1. Shankar Ramakrishnan, Jiyun Lee, Sam Pullen and Per Enge
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 San 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: Image Courtesy:

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: 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: 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) Differential Corrections
GPS clock error
Ephemeris error
Ionospheric delay
Tropospheric delay
Differential Corrections
Receiver noise
Multipath error

8. Local Area Augmentation System (LAAS)
Failure
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 Protection Level Alert Limit
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:

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
One of the residual errors that can build up for the user of a dGPS system like LAAS is the ionosphere spatial decorrelation error. This error is caused by the fact that two signals are passing through different region of the atmosphere and the ionospheric delays cannot be completely canceled out even after applying differential corrections. Such errors can grow specially under severe ionosphere storm and pose a threat to user integrity . So we are interested in finding out what the error in the worst case conditions could be along with developing an adequate mitigation method. In this study, we used simplified ionosphere front model with three parameters, which are front speed, slope and width, assuming the slope is linear and the front is moving with a constant speed. Then we try to estimate those parameters using data collected on ionosphere stormy days.
“We are interested in low elevation anomalies for the same reason we are interested in ionosphere anomalies at high elevations: An ionosphere anomaly can be parameterized by the things shown in the slide, and ---
One of the largest ionosphere gradients was observed during the November 2003 ionosphere storm in OH/MI region. If we model the ionosphere front as a linear flying wedge with a constant speed, the estimated slope of the ionosphere front was about 300 mm/km moving with a speed of 200 m/s. Let’s assume a stationary ionosphere front scenario i.e. the front and IPP of LGF move with the same speed and direction, the LGF cannot detect this event, and the resulting residual error is about 5.7 meters in range domain.
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. Protection Level and Sigmas
Vertical navigation error bound evaluated by aircraft
Standard deviation of differentially corrected pseudorange error
Vertical Protection Level (VPL)
Sigma of Vertical Ionosphere Gradient (vig) ;
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 PA = 170e 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 1 2 3 4 N
# unsafe subsets
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
RTCA 24
DH=6km
DH=5 km
RTCA24
DH=4 km
DH=3 km
DH=2 km
DH=1 km
Memphis (MEM)
1.000
Denver (DEN)
Dallas (DFW)
Newark (EWR)
Washington (DCA)
0.993
0.997
Los Angeles (LAX)
Orlando (MCI)
0.990
Minneapolis (MSP)
Chicago (ORD)
0.999
Seattle (SEA)

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