ASF Measurement and Processing Techniques, to allow ... · argued the case that reliance on GNSS as a sole means of Position, Navigation and Timing (PNT) can leave the UK’s critical

Version Date: Page 1 of 79 Version:

Chris Hargreaves

ASF Measurement and Processing Techniques, to allow Harbour Navigation at High Accuracy with eLoran.

Dissertation submitted to The University of Nottingham in partial fulfilment for the

degree of Master of Science in Navigation Technology.

September 2010


Abstract

To navigate a ship along an approach channel to enter a harbour a mariner

must be able to fix their position to a high degree of accuracy. The International

Maritime Organisation (IMO) have set out a list of requirements, which must be

met by any electronic positioning system during the various voyage phases

including port approach.

The ability of Global Navigation Satellite Systems (GNSS) to provide high

accuracy with high reliability is well known, and as such the Global Positioning

System (GPS) has become ubiquitous as the system of choice for position

fixing, in the maritime world and beyond. The General Lighthouse Authorities of

the UK and Ireland have expressed their concern that an over reliance on any

one system can leave critical infrastructure vulnerable if this system’s service is

disrupted or denied for any reason. As such they have argued for the

establishment of Enhanced Long Range Navigation (e-Loran) to be used in

parallel with, and as a backup to, GNSS for Position Navigation and Timing

(PNT).

This report describes the efforts of the GLAs to measure and process Loran

Additional Secondary Factors (ASF) in order to obtain sub-10m (95%) accuracy

from eLoran. Software applications have been written in MatLab™ to aid the

gathering and processing of eLoran data, and the current state-of-the-art in ASF

measurement and processing is described.


Contents

1 Introduction and Overview ....................................................................................... 5

1.1 The GLAs and the Case for eLoran ................................................................ 5

1.2 Outline of MSC ............................................................................................... 5

2 History and Background .......................................................................................... 6 2.1 A Brief History of Loran ................................................................................... 6

2.2 Loran-C ........................................................................................................... 6

2.3 The Northwest European Loran System (NELS) ............................................ 9

2.4 Towards eLoran .............................................................................................. 9

2.5 International Maritime Organisation (IMO) .................................................... 11

2.6 Realisation of eLoran .................................................................................... 12

3 Additional Secondary Factors (ASF) ..................................................................... 15 3.1 Theory ........................................................................................................... 15

3.2 Short History of ASF ..................................................................................... 17

3.2.1 Pre-NELS .................................................................................................. 17 3.2.2 ASF for NELS ........................................................................................... 18 3.2.3 ASF for the FAA eLoran Evaluation .......................................................... 19

3.3 ASF Today .................................................................................................... 20

3.4 ASF Measurement ........................................................................................ 21

3.5 ASF Measurement Equipment ...................................................................... 23

3.6 ASF Measurement Errors ............................................................................. 27

3.7 Summary ...................................................................................................... 30

4 ASF Processing ..................................................................................................... 32 4.1 ASF Measurement Campaigns ..................................................................... 32

4.1.1 Equipment ................................................................................................. 32 4.1.2 Sea Trials .................................................................................................. 33 4.1.3 ASF-Unit Calibration at Lowestoft ............................................................. 33 4.1.4 eLoran Assessment in the Orkney Islands ............................................... 34 4.1.5 GPS Jamming Trial in Newcastle ............................................................. 36

4.2 ASF Error Mitigation and Minimisation ......................................................... 37


4.2.1 Local Clock De-Synchronisation ............................................................... 37 4.2.2 Removal of Temporal Variations .............................................................. 39 4.2.3 Setting up a Differential-Loran Reference Station .................................... 41 4.2.4 Processing Differential-Corrections .......................................................... 42 4.2.5 Other Error Sources and Conclusion ........................................................ 43

4.3 Producing an ASF Grid ................................................................................. 44

4.3.1 The Basic ASF Grid .................................................................................. 45 4.3.2 The Interpolated ASF Grid ........................................................................ 48 4.3.3 Error Statistics .......................................................................................... 56 4.3.4 Standard Deviation of Residuals .............................................................. 59 4.3.5 Summary of ASF Processing .................................................................... 60

