loran integrity performance panel analysis of asf for rnp 0.3 sherman lo, stanford university...
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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?
Loran Integrity Performance Panel 3
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
Loran Integrity Performance Panel 4
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
Loran Integrity Performance Panel 5
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
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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
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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
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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
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Temporal ASF
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Historical ASF Variation (Temporal)
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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
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Monitor Data
Raw Data
“Decimated” Data
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Modeling at Sandy Hook (Not Using Caribou)
TOA(t)
c(t)
Car(t)
max
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Modeling at Sandy Hook (Not Using Nantucket)
TOA(t)
c(t)
Nan(t)
max
Loran Integrity Performance Panel 15
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
Loran Integrity Performance Panel 16
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?
Loran Integrity Performance Panel 17
Spatial ASF
Loran Integrity Performance Panel 18
Spatial ASF – Cape Elizabeth from Nantucket (D. Last, P. Williams)
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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
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HPL Contribution from Position Domain
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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
Cape Elizabeth: 1 loss 10 131.51
include Nantucket 20 191.85
Cape Elizabeth: 2 loss 10 344.02
20 546.06
Cape Elizabeth: 2 loss 10 252.2
include Nantucket 20 269.89
Loran Integrity Performance Panel 22
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
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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?
Loran Integrity Performance Panel 24
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
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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
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Test Case: Availability
Loran Integrity Performance Panel 27
Test Case: Continuity
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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
Loran Integrity Performance Panel 29
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 .