A Preliminary Study of LORAN-C Additional
Secondary Factor (ASF) Variations
CAPT Richard Hartnett, PhD, US Coast Guard Academy
Gregory Johnson, JJMA, Inc.
Peter F. Swaszek, PhD, University of Rhode Island
Mitchell J. Narins, US Federal Aviation Administration
Abstract
Currently, there is considerable interest in the LORAN community in the recognition of
LORAN-C as “the” backup navigation system for the global positioning system (GPS). A key to
this recognition is the demonstration to aviation navigation that LORAN-C can achieve the
accuracy, availability, integrity, and continuity to support non-precision approaches (RNP 0.3).
To do so, it is required that we better understand the variations in the LORAN positioin “fix” due
to the changing characteristics of the signal propagation path (so called additional secondary
factors or ASFs). The U.S. Coast Guard Academy, under contract to the Federal Aviation
Administration (FAA), is attempting to understand and characterize these variations for “all-inview” receivers using time-of-arrival (TOA) data. This paper reports on some recent results in
this arena.
Introduction
The Federal Aviation Administration (FAA) observed in its recently completed Navigation
Transition Study that LORAN-C, as an independent radionavigation (RNAV) system, is
theoretically the best backup for the Global Positioning System (GPS). However, the FAA also
observed that LORAN-C’s potential benefits to aviation hinges upon its ability to support nonprecision approach (NPA), which equates to a Required Navigation Performance (RNP) of 0.3.
The tests and evaluations the FAA is conducting and sponsoring will determine whether
LORAN-C can provide the accuracy, availability, integrity, and continuity to support NPA. A
key component in these evaluations is a better understanding of ASFs and how to apply them to
achieve more accurate LORAN-C positions while ensuring that the possibility of providing
hazardous and misleading information (HMI) will be no greater than 1 x 10-7. The U.S. Coast
Guard Academy, as a part of the FAA’s Government, Industry, and Academic team, is striving to
improve our understanding of both the temporal and spatial variations in time of arrival (TOA)
that could be mitigated through use of appropriate additional secondary factors (ASFs)
[4,5,9,10,11].
Flight tests conducted jointly with Ohio University in August 2002 employed a digital downconverter (DDC)-based LORAN-C receiver to collect LORAN position data concurrent with a
Novatel OEM-4 GPS receiver to collect WAAS GPS positions. A PC-104-form factor LORANC receiver utilizing an H-field antenna was used to collect TOA ASF data while the aircraft sat
on the ground in the vicinity of the intended flight. During post-processing of the recorded flight
data, ideal ASFs were applied to the TOAs recorded during the flight to determine a corrected
LORAN position. The WAAS GPS derived positions were used as “truth” to compute the
1
“error” in each LORAN provided position. These position errors were then plotted
geographically to show the position error as a function of distance from the ASF calibration
point which gives some insight into the spatial variation of the ASFs.
This paper presents preliminary results on characterizing the spatial variations in ASF
corrections. Other results include validation of the data collection methodology and equipment
and specification of the required data and formats. Plans for future testing and analysis to enable
compilation and validation of an initial ASF database are also provided.
Methodology of Data Collection
The Coast Guard Academy developed PC-104 H-field LORAN receiver [1, 7, 8] was used as the
primary component of the ASF data collection system. A block diagram of the overall system is
below in Figure 1. The receiver itself is implemented in an industry standard PC-104 form-factor
and consists of 3 PC-104 boards – a Gatefield board, a CPU board, and an oscillator board – that
are stacked together (see the photograph in Figure 2). Inputs to the PC-104 receiver are the two
RF channels from the H-field antenna, a GPS 1 PPS (pulse per second) signal for the timing
reference, and a 12.8 MHz clock signal from a stable signal source. In this case a DS-345
Function Generator that has been stabilized with a 10 MHz reference from a cesium oscillator.
1 PPS
Novatel OEM-4
WAAS GPS
H-field antenna
10 MHz
PC-104
Rcvr
DS-345
Signal
Generator
12.8 MHz
2 Channels RF
Save to disk: TIC, RAW TOA,
ECD, SNR, etc.
Figure 1 – Block diagram of ASF data collection system.
