International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 5
Number 1
March 2011
In recent years, Global Navigation Satellite Systems
(GNSS) have become an integral part of modern so-
ciety. Be it on land, at sea or in the air, GNSS are an
important and often the primary means of Position-
ing, Navigation and Timing (PNT). Although their
qualities make them, in many aspects, superior to
other PNT solutions, there is now broad agreement
within the radionavigation community that satellite
navigation systems are highly vulnerable to uninten-
tional and intentional interference.
The concerns about the vulnerability of GNSS
have sparked a renewed interest in the Loran PNT
system, or rather in its upgraded version now widely
called enhanced Loran or simply eLoran. The nature
of the eLoran system makes its potential failure
modes highly independent of GNSS. eLoran is a ter-
restrial system, which operates in the low-frequency
band, uses high-power transmitters and completely
different navigation signals. Its signals are also data
modulated, which enables eLoran to deliver differ-
ential corrections, integrity messages and other data
to users. Recently, considerable effort has thus been
put into investigating whether eLoran can provide a
viable backup to GNSS.
In Europe, the General Lighthouse Authorities of
the United Kingdom and Ireland (GLAs) lead the
way in eLoran research. The Czech Technical Uni-
versity in Prague (CTU) participates in the eLoran
research activities coordinated by the GLAs. In our
work we have focused on questions that arise when
considering introducing new eLoran stations into an
existing network. In particular, this paper explores
the issue of Cross-Rate Interference (CRI) among
eLoran transmissions and its impact on the position-
ing accuracy performance of eLoran.
In the first part of this paper we give a brief over-
view of the major factors that determine the achiev-
able positioning accuracy of the system. We then re-
port on the development of an experimental eLoran
signal simulator and we demonstrate its use in as-
sessing eLoran receiver performance under noise
and interference conditions. Finally, a sample case
study is presented that investigates the achievable
Assessing the Limits of eLoran Positioning
J. Safar & F. Vejrazka
The Czech Technical University, Prague
P. Williams
The General Lighthouse Authorities of the United Kingdom and Ireland
ABSTRACT: Enhanced Loran (eLoran) is the latest in the longstanding and proven series of low frequency,
LOng-RAnge Navigation systems. eLoran evolved from Loran-C in response to the 2001 Volpe Report on
GPS vulnerability. The next generation of the Loran systems, eLoran, improves upon Loran-C through en-
hancements in equipment, transmitted signal, and operating procedures. The improvements allow eLoran to
provide better performance and additional services when compared to Loran-C, and enable eLoran to serve as
a backup to satellite navigation in many important applications. The Czech Technical University in Prague
(CTU) participates in the eLoran research activities coordinated by the General Lighthouse Authorities of the
United Kingdom and Ireland (GLAs). In our work we have focused on questions that arise when considering
introducing new eLoran stations into an existing network. In particular, this paper explores the issue of Cross-
Rate Interference (CRI) among eLoran transmissions and possible ways of its mitigation at the receiver end.
An eLoran receiver performance model is presented and validated using an experimental eLoran signal simu-
lator developed by a joint effort of CTU and GLAs. The resulting model is used to evaluate the achievable
positioning accuracy of eLoran over the British Isles.
positioning accuracy of eLoran over the British
When referring to accuracy of a positioning system,
we need to distinguish between its absolute accuracy
and repeatable accuracy. In (USCG COMDTPUB
P16562.6), the absolute accuracy is defined as the
accuracy of a position with respect to the geographic
or geodetic coordinates of the Earth. The repeatable
accuracy, then, is the accuracy with which a user
can return to a position whose coordinates have been
measured at a previous time with the same naviga-
tional system.
Due to the nature of low-frequency signal propa-
gation, Loran systems may suffer from large meas-
urement biases, resulting in absolute accuracy on the
order of hundreds of meters. However, Loran’s re-
peatable accuracy is comparable to that of single-
frequency (L1) GPS. In the following we briefly dis-
cuss the major factors affecting the accuracy per-
formance of eLoran and we explain how eLoran’s
absolute accuracy can be enhanced to the level of its
repeatable accuracy.
