International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 5

Number 1

March 2011

1 INTRODUCTION

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

Accuracy

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

Isles.

2 ACHIEVABLE POSITIONING ACCURACY

OF ELORAN

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

Mitigation

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-

ceivers

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-

ceptable

Man-made noise and in-

terference

Careful receiver antenna installa-

tion, advanced receiver signal

processing

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-

ence?

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.

3 ELORAN SIGNAL SIMULATOR

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:

( )

∑∑ ∑∑

−

∞

−∞= =

⋅⋅−−−=

m c j

kGRIpmkmk

TcjTtlatr

( )

tnCt

kcjmk

+++

θω

cos

. (1)

Here,

K is the number of eLoran stations “in view”

and T

GRI,k

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

wave);

kcj

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

waveforms.

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.

4 RECEIVER PERFORMANCE MODEL

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

metric.

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

r(t)

, 20 ms/div

r(t)

, 20 ms/div

r(t)

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

WGN.

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:

SNRN

ToA

⋅

, (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

-6

)

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

-9

)

(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

-1

SNR [dB]

ToA

[ns]

M easurements

Model 1

Model 2

Model 3

-10 0 10 20 30 40

SIR [dB]

ToA

[ns]

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-

ly.

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:

iGRI

, (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

GRI,i

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

b,rx

. 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

b,rx,gri

, by summing the contri-

butions of individual stations, operating on a given

, 2 ms/div

r(t)