Targeted Ephemeris Decorrelation Parameter Targeted Ephemeris Decorrelation Parameter Inflation for Improved LAAS Availability during Inflation for Improved LAAS Availability during
Severe Ionosphere AnomaliesSevere 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 BreakerIce 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
OverviewOverview
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 RequirementIntegrity 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 RequirementIntegrity 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 SourcesGPS Error Sources
GPS clock errorEphemeris error
Tropospheric delay
Ionospheric delay
Multipath error
Receiver noise
GPS clock errorEphemeris error
Differential Corrections
Error Mitigation: Differential GPS (DGPS)
Receiver noise
Tropospheric delay
Ionospheric delay
Multipath error
Local Area Augmentation System (LAAS)Local Area Augmentation System (LAAS)
VHF Data Broadcast
Space Segment
Airborne User
Ranging SignalOrbit parameters
1) Differential corrections
LAAS Ground Facility (LGF)
Failure
2) Detect failure and Alarm user
Multiple Receivers
3) Integrity parameters
User Error BoundUser 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
Ionosphere – Something to Fear AboutIonosphere – 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
Imag
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Simplified Ionosphere Wave Front Model: a wave front ramp defined by the “slope”. “width” and the front “speed”
Front Speed
Airplane Speed
Front Width
LAAS Ground Facility
Front Slope
LGF IPP Speed
Modeling an Ionosphere FrontModeling an Ionosphere Front
Data from Past Solar Storms analyzed to determine upper and lower bounds for the three parameters.
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)
Ionosphere Induced Range ErrorIonosphere Induced Range Error
)2(1 acvxg
0 5 10 15 200
5
10
15
20
25
30
35
Time (hours)
Ver
tica
l Err
or
and
VP
L (
met
ers)
Meeting LAAS IntegrityMeeting LAAS Integrity
Protection Level
Alert Limit
Under Faulted Conditions;
Position Error < Total Error Limit
Position Error
Total Error Limit
Under Nominal Conditions;
Protection Level < Alert Limit
Position-Domain Position-Domain Geometry Geometry ScreeningScreening
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
221121 ,,, SSvertSSvertSS SSMIEV
Need an Efficient Algorithm to Eliminate Unsafe Subsets
Broadcast Integrity Parameters Sigma of Vertical Ionosphere Gradient (vig) ; vig
Protection Level and SigmasProtection Level and Sigmas
2 2H0 ,VPL
N
ffmd v i iK S i=1
LGF
Vertical navigation error bound evaluated by aircraft
Vertical Protection Level (VPL)
2 2 2 2, , , _ ,i air i tropo i iono i pr gnd i
Standard deviation of differentially corrected pseudorange error
0_
_,__ HApr
ffmd
emdairivertApreApr VPL
K
KiPxSiVPL
Real-Time P-Value Inflation: Real-Time P-Value Inflation: Step 1Step 1
Pnom
PA
Many small steps P
Satellites Approved by LGF
1 2 3 4 N
Increase P-value by a small amount P 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.
# unsafe subsets
Real-Time P-Value Inflation: Real-Time P-Value Inflation: Step 2Step 2
Pnom
PA
Satellites Approved by LGF
1 2 3 4 N
Increase P-value of one approved satellite by P 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.
# unsafe subsets
PB
P Current heuristic to select SV to inflate:
Maxi { Sverti (worst subset) /
Sverti (all usable) }
Pnorm = 135e-6 PA = 170e6 PB = 270e-6
Real-Time P-Value Inflation: Real-Time P-Value Inflation: Step 3Step 3
Pnom
PA
Satellites Approved by LGF1 2 3 4 N
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).