4.4 GLA eLoran Position-Solution Algorithm ...................................................... 61

5 GLA eLoran Survey Software ................................................................................ 65 5.1 Survey Mode ................................................................................................. 65

5.2 Validation Mode ............................................................................................ 69

6 Summary and Conclusions .................................................................................... 75 6.1 Summary ...................................................................................................... 75

6.2 Conclusions - ASF Measurement Technique ............................................... 75

6.3 Conclusions - ASF Gridding Technique ........................................................ 76

References ................................................................................................................... 78


1 Introduction and Overview

1.1 The GLAs and the Case for eLoran

The General Lighthouse Authorities of the UK and Ireland (the GLAs) have

argued the case that reliance on GNSS as a sole means of Position, Navigation

and Timing (PNT) can leave the UK’s critical infrastructure vulnerable. The

GLAs have demonstrated the effects of GPS jamming [1] on a typical modern

ship with an integrated bridge system, concentrating on the effect of GPS denial

on navigation. To mitigate the risk of GPS disruption, the GLAs have argued

that an alternative, dissimilar source of accurate PNT should be established as

a national backup to GNSS. eLoran is seen as the best available system which

can potentially meet all the requirements of the navigation and timing user

communities, and as such forms a core part of the GLAs’ strategy [2].

In light of recent developments in the USA, the GLAs have not altered their

stance on eLoran. It is, by design, a regional system, and can be used to

augment GNSS in much the same way as all regional augmentations such as

marine DGPS or EGNOS.

1.2 Outline of MSC

The work presented here comprises the efforts made by the candidate in

assisting the delivery of high-accuracy eLoran suitable for use by the mariner to

navigate the coasts and harbour approaches of the British Isles. The provision

of eLoran at 10m (95%) accuracy requires the accurate measurement of the

Loran signal propagation delay Additional Secondary Factors (ASF), and

appropriate mitigation at the user’s receiver. The candidate has furthered the

development of the data acquisition and processing techniques required to

measure, assess and distribute quality-assured ASF data. In addition, custom

software applications have been written to oversee the survey of ASF along a

harbour approach, and validate the gathered data. This software’s operation is

demonstrated with an example of an ASF survey conducted around the Orkney

Islands in 2009.


2 History and Background

2.1 A Brief History of Loran

Loran stands for Long Range Navigation and has existed in several forms over

the years. These incarnations are similar in that they have all been high-power;

terrestrial; pulsed; radio-navigation systems.

The first system, Loran-A was developed during the Second World War as a

navigation system for the US military. Loran-A operated at 1.95 MHz over a 400

mile range and provided very poor positioning accuracy. Improvements to the

signal-specification increased the accuracy of Loran-A, the improved signal was

broadcast under the name of Loran-B.

Developments in low-frequency radio-navigation led to the development of

Loran-C, which began broadcasting in 1958, and eventually took over from

Loran-A and B.

2.2 Loran-C

Loran-C is a terrestrial radio-navigation system, which consists of a number of

high-power radio transmitters operating at a centre frequency of 100kHz. These

transmitters are organised into Chains, with a single Master station and several

Secondary stations in each Chain. The Master station transmits groups of nine,

precisely timed and shaped pulses. Figure 2-1 illustrates the signal format.

Figure 2-1 – The Loran pulse shape


The leading edge of the pulse is precisely defined (1.1). The shape of the pulse

envelope is used to identify the Standard Zero Crossing (SZC), this is the point

of the signal that is tracked by a Loran receiver and used to make Time-of-

Arrival measurements.

( ) ( ) ( )2 2 -( ) - exp sin 0.2

65t t

i t A t t pt

=

(1.1)

Each Master (M) pulse group transmission is followed in sequential order by a

group of eight pulses from each of the Secondary stations in the same chain.

The delay between Master and Secondary transmissions is termed the

Emission Delay (ED), and is precisely controlled by the transmitter. Once all of

the Secondary stations have transmitted, the cycle begins again with the next

Master station transmission. The time between successive Master station group

transmissions is referred to as the Group Repetition Interval (GRI), this is shown

in Figure 2-2.