2
Figure 2 – Picture of USCGA PC-104 LORAN Receiver
The general procedure to collect ASF measurements is to run the PC-104 receiver in the location
for which the ASF’s are desired. The latitude and longitude of the location need to be known
very accurately. In practice a DGPS or WAAS GPS receiver is used to collect positions over a
period of time at the location. The actual position is taken to be the average of these position
samples. The PC-104 receiver can only track 3 chains simultaneously (a limitation of the
Gatefield board), so ASF corrections can only be calculated for stations in those 3 chains. The
receiver saves the TIC (time interval count), and the RAW TOA for each station at user
configurable intervals; typically 2 seconds. The receiver also saves the tracking point strength,
the SNR, and the ECD for each station as well as calculated latitude and longitude, time, and
heading. This data file is then post-processed using the calibrated location of the receiver (as
determined from DGPS/WAAS GPS). The timing relationships, and how the ASF is derived
from this information is illustrated in Figure 3 on the next page.
3
Emission Delay
Correction
Master Xmit
(Master offset from 1 PPS) mod
200 μsec = 0
Station Xmit
Emission Delay
Time Interval
Counter
1 PPS
Predicted all seawater
path TOA
Raw TOA
PCI Strobe
ASF
Loran signal
rcvd
Receiver Delay
Figure 3 – ASF definition.
Using the following definitions:
TIC (time interval counter) = time interval from 1 PPS pulse to start of PCI.
Raw TOA = time interval from start of PCI to when the receiver thinks the signal is
received.
Master offset = time interval from 1 PPS pulse to when the Master transmits. The Master
station is nominally synchronized to this so that Master offset mod 200 microseconds = 0.
Receiver (Rcvr) Delay = time delay introduced by receiver due to analog front end as
well as digital filtering.
ED = published Emission Delay for the Secondary station.
EDC = Emission Delay Correction = difference from when the Secondary should have
transmitted based upon the ED and when the Secondary actually transmits, referenced to
1 PPS.
TOA = Time of Arrival = propagation time from Secondary (known position) to receiver
(calibrated position) assuming an all-seawater propagation path.
ASF = Additional Secondary Factor = propagation time adjustment due to the fact that
the path is not all-seawater
and the diagram above (Figure 3), it is clear that:
TIC + Raw TOA - Rcvr Delay = Master offset + ED + EDC + TOA + ASF
Of these values, EDC and ASF are those that contribute to position error. Solving for these two
error terms:
ASF + EDC = TIC + Raw TOA - Rcvr Delay - Master offset - ED - TOA
Now, taking each side modulo 200 microseconds, we are left with:
ASF + EDC = (TIC + Raw TOA - Rcvr Delay - ED - TOA) mod 200
since Master offset mod 200 = 0 and ASF and EDC are both << 200. Thus, using the PC-104
receiver, it is possible to calculate the ASF at a known (in position) location by adding the TIC
and raw TOA values and subtracting off three terms, the receiver calibration (Rcvr Delay), the
4
published Emission Delay (ED), and the predicted TOA (based on the known station and
receiver locations). Taking this result modulo 200 microseconds, and subtracting off EDC yields
the ASF value. If the Emission Delay correction (EDC) is not known, then what is measured as
the ASF is actually the true ASF plus the EDC.
In order to resolve the true ASF (the error in the TOA due to just the propagation time
difference) the exact time of transmission of the LORAN stations must be known. For the Master
stations, the offset from UTC (referenced by a 1 PPS signal) is calculated by the TTM (Time of
Transmission Monitor) equipment. Currently a 23-hour average of the offset is calculated daily
as described in [3]. On dual-rated stations (with Master) the TTM equipment is only used to
measure the time of transmission offset on the Master rate, there is no measurement for the
Secondary rate. Also, at stations that are dual-rated Secondarys, there is currently no equipment
to measure this offset. The Coast Guard will be installing new Time and Frequency equipment
(TFE) starting in January that will have this capability, but this was not available for these tests.
