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)

GRI. In the following, g denotes the GRI of the in-

terfering station, s

identifies individual stations in

view, and S

is the set of stations operating on

GRI g:

[ ] [ ]

∑

∈

strxbgrirxb

sLgL

,,,,

. (5)

Simply summing the blanking loss values is justi-

fied, as signals of multiple interferers from a com-

mon chain cannot overlap.

Second, we assume that the effects of interference

from stations operating on different GRIs are statis-

tically independent, which allows us to calculate the

resulting blanking loss as:

[ ]

( )

∏

−−=

grirxbrxb

gLL

,,,

. (6)

In addition to ground wave, the effect of sky wave

borne CRI also needs to be taken into account. The

presence of sky waves increases the probability of

collision between the interfering pulse trains, de-

pending on the sky wave delay. We model this effect

by increasing the width of the blanking interval w

by the estimated sky wave delay at the point of sig-

nal reception.

As mentioned earlier, there is also a loss of signal

due to dual-rate blanking. In Europe, dual-rated

transmitters use priority blanking, where the same

rate is always blanked at every overlap (the priority

rate is not affected). The loss due to transmitter

blanking, L

b,tx

, can then be easily calculated using

Equation 4.

The total blanking loss for a particular signal of

interest, including the effects of dual rate transmitter

blanking, L

b,tot

, can be found in a similar fashion as

above:

Figure 8. Blanking loss for the 6731 Sylt rate under worst-case

sky wave conditions expected.

( ) ( )

rxbtxbtotb

LLL

,,,

111 −⋅−−=

. (7)

The impact of CRI blanking on the ToA meas-

urement error for a signal of a particular station re-

ceived at a given SNR can then be estimated using

one of the models presented in Subsection 4.2.2,

where the number of averaged pulses, N, needs to be

reduced accordingly, i.e. we use (1 – L

b,tot

)·N instead

of N. With this modification to the model, we

achieve nearly perfect agreement with our measure-

ments (see Figure 6, Model 4).

5 CASE STUDY

We will now demonstrate the use of the models pre-

sented in this paper through a case study investigat-

ing the achievable positioning accuracy of eLoran

over the British Isles. Our transmission network will

be formed by the 14 transmissions from the 9 Euro-

pean transmitters currently in operation, configured

according to Appendix B.

In our study we have made use of the GLA cov-

erage and performance model (Safar et al. 2010)

which provides estimates of ground wave and sky

wave signal parameters and atmospheric noise val-

ues over the area of interest. In accordance with

common practice (Last et al. 1991), we have used

annual atmospheric noise not exceeded 95% of the

time, and night-time sky wave field strength values

at 99 percentile, providing a conservative estimate of

own sky wave interference. The height of the iono-

sphere has been assumed to be 91 km.

Figure 9. Blanking loss for the 7499 Sylt rate under worst-case

sky wave conditions expected.

ToA measurement errors for individual stations

have been estimated using the receiver performance

models described in Section 4. The signal averaging

Anthorn

Sy ltSy lt

LessayLessay

VaerlandetVaerlandet

Ejde

Blanking loss [%]

for night-time sky wave f. s. not exceeded 99% of the time

Anthorn

Sy ltSy lt

LessayLessay

VaerlandetVaerlandet

Ejde

Blanking loss [%]

for night-time sky wave f. s. not exceeded 99% of the time

100

time has been assumed to be 5 seconds – a typical

value for a marine receiver. The receiver is assumed

to acquire and track a signal of a particular station

only if the SNR is higher than 0 dB (BS EN

61075:1993) and the sky wave field strength to

ground wave field strength ratio and sky wave delay

are within the limits prescribed by the receiver Min-

imum Performance Standard (BS EN 61075:1993).

CRI at SIR values higher than 10 dB has been as-

sumed to be perfectly cancelled (Model 2); interfer-

ing signals at SIR lower than 10 dB and SNR above

0 dB have been blanked (Model 4). SIR in our CRI

analysis has been defined as the ratio of the power of

the ground wave of the useful signal to the power of

the interfering signal, calculated either from the

ground wave or the sky wave field strength (which-

ever is higher). As an example of the expected ef-

fects of CRI, Figures 8, 9 show the estimated blank-

ing loss for both rates of the dual-rated transmitter at

Sylt.

Finally, based on the predicted ToA measurement

errors and transmitter geometry, positioning errors

have been estimated as described in our previous

paper (Safar et al. 2010). Figure 10 shows the pre-

dicted 95 percent radius (R95) accuracy calculated

under the assumption of Gaussian-distributed meas-

urement errors. As explained above, the plot also as-

sumes that differential eLoran and ASFs are availa-

ble over the entire area.

6 KNOWN ISSUES & FUTURE WORK

There are a number of reasons why the figures pre-

sented in this paper should be interpreted with cau-

tion. Let us briefly mention the most important ones.

First of all, we still do not have a rigorous defini-

tion of SNR in eLoran. It is therefore difficult to

compare measurements obtained using different re-

ceivers, and also to translate SNR values from cov-

erage prediction models to actual SNRs as would be

seen by a practical receiver. This issue is currently

being discussed within the Radio Technical Com-

mission for Maritime services - Special Committee

127 on eLoran Systems (RTCM SC-127).

In developing our receiver performance model we

have approximated atmospheric noise by Gaussian-

distributed noise. It is well known that real atmos-

pheric noise also contains an impulsive component.

eLoran receivers, if properly designed, can benefit

from that and may achieve substantial processing

gain by suppressing the impulsive part of the noise.