2.1 Factors affecting accuracy
Unlike its predecessors, eLoran is a ranging system,
which means that obtaining an accurate (2D) posi-
tion fix generally requires:
1 Accurate Time-of-Arrival (ToA) measurements
of signals from at least three transmitters,
2 Accurate ToA to range conversion,
3 Good geometry of the transmitters in view.
Transmitter geometry is a crucial factor in
eLoran; however, the impact of geometry on the ac-
curacy performance of a ranging system is well un-
derstood and will not be discussed in this paper.
Accurate conversion of ToAs to ranges from
transmitters is hampered mainly by signal propaga-
tion irregularities when the signals travel over land.
In eLoran we account for these irregularities by so-
called Additional Secondary Factors (ASF). In order
to achieve the best possible positioning accuracy,
these correction factors in the area of interest need to
be measured and stored in the receiver. Fluctuations
in the ASF values should also be monitored and
broadcast to the user in the form of differential cor-
rections, e.g. using the eLoran data channel.
Table 1. Meeting the maritime accuracy requirement.
Accuracy Limiting Factor
Poor geometry
Installation of additional eLoran
transmitters, perhaps using low
power mini-eLoran stations as
coverage gap fillers
ASF spatial variation
Detailed ASF maps stored in re-
ASF temporal variation
Differential reference stations
generating real-time corrections,
broadcast to users e.g. by the
eLoran data channel
Uncorrelated noise
Integration time ~ 5 sec is ac-
Man-made noise and in-
Careful receiver antenna installa-
tion, advanced receiver signal
Accuracy of the ToA measurements themselves is
a function of many variables. It is predominantly de-
termined by the Signal-to-Noise Ratio (SNR) of the
received signals. In the Loran frequency band, the
dominant sources of noise are atmospheric noise,
which is caused by lightning discharges, and man-
made noise and local interference from, for example,
switch-mode power supplies. Other sources of noise
may include transmitter pulse timing jitter or receiv-
er related noise.
Besides noise, another important source of ToA
measurement error is interference caused by other
radio signals. Currently the biggest source of inter-
ference to eLoran is eLoran itself, in the form of
CRI. So what exactly is the cause of this interfer-
eLoran transmitters are organised in groups of
usually 3 to 5 stations called “chains” or “rates”. The
stations periodically broadcast groups of 8 or 9 spe-
cially shaped low-frequency, high-power, pulses (see
Figures 2, 3). The interval between successive repe-
titions of the groups of pulses is unique to each
chain and known as the Group Repetition Interval
(GRI). Careful selection of GRIs and transmission
times ensures that stations operating in a chain do
not interfere with each other. However, the nature of
the system is such that the signals from different
chains overlap from time to time (see Figure 4) and
may introduce errors into our ToA measurements
this is referred to as CRI.
Another effect of CRI is transmitter dual-rate
blanking. As a legacy from the Loran-C era, some
Loran transmitters are dual-rated, i.e. they broadcast
signals on two GRIs. Such transmitters are periodi-
cally faced with the impossible requirement of radi-
ating overlapping pulse groups simultaneously. Dur-
ing the time of overlap, those pulses of one group
that overlap any part of the other group’s blanking
interval are suppressed (note e.g. the fourth group of
pulses in Figure 2). The blanking interval extends
from 900 µsec before the first pulse to 1600 µsec af-
ter the last.
2.2 Maritime eLoran
Accuracy is the major factor affecting the suitability
of eLoran for maritime navigation. IMO standards
for the region of Port Approach specify a stringent
accuracy requirement of 10 meters (95 percent of the
time). A number of studies in the past have shown
that accuracies better than 10 m are achievable
(Basker et al. 2008, Johnson et al. 2007). Table 1
summarises measures that need to be taken in order
to meet the 10 m accuracy requirement in the mari-
time environment.
From the above it follows that the major error
sources in maritime eLoran are the residues of at-
mospheric noise, transmitter related noise, and CRI.
While the impact of the first two factors is well un-
derstood and can be modelled (Safar et al. 2010), the
issue of CRI has not been sufficiently described so
far. In the rest of this paper we will therefore attempt
to quantify the effects of CRI and provide CRI mod-
els for use in eLoran coverage prediction tools.
Figure 1. Schematic diagram of the GLA-CTU experimental
eLoran signal simulator set-up.