In order to get some estimate of the time of transmission offset at the dual-Secondary stations,
the Coast Guard Loran Support Unit (LSU) and Peterson Integrated Geopositioning (PIG)
developed and installed some Secondary Time of Transmission Monitors (TOTM). For the
August flight tests, two were installed: at Nantucket and Carolina Beach. These monitors provide
an estimate of the offset from the published Emission Delay (ED) that the station actually
transmits (referenced to a 1 PPS). The details of how these operate are described in [6]. The
monitors save the statistics on the samples at 2 or 4 minute intervals. As recommended by PIG,
due to the many outliers in the sample sets, we have used the median of each sample set to
reduce this data. Figures 4 and 5 on the next two pages contain plots of the medians taken from
Nantucket and Carolina Beach over the period of the flight tests. The medians are plotted only if
there was a sufficient number of samples in each set (threshold used was 400 samples).
5
Figure 4—Nantucket Time of Transmission data: top – 9960, bottom – 5930.
6
Figure 5 – Carolina Beach Time of Transmission data: top – 9960, bottom – 7980.
7
Error Sources and Bounds
In this ASF calculation methodology there are several possible sources of error that need to be
examined in order to bound the solution. These are the errors in the Master and Secondary timing
offset measurements and receiver errors. Dilution of Precision effects due to the station geometry
contribute to the error in the position determination, but do not affect the individual station TOA
measurements. Channel noise impacts the ability of the receiver to make accurate measurements
and is discussed under receiver errors.
If we examine the difference between the measured TOA and that predicted based on the
positions of the station and the receiver using an all-seawater path there are actually two
components. This difference can be broken up into the actual propagation delay difference
(which we’ll define as the ASF) and the time offset (for Master station, the time difference from
UTC, for Secondary station the time difference from the published Emission Delay) which we’ll
call the Emission Delay Correction (EDC). From a receiver perspective, it doesn’t matter
whether the receiver knows each of these corrections separately or in a lump sum. However,
from the perspective of knowing and being able to publish the true ASF value, it is necessary to
separate out the timing corrections.
The Master offset as described above is currently available only as a 23 hour average value from
the TTM equipment. No statistics on the estimate is available. Currently, the Master stations do
not remain within 100ns of UTC as they are controlled based upon USNO measurements. The
USNO monitoring sites are not co-located with the Master stations and do not take into account
any ASF effects of the propagation from the Master to the monitoring site. The TTM values are
probably much more accurate, even if not used by the Coast Guard for control purposes. The
new TFE should provide better statistics on the data.
Since the US LORAN system uses SAM control, the transmission time of the Secondary station
is adjusted by the SAM site in order to maintain a consistent time delay (TD) at the SAM site.
This leads to the Secondary stations not transmitting exactly at the published EDs. These
Secondary station offsets or EDCs are currently obtained from the Secondary TOTM equipment
installed by LSU and PIG. The TOTM equipment uses a TrueTime XL-DC timing receiver.
According to their manual, this has a timing accuracy of better than 40 ns. However, looking at
Figures 4 and 5 above it is apparent that the data has more error than this. The Secondary stations
use cesium clocks to maintain stability in the transmissions and thus there should not be as much
variability in the transmission time as the measurements indicate. This leads to the conclusion
that the data sampling method is somewhat noisy and thus it is difficult to get an accurate
characterization of the EDC (both mean and variance). This data is from the initial versions of
the TOTM systems; more recent revisions are somewhat better. Also, the new TFE should
provide better data once it is installed. For the August flight tests we used an average over the
time period of the ASF data collection. This estimate appears to be accurate to within ± 50 ns.
There are several possible sources of error in the ASF measurement due to the receiver. These
are the 1 PPS accuracy, the sampling clock resolution, the signal acquisition accuracy, the
receiver calibration, and the loop cross-coupling.
The 1 PPS signal is used as the timing reference (see Figure 1). Any local jitter in this signal will
directly affect the resulting ASF measurement. As a side note, if the GPS system time drifts,
there will be no net affect as all measurements are referenced to this time. However, if the locally
generated 1 PPS signal is off, this will cause an error. In order to estimate this error, a Universal
8
Counter, stabilized with a 10 MHz reference from a cesium clock, is used to count the period of
the 1 PPS signal from the various receivers. A test program to collect long-term statistics on this
error has not been run yet, but will be done as soon as interface hardware for the Universal
Counter is received. The error in the 1 PPS signal from the GPS receiver used in the testing (a
Novatel OEM-4 Powerpak) was about ± 1ns whether in WAAS mode or standard GPS mode.
