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

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

e C

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esy:

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asa.

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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


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


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)


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


0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160

180


inflation at 13 km

Time Index

MIE

V (

m)



OCS Limit (m)


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)


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)


Uninflated VPL

e

Inflated VPLe


0 50 100 150 200 250 30010

15

20

25

30

35

40

45


inflation at 3 km

Time Index

MIE

V (

m)



OCS Limit (m)


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)


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)


Uninflated VPLe

Inflated VPLe


0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160


inflation at 10 km

Time Index

MIE

V (

m)



OCS Limit (m)


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)


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)


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

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

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