In order to meet the stringent eLoran accuracy per-
formance standards, it is necessary that eLoran re-
ceivers employ special CRI mitigation algorithms
(Safar et al. 2009). Quantifying the negative effects
of CRI is therefore largely a receiver-oriented prob-
lem. Unfortunately (but not surprisingly), receiver
manufacturers have not widely published the intrica-
cies of their eLoran receivers. In order to get a better
understanding of the performance of typical com-
mercial eLoran receivers, an experimental eLoran
signal simulator set-up is being developed through
cooperation between the GLAs and CTU Prague.
Using this set-up, it is possible to work with a re-
ceiver in a controlled environment and separate the
negative effects of various error sources.
Figure 1 depicts the current simulator set-up. At
the heart of the simulator is a DA converter board
equipped with four 14-bit converters, providing us
with four independent output channels each with a
maximum analogue bandwidth of 52.5 MHz. The
board is installed in a PC workstation (PC1) and
communicates with the host system through the
standard 32-bit PCI bus. In the current set-up a sta-
ble external 10 MHz clock signal from a GPS-
disciplined Rubidium clock is supplied to the board.
The output of the board is connected to the anten-
na input of the receiver under test through a coupler,
which galvanically isolates the receiver’s input from
the simulator and protects it from overloading.
eLoran receivers can either use an E-field “whip”
antenna or an H-field antenna. The latter typically
consists of two loops whose outputs are combined in
the receiver in software in order to provide a beam-
steering capability. The simulator currently operates
in the E-field (single-channel) mode only. The out-
puts of the receiver under test are monitored using a
separate PC.
The simulator software currently allows the gen-
eration of ground wave and sky wave E-field sig-
nals, atmospheric noise, and simulation of the pulse
timing jitter and transmitter dual-rate blanking. The
parameters of the signals are either user defined or
calculated for a specified location from correspond-
ing propagation and noise models (Safar et al. 2010).
In mathematical terms, the output signal of the simu-
lator can be described as follows:
( )
( )
. (1)
K is the number of eLoran stations “in view”
and T
are their respective group repeti-
tion intervals (in seconds);
M - 1 is the number of sky waves considered,
each with a different amplitude a
, delay τ
and phase θ
(m = 0 represents the ground
are the phase code values (0 or π, according
to a standardised pattern), k is the transmit-
ter number, c is the GRI number and j de-
notes the pulse number within a GRI;
= 1 ms;
= 2π·100·10
rad/s corresponds to the
eLoran carrier frequency of 100 kHz; note,
that ω
is common to all stations;
l(t) represents the envelope of a single eLoran
pulse; for 0 t 300 µs it is given by
Equation 2 and l(t) = 0 otherwise; t
is the
instant when the pulse reaches its maximum
value, t
= 65 µs;
n(t) is the noise waveform;
( )
tl 22exp
. (2)
Figures 2-4 show some example eLoran signal
Figure 2. Ideal eLoran pulse (far E-field).
Figure 3. Simulated ground wave signals of GRI 6731 as
would be received at Harwich, UK.
Figure 4. Simulated ground wave signals of all European
chains as would be received at Harwich, UK.
There are no limitations to the number of chains
or stations used in the simulation. The simulator
therefore provides an excellent tool for studying the
effects of CRI.
As discussed earlier, positioning performance of a
marine eLoran receiver is primarily determined by
the errors in signal ToA measurements. In maritime
eLoran, measurement biases are nearly perfectly
eliminated through the use of ASF maps and differ-
ential corrections. In the following we therefore
need be concerned only with the random fluctuations
of the ToA error caused mainly by atmospheric
noise and CRI, and we will use the standard devia-
tion of the ToA measurements as our performance
4.1 Basics of eLoran receiver signal processing
How does an eLoran receiver obtain a ToA meas-
urement at the first place? The ToAs are measured in
two stages. First, coarse signal delay relative to the
origin of the receiver’s time base is measured, based
on the shape of the leading edge of the ground wave
eLoran pulse. In the model of received signal repre-
sented by Equation 1 above, this delay is denoted τ
When the approximate ToA is known, carrier phase
of the eLoran ground wave signals, θ
, is measured
which allows the receiver to calculate more accurate
ToA values. The coarse estimates are only needed to
resolve the ambiguity of the phase measurements; it
is therefore the carrier phase measurement error
which determines the accuracy of our ToAs, and
which will be of interest in the following.