The sampling frequency of the A/D converters puts a limit on the time resolution possible in the
ASF measurement. A sampling frequency of 12.8 MHz is used, which means that samples are
taken every 78.1 ns, which corresponds to a resolution limit of ± 39.1 ns. This is the lower bound
on what is measurable. Any error sources less than this will thus not be visible in the data.
The accuracy of the Raw TOA (Figure 3) is dependent upon how well the receiver can track the
signal (third zero crossing). Typical legacy receivers can track this point within 30-60 ns [4].
This value will be SNR dependent; the higher the signal strength, the better the tracking. The PC104 receiver, with a strong signal, will track to within about 20 ns.
A certain amount of delay is introduced by the analog front end of the receiver and by the digital
filtering. This delay value is a constant that applies to all TOAs measured. A calibration of the
receiver as described in [2] was attempted with mediocre results. For the flight tests a calibration
value was measured with the receiver at Hyannis, MA. This is a short (24 NM) all seawater path
to Nantucket, thus the ASF for Nantucket should be zero at this location. The calibration factor
was set to make the ASF zero at this location. This is probably accurate to within 100ns. Any
errors in this value will be a fixed offset to all ASFs measured.
The final source of error is the loop cross-coupling in the H-field antenna. The H-field antenna
consists of 2 loops crossed at a 90 degree angle. They should be independent; however, in
practice each loop cross-couples slightly with the other, distorting the signal. This can be seen by
rotating the antenna through 360 degrees and observing the measured TOAs. For example, in
Figure 6 on the next page, as the antenna is rotated (720 degrees) on the roof of McAllister Hall
(USCG Academy) the value of the TOA for Nantucket varies ± 145ns. This error source is
currently not fully accounted for in the ASF measurements. This will show up as a heading
dependent correction to the ASF; i.e. all ASFs measured at a given heading will be consistent,
but will be off by the loop cross-coupling when compared to ASFs measured at a different
heading. We are currently working to resolve this error.
9
Antenna rotation 11 Sept 02; ASF Corrections for 9960
6
5
Microseconds
4
3
2
1
0
-1
-2
10
15
20
25
30
35
40
45
50
55
Time (minutes) Seneca - black Caribou - blue Nantucket - green Carolina-B - read Dana - cyan
TOA Changes Due to Rotation for Nantucket
0.15
0.1
Microseconds
0.05
0
-0.05
-0.1
-0.15
-0.2
0
100
200
300
400
500
Data Points
600
700
800
900
Figure 6 – Antenna delay as a function of rotation angle: top – effect on 5 stations, bottom –
expanded view of the effect on Nantucket.
10
August Flight Test Data
In August of 2002, flight tests were conducted jointly between Ohio University and the Coast
Guard Academy. Equipment was installed on Ohio University’s aircraft (see photographs in
Figures 7 and 8). The long-term goal of the August flight tests was to collect data in order to
characterize temporal and spatial variations in ASF corrections in order to answer the questions:
Can a model for ASF corrections be developed? And for how long and over what area is a static
ASF correction valid? The specific goal of the test was to validate data collection methodology
and equipment as well as the required data and formats.
The basic concept of the test was to use the DDC-based receiver in the aircraft to collect
LORAN position data and a Novatel OEM-4 to collect WAAS GPS positions. The PC-104
receiver was used to collect ASF data while the aircraft was sitting on the ground in the vicinity
of the flight data. The ASFs were calculated for each ground location using post-processing of
the PC-104 receiver data. These ASF corrections could then be added to the aircraft LORAN
TOA data in order to determine the corrected aircraft LORAN position. Using the WAAS GPS
positions as “truth”, the error in each LORAN position could be determined and plotted
geographically to show spatial variation in errors.
The daily flight plan was to depart Westerly enroute some location, fly around the area as much
as possible including flying over the airfield at various altitudes (1000, 1500, 2000 ft), shoot
several approaches, and then land. The plane remained on the ground for approximately two
hours to record data for ASF estimation. It would then depart the location, fly around the area,
and then return to Westerly. The locations visited are listed in Table 1 on the next page. Due to
mechanical problems with the aircraft, there were no test flights on Friday, 23 August. A map of
the rough flight locations is included as Figure 9.
Figure 7 – Ohio University C90 King Air.