Figure 2-2 – Example of a Loran chain with three Secondary stations (X, Y and Z)

Each Chain is named after the Master station and is identified by its GRI,

quoted as a multiple of 10μs. For example, the transmitter at Lessay in Northern

France has a repetition interval of 67310μs, and is the Master of the GRI 6731.

Secondary stations are identified by the letters W; X; Y; Z, depending on the

order they transmit. The GLAs operate a station at Anthorn in Cumbria, which is

the third station to transmit in the Lessay chain, and is given the designation

Anthorn 6731Y.


With the Loran-C system, a user obtains their position by measuring time

differences (TD) between the reception of a Master (identified by its ninth pulse)

and a Secondary. Each TD measurement places the user on a hyperbolic line

of position, and at least two such time-difference measurements are needed to

obtain a fix. Originally these hyperbolic TD lines were overlaid onto navigation

charts and plotted by hand. An experienced navigator would expect to be able

to fix their position with an absolute accuracy of ¼ of a nautical mile with Loran-

C using these hyperbolic charts.

Figure 2-3 – Hyperbolic lines of position (LOP) for an example Master-Secondary pair. Image reproduced from [3]

In a hyperbolic system it is not necessary to precisely control the timing of each

Master transmission, rather it is the stability of the Emission Delay (ED)

between the Master and Secondary transmissions that is important. Timing of

the Secondary transmissions was originally controlled by reception of the

Master’s transmission at the Secondary, with the Secondary station transmitting

a certain time following Master signal reception.


In recent years development work has been carried out, particularly in Europe

and the USA, to improve the Loran-C system, in an attempt to bring it into line

with modern navigational requirements.

2.3 The Northwest European Loran System (NELS)

The Northwest European Loran System (NELS) Consortium was established in

1994 and consisted of several National Operating Agencies (NOAs), Norway;

France; Denmark; Germany; Ireland. Norway was also the host of the

Coordinating Agency Office (CAO) – the organisation that was in overall charge

of NELS.

NELS began the process of upgrading the existing Loran-C infrastructure to

improve its performance. In particular the work included pioneering Time-of-

Emission (TOE) control, whereby the transmission of the Loran signal at each

site is maintained relative to UTC. This means all Loran signals can be related

to a common time-reference, or ‘paper clock’. This improvement allows a user

to compare pseudo-range measurements from all available Loran transmitters

(the all-in-view concept) irrespective of the chain’s GRI or the Master /

Secondary relationships. A position fix can then be derived by using Least

Squares, or a similar technique. This all-in-view method overcomes many of the

limitations of TD hyperbolic positioning, and also enables Loran to be an

independent source of UTC time.

NELS also reassigned GRIs to improve Loran performance in the noisy

European radio environment, developed coverage prediction techniques and

produced maps of the signal propagation delays, the latter are discussed in

Chapter 3

2.4 Towards eLoran

On 10th September 2001 the Volpe Transportation Centre in the USA published

a report [4] into GPS vulnerability and the reliance on GPS of US critical

infrastructure. The timing and prescience of such a report into the potential

impact of an attack on the country’s critical infrastructure led to increased

concern about the vulnerability of GPS and the need for a national backup

system. A study was carried out to investigate whether Loran-C could


potentially act as a backup and complementary Position Navigation and Timing

(PNT) system for maritime, aviation and timing [5].

This study involved a large number of organisations including academia,

consultancies and the US Coast Guard (USCG), under the sponsorship of the

Federal Aviation Administration (FAA). This study was divided along two lines.

The Loran Integrity Performance Panel (LORIPP) was concerned with

identifying whether the system could meet the stringent integrity requirement for

the duration of an aircraft Non-Precision Approach (NPA). The Loran Accuracy

Performance Panel (LORAPP) was not so much interested in integrity but

whether the system could meet the accuracy requirement of 8-20m (95%) for

the Harbour Entrance and Approach (HEA) phase of a voyage. These two sets

of requirements are outlined in Table 1.

