Loran Integrity Performance Panel Analysis of ASF for RNP 0.3 Sherman Lo, Stanford University...

Loran Integrity Performance Panel

Analysis of ASF for RNP 0.3

Sherman Lo, Stanford UniversityInternational Loran Association

Boulder, CO, Nov 3-7, 2003

Loran Integrity Performance Panel 2

Additional Secondary Factors

• Additional Secondary Factor (ASF) Delay in propagation time due to traversing

heterogeneous earth relative to sea water path Major source of error for Loran navigation

• Why are we studying this? Need to understand effects of ASF to meet

aviation requirements Integrity: Bound the worst caseHaven’t we been here before?

Hasn’t this been studied before?


Aviation Requirements

HAL

• Integrity: Does our protection level bound position error• Requirement: 99.99999% (1-10-7)

• Availability: How often is the solution valid for RNP 0.3• Requirement: > 99.9% (HAL = 556 m)

• Continuity: Is solution available for entire approach if initially available

• Requirement: > 99.9% (150 sec)

HPL


Calculating HPL

• i is the standard deviation of a normal distribution

that overbounds the randomly distributed errors SNR, transmitter jitter

• i an overbound for the correlated bias terms Correlated temporal ASF

• i an overbound for the uncorrelated bias terms Uncorrelated ASF temporal errors, ASF spatial error

• PB is a position domain overbound ASF spatial error

2i i i i i i

i i i

HPL K K K PB


Temporal & Spatial Effects

• ASF is modeled in two components: temporal & spatial.• ECD is can be modeled similarly though with other

components (transmitter effects, etc.)

1

ECD1

2

ECD2

3

ECD3

4

ECD4

5

ECD5

6

ECD6

7

ECD7

8

ECD8

N

ECDN

rx

tx

x

x

ASF t x s terrain dx

rx

tx

x

x

ECD p x q terrain dx Varies temporally Varies spatially


Average ASF Value At Calibration Point xo

Provided

At Aircraft Location User ASF will differ from provided ASF

Variation of ASF

•User has an average ASF

•ASF look up table is to be provided to user (at each calibration pt)

,, ,user ave o o oASF x t ASF x ASF x t ASF x x ASF used by

receiver (rx ASF)Difference from rx ASF from using a different location

Difference from rx ASF from seasonal

changes


One Important Concept …

• Assumption: Time of Transmission (TOT) Eliminate effect of SAM Otherwise SAM induced changes need to be accounted for when

using TOA

• TOT control eliminates a potential source of error While the SAM may reduce the actual error, since we do not

know its effects, we have to assume it does not

TOT aids in reducing bound on ASFResults in better availability, continuity

,

, ,N N N N

N

tx tx tx tx

user mean o o o

tx

ASF x t ASF x ASF x t ASF x x

SAM t


Data Collection

• TOA and TOT monitors; FAATC/JJMA/USCGA flight tests

• USCG data from transmitters, SAM (TINO, etc.)

TOT Master

TOT Monitor

TOA Monitor

TOA MonitorSpatial ASF

Spatial ASF


Temporal ASF


Historical ASF Variation (Temporal)


Temporal ASF Model

ASFN,mean = mean ASF used by the receiver

TOAN(t) is the TOA relative to the nominal for the Nth signal (transmitter) at time t

dN,land are the relative amplitudes for the time varying components depending on distance (initially assumed known)

TOA(t) are the common time varying components that have different amplitudes for different signals (propagation)

c(t) are the common time varying components that have the same amplitudes for different signals (mainly clock error)

N(t) are what remains after taking out the correlated part of the TOAs (residual error)

, ,*N N mean N land NASF t ASF TOA t d c t t

,N N N meanTOA t ASF t ASF


Monitor Data

Raw Data

“Decimated” Data


Modeling at Sandy Hook (Not Using Caribou)

TOA(t)

c(t)

Car(t)

max


Modeling at Sandy Hook (Not Using Nantucket)

TOA(t)

c(t)

Nan(t)

max


Temporal ASF at Other Locations

Monitor Num Stations

TOA(All Sta)

Residual Error (All Sta)

Cape Elizabeth, ME

5 1089 307

Sandy Hook, NJ 5 1116 297

Annapolis, MD* 7 299 390


Conclusions on Temporal ASF

• Bound on Temporal ASF Variations is a significant factor in the HPL Should be worst in NEUS

• Important to divide temporal ASF into correlated and uncorrelated contributions Correlated error does not need to be treated in the worst

possible manner

• Current values used (NEUS) 1000 ns/Mm (correlated) 300 ns (uncorrelated) Are these values adequate for integrity? Can we do better with another model?