11
Figure 8 – USCGA equipment installed in the King Air.
Table 1 – August Flight Test Locations
Date
Location and Airport Designator
21 Aug
Hyannis, MA (HYA)
22 Aug
Sandy Hook, NJ (BLM)
26 Aug
Cape Elizabeth, ME (PWM). Return via Nantucket.
27 Aug
Bay Bridge area (W29)
Mayport, FL (CRG)
28 Aug
Plumbrook, OH (5A1)
Westerly, RI (WST)
29 Aug
FAA Tech Center (ACY)
12
Seneca
Dana
Carolina Beach
Malone
Figure 9 – Map of the August flight test routes.
In the graphs to follow histograms of the measured TOA distribution for each station are
presented. The x-axis bins are the difference of the measured TOA value to that predicted using
the all seawater path; the y-axis count is the percentage of time that the given TOA difference
value was measured. As such, the histogram is an estimate of the probability density function of
the TOAs. For a given location (BLM and W229 are presented) there are 9 stations available
counting dual-rated stations twice. In each graph, the predicted TOA is shown by the dashed red
line at x = 0. The offset between the center of the TOA distribution and x = 0 is a combination of
the ASF and the timing offsets.
13
Figure 10 – TOAs measured on August 22 at BLM.
14
Figure 11 – TOAs measured on August 27 at W29.
15
Highlights of corrected data
As stated above, the utility of measuring ASFs at selected ground locations was to be able to use
the estimated ASF as a correction to TOAs recorded during a flight, yielding a zero-order (zeroorder since we do a constant correction) corrected LORAN position. These positions can then be
compared to GPS ground “truth”. Figure 12 shows one example of such a comparison for an
approach into Portland, ME on Aug. 26. The red line is the uncorrected LORAN positions while
the blue and green (indistinguishable on this scale) are the GPS and corrected LORAN positions.
Portland Me, 26 Aug 02; Uncorrected and Corrected LORAN-C verses DGPS
Uncorrected LORAN-C
Corrected LORAN-C
DGPS
43.85
43.8
43.75
43.7
43.65
43.6
43.55
43.5
43.45
-70.7
-70.6
-70.5
-70.4
-70.3
Figure 12 – Map of Portland, ME approach.
17
-70.2
-70.1
Portland Me, 26 Aug 02; Uncorrected and Corrected LORAN-C Error
0.45
0.4
0.35
Error, Nautical Miles
0.3
Uncorrected LORAN-C
Corrected LORAN-C
0.25
0.2
RNAV goal of .165 NM
0.15
0.1
0.05
0
13.9931
14.0131
14.0331
14.0531
14.0731
14.0931
GPS time, HH.hhhh
Figure 13 – Radial error in the corrected LORAN position.
This same flight data is redrawn as Figure 13 to show the radial error (actual difference between
the GPS and LORAN positions) as a function of time in the approach (note that the approach
starts at the bottom point in Figure 12, proceeding to the left, up, and finally to the right). The red
curve in Figure 13, uncorrected LORAN, shows an error of approximately 0.35 NM. The blue
curve, LORAN corrected by the ASF estimate, shows the dramatic improvement averaging
approximately 0.05 NM; the green line shows the 1/6 NM requirement for RNP 0.3.
Conclusions
Several conclusions can be drawn from this preliminary analysis of the August flight test data:
1. The data collection methodology works; further resolution of the error sources is necessary
2. A TOA all-in-view receiver (with timing corrected and static, local ASF correction) can
provide position accuracy well below 1/6 NM accuracy on approaches (to 20 miles out) –
hence, LORAN-C has the potential to achieve RNP 0.3.
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Future Work
Future work includes:
 Examination of spatial and temporal variations of ASFs through additional data
collection
 Receiver improvements such as increasing sampling rate to 25.6 MHz to improve
resolution and resolving receiver calibration
 Applying ASF corrections to LOCUS receiver TOAs
References
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Ottawa, Canada, October 1997.
2
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3
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4
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5
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8
U.S.C.G. Academy, “LORAN C H-Field Research Receiver,” White Paper, 2000.
9
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19
10
Williams, P and Last, J.D., “Mapping Additional Secondary Factors for the NorthWest European Loran-C chains – Initial Results and Further Work,” 27th Annual
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11
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20