In real atmospheric noise conditions, the receiver

may therefore perform better than our model pre-

dicts. Quantifying the achievable processing gain,

however, requires knowledge of the amplitude dis-

tribution of the noise (Boyce 2007).

Further performance improvements may be

achieved through sky wave aided tracking. Simula-

tor experiments could be conducted to verify this.

We might also want to explore alternative sky wave

propagation models, such as the USCG-Decca mod-

el (Last et al. 1991) which was specifically designed

for the Loran frequency band.

On the other hand, there are a number of factors

that haven’t been considered and may negatively

impact the tracking performance. These are for ex-

ample residual errors due to CRI cancelling, back-

ground CRI from distant stations that cannot be

tracked, residual Carrier-Wave Interference, or the

impact of transmitter timing jitter. These factors may

be important at high SNRs.

Finally, we might also want to include differential

eLoran in the model. This requires a study of spatial

decorrelation of the differential corrections as the

user receiver moves away from the reference station.

Also the accuracy of ASF maps used in user receiv-

ers needs to be assessed and included into the overall

error budget.

7 CONCLUSIONS

We have studied the tracking performance of a typi-

cal commercially available eLoran receiver under

Gaussian noise and CRI conditions. Based on our

findings we have developed an updated receiver per-

formance model for the purpose of coverage predic-

tion and optimisation.

Using this new model we have analysed the pos-

sibility of mitigating CRI within the European

transmission network through blanking at the re-

ceiver end. Our analysis suggests that with the cur-

rent configuration of the network, blanking results in

a substantial loss of tracking energy, and we recom-

mend that a study is conducted to examine the po-

tential gains of redesigning the timing of the

(e)Loran transmissions in Europe.

We have also used the updated receiver model to

generate a positioning accuracy plot for the GLAs’

service area. Despite the relatively high blanking

loss values assumed in the analysis, the plot suggests

that sub-10 m accuracy with eLoran should be

achievable in areas of good transmitter geometry,

such as off the north and east coast of Britain. The

performance figures presented herein should, how-

ever, be interpreted with caution, as this is still work

in progress.

101

Figure 10. Achievable positioning accuracy of eLoran (R95)

under worst-case sky wave conditions expected.

ACKNOWLEDGEMENTS

This work has been supported by the General

Lighthouse Authorities of the United Kingdom and

Ireland.

REFERENCES

Basker, S. et al. 2008. Enhanced Loran: real-time maritime tri-

als. In Proceedings of Position, Location and Navigation

Symposium, 2008 IEEE/ION.

Boyce, C.O.L. 2007. Atmospheric noise mitigation for LORAN.

PhD thesis, Stanford University.

BS EN 61075:1993. Loran-C receivers for ships - Minimum

performance standards - Methods of testing and required

test results, British Standards Institution.

Hua, F. & Pooi Y. K. 2006. ML estimation of the frequency

and phase in noise. In Global Telecommunications Confer-

ence, 2006. GLOBECOM '06. IEEE.

Johnson, G. et al. 2007. Navigating harbors at high accuracy

without GPS: eLoran proof-of-concept on the Thames river.

In Proceedings of ION National Technical Meeting,

San Diego, CA, 22-24 January, 2007.

Last, D. et al. 1991. Ionospheric propagation & Loran-C range

- the sky's the limit. In Proceedings of the 20th Annual

Technical Symposium, Wild Goose Association, Williams-

burg, VA, 1-3 October, 1991.

Pelgrum, W. 2005. Noise - from a receiver perspective. In Pro-

ceedings of the 34th Annual Convention and Technical

Symposium of the International Loran Association.

Safar, J. et al. 2010. Accuracy performance of eLoran for mari-

time applications. Annual of Navigation, 16:109–122.

Safar, J. et al. 2009. Cross-rate interference and implications

for core eLoran service provision. In Proceedings of the In-

ternational Loran Association 38th Annual Meeting, Port-

land ME.

US Coast Guard COMDTPUB P16562.6 1992. Loran-C user

handbook.

APPENDIX A NOTES ON MEASUREMENTS

In our experiments we have been using the Reel-

ektronika LORADD receiver updated with a new

firmware developed by Plutargus (v. 1.0), running in

the E-field mode.

The LORADD receiver is not capable of measur-

ing absolute ToAs, as it is not equipped with an

atomic clock. Instead, we can measure Time Differ-

ences (TD) between two selected signals and thus

remove the common clock drift. Note, however, that

the error in the TD measurements is a combined er-

ror, composed of errors of both the signals used in

that measurement. In our experiments we have com-

pensated for this effect mathematically.

We have used 1000 seconds worth of data to cal-

culate the tracking errors in Figures 5, 6.

APPENDIX B

Table B.1: European Loran stations.

___________________________________________________

GRI ID and station name Dual-rate blanking

___________________________________________________

6731 Lessay Priority 6731

6731 Soustons Not dual-rated

6731 Anthorn Not dual-rated

6731 Sylt Priority 7499

7001 Bø Priority 9007

7001 Jan Mayen Priority 9007

7001 Berlevag Not dual-rated

7499 Sylt Priority 7499

7499 Lessay Priority 6731

7499 Værlandet Priority 7499

9007 Ejde Not dual-rated

9007 Jan Mayen Priority 9007

9007 Bø Priority 9007

9007 Værlandet Priority 7499

___________________________________________________

Anthorn

Sy ltSy lt

LessayLessay

VaerlandetVaerlandet

Ejde

Accuracy, R95 [m]

for noise values not exceeded 95% of the time

35+