# unsafe subsets
PB
P
Pseudocode for Targeted “P-value” InflationPseudocode 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. AirportResults – Memphis Intl. Airport
0 50 100 150 200 250 30010
15
20
25
30
35
40
45
MIEV Plot with Real-Time Pvalue
inflation at 6 km
Time Index
MIE
V (
m)
MIEV Pre-Inflation (m)
MIEV Post-Inflation (m)
OCS Limit (m)
Results – Memphis Intl. AirportResults – Memphis Intl. Airport
0 50 100 150 200 250 3002
2.5
3
3.5
4
4.5
5
5.5
6
Time Index
Pro
tect
ion
Lev
el (m
)
Vertical Protection Levels at 6 - 0 km
Uninflated VPLH0
Inflated VPLH0
0 50 100 150 200 250 3002
3
4
5
6
7
8
Time Index
Pro
tect
ion
Lev
el (m
)
Ephemeris Protection Levels at 6 - 0 km
Uninflated VPLe
Inflated VPLe
Results – Memphis Intl. AirportResults – Memphis Intl. Airport
0 50 100 150 200 250 3000
20
40
60
80
100
120
140
160
180
MIEV Plot with Real-Time Pvalue
inflation at 13 km
Time Index
MIE
V (
m)
MIEV Pre-Inflation (m)
MIEV Post-Inflation (m)
OCS Limit (m)
Results – Memphis Intl. AirportResults – Memphis Intl. Airport
0 100 200 3002
2.5
3
3.5
4
4.5
5
5.5
6
Time Index
Pro
tec
tio
n L
ev
el (
m)
Vertical Protection Levels at 6 - 7 km
Uninflated VPL
H0
Inflated VPLH0
0 100 200 3003
4
5
6
7
8
9
10
11
12
13
Time Index
Pro
tec
tio
n L
ev
el (
m)
Ephemeris Protection Levels at 6 - 7 km
Uninflated VPL
e
Inflated VPLe
Results – Memphis Intl. AirportResults – Memphis Intl. Airport
0 50 100 150 200 250 30010
15
20
25
30
35
40
45
MIEV Plot with Real-Time Pvalue
inflation at 3 km
Time Index
MIE
V (
m)
MIEV Pre-Inflation (m)
MIEV Post-Inflation (m)
OCS Limit (m)
Results – Memphis Intl. AirportResults – Memphis Intl. Airport
0 100 200 3002
2.5
3
3.5
4
4.5
5
5.5
6
Time Index
Pro
tec
tio
n L
ev
el (
m)
Vertical Protection Levels at 3 - 0 km
Uninflated VPLH0
Inflated VPLH0
0 100 200 3002
2.5
3
3.5
4
4.5
5
5.5
6
6.5
Time Index
Pro
tec
tio
n L
ev
el (
m)
Ephemeris Protection Levels at 3 - 0 km
Uninflated VPLe
Inflated VPLe
Results – Memphis Intl. AirportResults – Memphis Intl. Airport
0 50 100 150 200 250 3000
20
40
60
80
100
120
140
160
MIEV Plot with Real-Time Pvalue
inflation at 10 km
Time Index
MIE
V (
m)
MIEV Pre-Inflation (m)
MIEV Post-Inflation (m)
OCS Limit (m)
Results – Memphis Intl. AirportResults – Memphis Intl. Airport
0 100 200 3002
2.5
3
3.5
4
4.5
5
5.5
6
Time Index
Pro
tec
tio
n L
ev
el (
m)
Vertical Protection Levels at 3 - 7 km
Uninflated VPL
H0
Inflated VPLH0
0 100 200 3002
3
4
5
6
7
8
9
10
11
Time Index
Pro
tec
tio
n L
ev
el (
m)
Ephemeris Protection Levels at 3 - 7 km
Uninflated VPL
e
Inflated VPLe
Results – Major US AirportsResults – Major US Airports
AirportRTCA 24DH=6km
RTCA 24DH=5 km
RTCA24DH=4 km
RTCA 24DH=3 km
RTCA 24DH=2 km
RTCA 24DH=1 km
Memphis (MEM) 1.000 1.000 1.000 1.000 1.000 1.000
Denver (DEN) 1.000 1.000 1.000 1.000 1.000 1.000
Dallas (DFW) 1.000 1.000 1.000 1.000 1.000 1.000
Newark (EWR) 1.000 1.000 1.000 1.000 1.000 1.000
Washington (DCA) 0.993 0.997 1.000 1.000 1.000 1.000
Los Angeles (LAX) 1.000 1.000 1.000 1.000 1.000 1.000
Orlando (MCI) 0.990 1.000 1.000 1.000 1.000 1.000
Minneapolis (MSP) 1.000 1.000 1.000 1.000 1.000 1.000
Chicago (ORD) 0.999 1.000 1.000 1.000 1.000 1.000
Seattle (SEA) 1.000 1.000 1.000 1.000 1.000 1.000
SummarySummary
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
BackupBackup
OutlineOutline
Overview of Problem
Updated Ionosphere Threat Model
Ionospheric Anomaly Induced Range Error Computation
Position-Domain Geometry Screening
Proposed Algorithm for Geometry Screening
Results & Conclusion