Navigation

Phase

Accuracy

(95%)

Availability Continuity Integrity

Risk

Definition of

Loran Capability

(US FRP)

¼M

(460m)

99.7% 99.7% 10-5

FAA NPA

Requirements

300m 99.9% to 99.99%

99.9% to 99.99% (over 150 s)

10-7

USCG HEA

Requirements

8-20m 99.7% to

99.9%

99.85% to 99.97%

(over 3 hours)

10-5

Table 1 – US performance requirements for eLoran, the most stringent requirements are shown in bold.

The results of this study indicated that if Loran-C was significantly improved it

could meet the requirements of both the FAA and USCG. The improvements,

illustrated in Table 2, meant sweeping changes to Loran-C of such magnitude

that it was appropriate to rename the system enhanced-Loran, or e-Loran.


Table 2 – Proposed improvements to Loran-C to move the system towards eLoran. After [5].

This improvement work was about to enter an implementation phase when

funding was halted for Loran-C in the US and transmissions were ceased earlier

this year. The United States Coast Guard are currently in the process of

“mothballing” the stations pending a decision on whether to move to full eLoran

implementation.

2.5 International Maritime Organisation (IMO)

Internationally, the IMO has set out its own standards that any electronic

position-fixing system must meet for it to be considered safe for maritime use

[6]. These requirements are a little more stringent than those stated by the

USCG in their evaluation of Loran-C, and are shown in Table 3.

Of particular interest to the GLAs is the target accuracy set at 10m (95%) for

Harbour Entrance/ Approach, meaning that 95% of all position fixes must lie

within 10m of the vessel’s true position.


Navigation

Phase

Accuracy

(95%)

Availability Continuity Alert

Limit

Time

to

Alarm

Integrity

Risk

Coastal

Navigation

10m 99.8% N/A 25m 10s 10-5

Harbour

Approach

10m 99.8% 99.97% 25m 10s 10-5

Port

Navigation

1m 99.8% 99.97% 2.5m 10s 10-5

Table 3 - IMO standards for electronic position-fixing at sea

Attaining 10m-level accuracy from GPS is no challenge, however Loran-C as it

stands will not provide this level of accuracy. The GLAs have built on the work

of NELS and the USCG to implement the necessary improvements introduced

above so that 10m (95%) accuracy can be met by eLoran.

2.6 Realisation of eLoran

In order to make eLoran a reality, and to meet the IMO’s requirements, the

following are necessary:

• Modern solid-state transmitters, with Time-of-Emission (TOE) control of

transmitted signals (completed in Europe under NELS)

• Modern timing and frequency equipment (TFE) at the transmitter sites

• The calibration of Loran propagation delays along harbour approach

channels and within harbour areas

• The installation of local differential-Loran monitoring stations at harbour

entrances to correct for temporal variations in the time-of-arrival of the

eLoran signals


• Provision of a data-communications channel on the eLoran signal to

broadcast differential corrections to the mariner (also completed by

NELS)

• The development of all-in-view Loran receivers

One of the major changes from Loran-C to eLoran was the addition of a data

communications channel (Loran Data Channel) to the navigation signal. This

would be used to broadcast differential corrections and integrity data to the

user. The method uses the Loran signals themselves by modulating the time-of-

emission of one or more pulses in a group either early or late. In the USA this

was achieved by modulating the position of the Master station’s ninth pulse. In

Europe, and other regions, the Loran Data Channel (LDC) is implemented by

Eurofix, a method of balanced pulse position modulation on the last 6 pulses of

each 8-pulse group [7].

Table 4 summarises a comparison between the different forms of Loran-C seen

over the years. The GLAs are currently at the prototype eLoran phase,

performing various technical projects in order to roll-out their final eLoran

services including a differential-Loran service covering the entire GLA service

area.


Loran Notes Accuracy

USCG Loran-C

(c. 1960s)

The original version of Loran-C based on

tube transmitters, SAM control and

hyperbolic navigation.

