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 - 2008 San Diego, California Session A2: Algorithms & Methods 1 January 28, 2008

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

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

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)

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

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

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

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

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

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

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.

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)

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

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

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

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

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

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

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

Results – Memphis Intl. Airport

Results – Memphis Intl. Airport

Results – Memphis Intl. Airport

Results – Memphis Intl. Airport

Results – Memphis Intl. Airport

Results – Memphis Intl. Airport

Results – Memphis Intl. Airport

Results – Memphis Intl. Airport

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)

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.

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

Backup

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