Transcript No Slide Title

Analysis of ASF for RNP 0.3
Sherman Lo, Stanford University
International Loran Association
Boulder, CO, Nov 3-7, 2003
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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
worst
casebefore?
Haven’t
wethe
been
here
Hasn’t this been studied before?
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Aviation Requirements
• Integrity: Does our protection level bound position error
• Requirement: 99.99999% (1-10-7)
HPL
• Availability: How often is the solution valid for RNP 0.3
• Requirement: > 99.9% (HAL = 556 m)
HAL
• Continuity: Is solution available for entire approach if
initially available
• Requirement: > 99.9% (150 sec)
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Calculating HPL
HPL  
2
K
a
 i i
i
K b   K g
i
i
i
i i
 PB
i
• ai is the standard deviation of a normal distribution
that overbounds the randomly distributed errors
SNR, transmitter jitter
• bi an overbound for the correlated bias terms
 Correlated temporal ASF
• gi an overbound for the uncorrelated bias terms
Uncorrelated ASF temporal errors, ASF spatial error
• PB is a position domain overbound
ASF spatial error
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Temporal & Spatial Effects

s1
ECD1
s2
ECD2
s3
ECD3
ASF 
s4
ECD4
s5
ECD5
s6
ECD6
s7
ECD7
s8
ECD8
sN
ECDN
xrx
 t s  x    s  terrain dx
xtx
ECD 
xrx
  p s  x    q  terrain dx
xtx
Varies temporally
Varies spatially
• ASF is modeled in two components: temporal & spatial.
• ECD is can be modeled similarly though with other
components (transmitter effects, etc.)
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Variation of ASF
At Aircraft Location
User ASF will differ
from provided ASF
Average ASF Value At
Calibration Point xo
Provided
ASFuser  x, t   ASFave  xo   ASF  xo ,t   ASF  x, xo 
ASF used by
receiver (rx ASF)
Difference from rx
ASF from seasonal
changes
Difference from rx
ASF from using a
different location
•User has an average ASF
•ASF look up table is to be provided to user (at each calibration pt)
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One Important Concept …
tx N
ASFuser
SAM
tx N
 x, t   ASF  x   ASF  x t   ASF  x , x 
tx N
mean
tx N
o
tx N
o,
o
t 
• 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 ASF
Results in better availability, continuity
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Data Collection
TOT Master
TOT Monitor
Spatial ASF
TOA Monitor
TOA Monitor
Spatial ASF
• TOA and TOT monitors; FAATC/JJMA/USCGA flight tests
• USCG data from transmitters, SAM (TINO, etc.)
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Temporal ASF
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Historical ASF Variation
(Temporal)
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Temporal ASF Model
ASFN t   ASFN ,mean  d TOAt  * d N ,land  c t   e N t 
TOAN t   ASFN t   ASFN ,mean
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)
dTOA(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)
eN(t) are what remains after taking out the correlated part of the TOAs
(residual error)
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Monitor Data
Raw Data
“Decimated” Data
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Modeling at Sandy Hook
(Not Using Caribou)
dTOA(t)
c(t)
emax
eCar(t)
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Modeling at Sandy Hook
(Not Using Nantucket)
dTOA(t)
c(t)
emax
eNan(t)
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Temporal ASF at Other
Locations
Monitor
dTOA
Num
Stations
Residual
Error (All Sta)
(All Sta)
Cape Elizabeth,
ME
5
1089
307
Sandy Hook, NJ
5
1116
297
Annapolis, MD*
7
299
390
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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?
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Spatial ASF
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Spatial ASF – Cape Elizabeth from
Nantucket (D. Last, P. Williams)
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Comparison of Spatial ASF
Data vs. Model (G. Johnson)
Boise City
5.00
High std dev
Measured
4.50
Predicted
Relative ASF
4.00
3.50
3.00
2.50
2.00
38.10
38.30
38.50
38.70
38.90
39.10
39.30
39.50
Latitude
• Greg Johnson will present more about this next!
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HPL Contribution from Position
Domain
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Cape Elizabeth Spatial ASF
Bounds
Situation
Radius (nm)
Cape Elizabeth nominal
Bound PD (m)
10
87.30
20
165.80
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
Cape Elizabeth: 1 loss
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Bounds for Spatial ASF
Location
Terrain Type
Number Nom PD (m)
Sta
10 nm
1 Loss PD (m)
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?
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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
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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
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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 .
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