460m (95%)

Modernised Loran-C

(c. 1990s)

The original version of NELS based on solid-

state transmitters, time-of-emission timing,

hyperbolic or rho-rho navigation.

100m (95%)

Prototype eLoran

(c. 2008)

The GLAs’ system currently in operation

based on modernised Loran-C together with:

1. Eurofix LDC

2. all-in-view navigation

3. differential Loran for maritime use

10-20m

(95%).

Operational eLoran

(Estimated 2013)

The future, based on prototype eLoran with:

1. updated station equipment to improve

timing stability,

2. mitigation of vulnerabilities to ensure high

availability

3. Eurofix LDC at all stations

10m (95%).

Table 4 – Comparison of the various forms of Loran.

A key part of all of this work is the calibration of the signal propagation delays,

these delays are typically divided into three Factors, the Primary factor (PF);

Secondary Factor (SF); and Additional Secondary Factor (ASF). The work

described in this dissertation forms the core of the GLAs work in measuring and

charting the Additional Secondary Factors. The next chapter describes what an

Additional Secondary Factor is, together with the theory and history of ASF

production.


3 Additional Secondary Factors (ASF)

3.1 Theory

The Loran signal propagates out radially from the transmitter by groundwave,

travelling parallel to the surface of the earth. It does not travel at the free space

speed of light however; rather it is slowed by the atmosphere and the surface of

the Earth. The groundwave accumulates a delay compared to the expected

propagation time over the same distance in free space. This delay is the

accumulation of three components or factors:

Primary Factor: The refractive index of the atmosphere means that the speed

of the signal (cPF) is a fraction lower than the speed of light in vacuum (c0).

Modelling of the Primary Factor is performed by assuming a nominal refractive

index (nPF) of the atmosphere at the surface of the earth, this nominal value is

defined by the RTCM [8] as:

1.000338PFn = (1.2)

Where:

0

PFPF

cnc

= (1.3)

Since the speed of light in a vacuum is given by:

0 299,792,458 /c m s= (1.4)

The Primary-Factor speed of light through the atmosphere is defined as:

299,691,162 /PFc m s= (1.5)

Secondary Factor: In addition to propagating through the atmosphere, a

significant proportion of the Loran signal wave-front will penetrate the surface of

the Earth as it travels – the surface wave. Due to the dielectric properties of the

surface this part of the signal will travel more slowly than in the atmosphere. As

the electrical conductivity of the surface decreases a greater proportion of the

signal will penetrate the ground and the wave-front will propagate more slowly.


The best conducting surface is seawater (with an assumed nominal conductivity

of 5S/m). When receivers compute a Loran position they do so in two stages.

First, they assume that the signal follows an all-seawater path from transmitter

to receiver – the world is assumed to consist entirely of sea-water. It is possible

to model and account for the SF using the equations described by P. Brunavs

[9], as shown in Figure 3-1.

Figure 3-1 – Secondary Factor Delay from Brunavs’ equations

Often both PF and SF corrections are combined into a single formulation of the

Brunavs’ equations, and are applied as a single correction.

Additional Secondary Factor: The second stage in a receiver’s position

computation is to take into account the land along the propagation path. Any

land encountered with a surface conductivity lower than seawater will delay the

signal further. This additional delay is termed the Additional Secondary Factor,

or ASF. To account for land propagation, the receiver must be provided with

built-in tables of ASF values, which would be measured and published by the

service provider. A value for ASF is required for each transmitter, and at each

location at which the receiver is to be used. The principal factor limiting

positioning accuracy is how well the ASF values are known for a particular

location.


3.2 Short History of ASF

3.2.1 Pre-NELS

Traditionally ASFs for Loran-C were accounted for in one of two ways. The first

way was by publishing look-up tables of ASF corrections. These were published

in the USA by the Defence Mapping Agency (Hydrographic/ Topographic

Centre), and were used by hand to correct the Master-Secondary TD

measurements which were output by a Loran-C receiver. An example of such a

look-up table is shown in Figure 3-2. These tables were based on sparse

measurements and were only quoted to within an accuracy of 0.1μs (30m

equivalent position accuracy).