Spatial ASF


Spatial ASF – Cape Elizabeth from Nantucket (D. Last, P. Williams)


Comparison of Spatial ASF Data vs. Model (G. Johnson)

• Greg Johnson will present more about this next!

Boise City

2.00

2.50

3.00

3.50

4.00

4.50

5.00

38.10 38.30 38.50 38.70 38.90 39.10 39.30 39.50

Latitude

Re

lati

ve

AS

F

Measured

Predicted

High std dev


HPL Contribution from Position Domain


Cape Elizabeth Spatial ASF Bounds

Situation Radius (nm) Bound PD (m)

Cape Elizabeth nominal 10 87.30

20 165.80

Cape Elizabeth: 1 loss 10 220.94

20 373.78


include Nantucket 20 191.85


20 546.06


include Nantucket 20 269.89


Bounds for Spatial ASF

Location Terrain Type NumberSta

Nom PD (m) 1 Loss PD (m)

10 nm 20 nm 10 nm 20 nm

Cape Elizabeth, ME Coast 7 87 166 221 374

Destin, FL Coast 7 319 439 395 545

Grand Junction, CO Mountain 9 205 266 259 291

Point Pinos, CA Coast, Mountain

7 181 371 540 846

Spokane, WA Mountain 11 60 103 80 138

Plumbrook, OH Interior 9 22 39 28 63

Bismarck, ND Interior 7 36 55 64 67

Little Rock, AR Interior 9 36 48 51 65


Conclusions on Spatial ASF

• Bound on Spatial ASF Variations is a significant factor in the HPL Should be worst in mountainous and coastal regions

• Position Domain Bound used Allows the incorporation of correlation Limits allowable station sets

• Current values used 120 m (PD) for interior Good for up to 20 km with 1-2 station(s) missing How much an inflation factor is necessary?


Availability & Continuity

• Bound on ASF variations allows calculation of HPL Need bound for noise, transmitter error

• Availability occurs when: Pass Cycle Resolution Test HPL < HAL (556 meter)

• Continuity occurs when: Initially Available Available over next 150 seconds


Caveats

• Models dependent on many assumed values Errors (ASF, tx, noise) Noise Algorithm (Cycle, etc.) Station availability

• Need to aggregate for all scenarios interference, early skywave, different noise levels Only one case shown: 99% noise level, etc.

• Weighted by assumed regional ASF variations, etc.

RESULTS SHOWN ARE NOT FINAL NOR NECESSARILY REPRESENTATIVE


Test Case: Availability


Test Case: Continuity


Conclusions …

• Need to bound ASF – largest error source TOT reduces error to be bounded Separate ASF into temporal & spatial

• Temporal ASF Separate into correlated & uncorrelated terms

• Spatial ASF Use position bound Bounds can be very high on coast, mountain

• Have tools in place so that once we have results for all hazards, the continuity and availability can be quickly determined

• Story is not complete – more to come


Acknowledgements

• Federal Aviation Administration Mitch Narins – Program Manager

• Contributors Bob Wenzel, Ben Peterson Prof. David Last, Paul Williams Greg Johnson, CAPT Richard Hartnett, FAATC LT Dave Fowler, LT Kirk Montgomery

• The views expressed herein are those of the presenter and are not to be construed as official or reflecting the views of the U.S. Coast Guard, Federal Aviation Administration, or Department of Transportation .

Loran Integrity Performance Panel Analysis of ASF for RNP 0.3 Sherman Lo, Stanford University...

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