4.2 Receiver performance in white Gaussian noise
Let us first investigate the impact of atmospheric
noise on our measurements. In the first approxima-
tion, atmospheric noise may be regarded as a white
Gaussian stochastic process. We are therefore facing
a problem of estimating the phase of a sinusoid em-
bedded in White Gaussian Noise (WGN). This is a
classical problem in estimation theory, and perfor-
mance analyses of practical phase estimators typical-
ly reveal (see e.g. Hua & Pooi 2006) that the vari-
ance of the estimates is inversely proportionate to
the SNR and the number of signal observations
available. In case that the useful signal is a pure si-
nusoid, the SNR is simply defined as the ratio of the
power of the sinusoid to the power of the noise in
the signal samples. But how shall we define SNR of
an eLoran pulse train?
4.2.1 Defining SNR
Unfortunately there is no universally accepted
definition of SNR in eLoran; we propose a working
definition to be used within this paper.
With conventional Loran signal processing the
receiver uses, in the phase estimation process, one
signal sample per each received pulse. Signal power
can then be defined as the power of a sinusoid hav-
ing the same amplitude as the envelope of the Loran
pulse at the sampling point. There is a hitch, howev-
er. The position of the sampling point within the
t, 50 µs/div
, 20 ms/div
, 20 ms/div
pulse is a compromise between a low SNR at the
beginning of the pulse and an increased probability
of sky wave contamination later in the pulse; the po-
sition is dependent on the receiver’s architecture and
is generally unknown. Also, the pulse shape is dis-
torted during propagation, reception and signal pre-
processing at the receiver, which makes it even
harder to determine the effective signal level at the
sampling point.
To avoid possible ambiguities, we decided to de-
fine SNR external to the receiver. In our simulator
experiments we are using the following definition:
SNR is calculated as the ratio of the power of the
useful signal at the output of the simulator to the
power of the radio-frequency noise present after fil-
tering by the standard front-end filter (8
order But-
terworth, 3 dB bandwidth of 28 kHz, centred at
100 kHz).
This definition assumes the use of ideal signal wave-
forms (see Equations 1, 2 above) and the power of
the useful signal is calculated as the power of a si-
nusoid having the same amplitude as the ideal
eLoran pulse envelope 30 µs into the pulse.
Figure 5. ToA standard deviation vs. SNR for eLoran signals in
In the performance analysis of a specific receiver
we then need to bear in mind that the SNR seen by
the receiver’s phase estimation algorithms may dif-
fer from that above, e.g. due to signal distortion
caused by the front-end filter.
4.2.2 Developing the performance model
Based on the cursory analysis above, we may as-
sume that the ToA error model takes the form:
, (3)
where N is the number of signal samples used in the
phase estimation process, SNR is expressed as a
power ratio as defined above, c
= (1.1254 10
takes account of the conversion from phase variance
to ToA variance, and c
accounts for the pulse dis-
tortion during signal pre-processing. Estimated value
of this constant for the Reelektronika LORADD re-
ceiver used in our analysis, based on information
available to the authors, is c
= (1.44)
Figure 5 shows the predicted ToA standard devia-
tion as a function of SNR. Predictions according to
Equation 3 are shown by the dash-dot line (Mod-
el 1). In this example it is assumed that the receiver
is tracking a GRI 6731 signal and uses a 5 second
averaging time, which gives N = 594 pulse samples
per ToA measurement.
Also shown in Figure 5 are results of a simulator
experiment conducted using the LORADD receiver
and our prototype signal simulator (see also AP-
PENDIX A). The actual ToA measurement errors
turned out to be a little higher than our predictions.
The offset can be calibrated out using another multi-
plicative constant, c
= (1.55)
. The cause of this off-
set is unclear. The calibrated function is plotted as
the dashed line in Figure 5 (Model 2).
It can also be seen from our measurements that
the ToA vs. SNR characteristics flattens at high
SNRs. This is presumably a result of the receiver’s
internal noise. The effect can be modelled using an
additive constant, c
= (1.5·10
(solid blue line,
Model 3). With the LORADD receiver, however,
this effect occurs at very high SNRs unlikely to be
encountered in practice, and can safely be neglected.
Figure 6. ToA standard deviation vs. SIR; GRI 6731 signal at
SNR = 30 dB interfered with signals of GRI 7001 (M,X,Y).
All the interfering signals in a particular experiment were set to
the same level.
