on a Intel Core 2 Duo 2.2 Ghz Processor. • Scope for further optimization of performance • Algorithm scalable to changes in satellite constellation.

30. Acknowledgement This work was supported by the affiliated members of the Stanford Center for Position Navigation and Time (SCPNT) Question Time

31. Backup

32. Outline • Overview of Problem • Updated Ionosphere Threat Model • Ionospheric Anomaly Induced Range Error Computation • Position-Domain Geometry Screening • Proposed Algorithm for Geometry Screening • Results & Conclusion