10 15 20 25 30 35 40
SNR [dB]
M easurements
Model 1
Model 2
Model 3
-10 0 10 20 30 40
SIR [dB]
M easurements
Model 2 (no CRI)
Model 4 (CRI blanking)
4.3 Receiver performance under CRI conditions
As mentioned before, in order to meet the stringent
eLoran performance standards, the impact of CRI
within the system must be greatly reduced. Several
strategies concerning how the receiver can reduce
the effects of CRI have been described in the litera-
ture (Pelgrum 2005). There are two prevalent CRI
mitigation techniques, commonly referred to as CRI
cancelling and CRI blanking.
eLoran employs all-in-view receivers capable of
simultaneously tracking signals of many rates. When
an eLoran signal is being tracked, a footprint of the
received pulse waveform is available. With cancel-
ling, the receiver uses this footprint to reconstruct
accurate replicas of the individual signals and sup-
press the signals of all unwanted rates (Esti-
mate & Subtract). This allows the receiver to miti-
gate the effects of CRI almost perfectly, however the
technique has its limitations, as will be shown short-
With CRI blanking, the receiver detects the puls-
es likely corrupted by CRI and discards them. The
interference is thus completely suppressed, but the
price we pay is a (sometimes excessive) loss of
tracking energy.
4.3.1 Simulator experiments
In order to assess the effects of CRI on a modern
eLoran receiver, a series of simulator experiments
were conducted in which signals of a selected chain
were disturbed by white Gaussian noise and inter-
fered with signals of another chain at different lev-
els. Figure 6 plots the ToA standard deviation versus
the Signal-to-Interference Ratio (SIR) for a GRI
6731 signal at 30 dB SNR, interfered with the sig-
nals of GRI 7001.
We can see from the plot that for high enough
SIR values, the errors are largely determined by the
Gaussian noise (see the dashed line in Figure 6,
Model 2) and can easily be modelled as described in
the previous subsection.
As the interference grows stronger, the measure-
ment errors gradually increase. This gradual increase
suggests that in the region of relatively weak inter-
ference (SIR above 10 dB) the receiver is using
some kind of cancelling algorithm to mitigate CRI.
Since the signal replicas used in the CRI cancelling
process are mere estimates of the true interfering
waveforms, there is always some residual effect on
our ToA measurements. This effect is more pro-
nounced as the SIR decreases. With SIR values ap-
proaching 10 dB the residual error rises sharply and
when the SIR is further decreased, the receiver ap-
parently switches to CRI blanking. A model for the
transitional region is currently being developed and
will be presented in a follow-up paper. We will now
concentrate solely on the CRI blanking.
4.3.2 Modelling the impact of CRI blanking
As explained above, with CRI blanking all the
colliding pulses are completely removed from the
signal processing. The task of quantifying the impact
on the ToA measurements thus reduces to estimating
the percentage of discarded pulses and decreasing
accordingly the number of samples per ToA meas-
urement in Models 1 to 3 above.
In the following considerations we will ignore the
influence of the ninth master Loran pulse, as well as
any data modulation of the signals. We will assume
that the receiver uses the same blanking strategy as
is used on Loran dual-rated transmitters, i.e. that it
discards all pulses that overlap any part of the blank-
ing interval of the cross-rating pulse groups (see
Figure 7). This is a different approach from the one
in our previous paper (Safar et al. 2010), where we
had assumed that blanking only occurred when indi-
vidual pulses overlap each other.
Let us first consider the case of two interfering
eLoran ground wave signals. It can easily be shown
(Safar et al. 2009) that the average portion of
blanked pulses of the desired signal, or the blanking
loss, can be calculated as:
, (4)
where w
is the pulse width for the desired signal, w
is the width of the blanking interval for the interfer-
ing signal, and T
is the length of the group repe-
tition interval of the interfering station. In our anal-
yses we set w
= 250 µsec, and w
= 9500 µsec.
Figure 7. CRI blanking. Dashed line shows the blanking inter-
val extending over the pulse group of the unwanted cross-
rating signal. In this example, samples of the first three pulses
of the second group will be discarded.
When analysing real-world eLoran systems we
also need to evaluate the blanking loss due to multi-
ple cross-rating stations, L
. In this case, the eval-
uation needs to be broken down into two stages.
First, we calculate the blanking loss due to stations
of individual GRIs, L
, by summing the contri-
butions of individual stations, operating on a given
, 2 ms/div