Alternatively, ASF was often incorporated into the over-printed charts used for

plotting Loran-C TD Lines-of-Position. In this case the hyperbolic lines printed

on the chart were distorted to account for the effect of ASF, so the user could

plot the output from the Loran-C receiver directly onto the corrected chart. Later

receiver developments meant ASF tables could be loaded in a digital format into

a receiver, and the conversion from TD to a Latitude and Longitude position

could be done automatically. By the time of the NELS organisation this was

common practice, and the question now was how to measure ASF to begin

with.


Figure 3-2 – An example of an ASF look-up table for the US Loran-C system.

3.2.2 ASF for NELS

ASF may either be measured directly, or may be modelled. It has long been

known that the propagation of 100kHz radio-waves across the surface of the

Earth can be modelled with reasonable accuracy. There exist a number of

techniques to predict the delay, relative to the speed of light, of a signal

propagating along a path of given conductivity. A method developed by

Millington [10] involves dividing the path into small sections of constant

conductivity, and computing the phase delay for each section in turn. Modelling

ASF using this method requires a detailed and accurate database of ground


conductivity. Additional methods also exist to account for terrain elevation, and

again a detailed terrain-elevation database is needed for accurate modelling.

Under NELS, ASFs were needed for the entirety of North-West Europe, to

survey the whole area and measure ASF directly would have been extremely

costly. The decision was made that modelling should be used extensively to

generate databases of ASF. Work was done at the University of Wales in

Bangor to develop a software suite (named ‘BALOR’) designed to model ASF,

based on Millington’s methods [11, 12]. However, as mentioned above, the

accuracy of the model is limited by the available accuracy of ground-

conductivity data. ASF data modelled using BALOR therefore needed

calibrating by making sparse measurements at certain locations to ensure the

accuracy of the database. Problems in developing reliable ASF measurement

equipment at the time meant that the calibration phase of the project was not

completed.

3.2.3 ASF for the FAA eLoran Evaluation

From 2005 attempts were made at Ohio University to improve the accuracy of

the BALOR modelling techniques, including changing the modelling of the

effects of terrain height on signal delay. However, since such methods were still

hampered by the limitations of available ground-conductivity data, the use of

modelling has fallen out of favour, particularly for high-accuracy applications.

To meet the USCG accuracy target of 8-20m (95%), extremely accurate ASF

data is needed. This level of accuracy can only be achieved by direct

measurement campaigns, and as such an extensive programme of harbour-

surveying was planned for the US. This project was well under-way [13] at the

time of the decision to terminate Loran-C in the US, and had demonstrated

many of the techniques for ASF measurement and mapping. This included a

proof-of-concept demonstration [14] that measured ASFs could be uploaded

into a software eLoran receiver and used to navigate a harbour approach at

sub-10m (95%) accuracy.


3.3 ASF Today

The current method for providing ASF data, for a limited geographical area, say

a harbour approach channel follows the work done in the USA. This involves a

comprehensive measurement campaign of the area, the surveyed data is then

uploaded to the user’s receiver. This survey will have been carried out on a

particular day to fix the ASF values once and for all.

Over time there will be some variation from the fixed ASF values stored in the

receiver. Since ASF depends on the ground conductivity along the propagation

path of the signal, any changes in conductivity will change the ASF. Seasonal

effects such as the amount of rain-water soaking into the soil, or the formation

of ice in the winter will change the electrical conductivity of the land. In addition,

changes in the temperature, pressure or moisture content of the atmosphere

will alter the PF speed of light. Although this is technically not a change in ASF,

it will appear so to the user, and PF variations are often lumped together with

ASF variations. To account for these variations, a differential-Loran service can

be established to continually measure the ASF at a particular site and monitor

any changes over time. These changes can then be provided to the user in the

form of updates at regular intervals. The situation is analogous to the way that

DGPS accounts for changes in the Ionospheric and Tropospheric delay of the

GPS signal by broadcasting pseudorange corrections to a user (see Figure

3-3).

These corrections may be broadcast on the Loran Data Channel via Eurofix, or

by another convenient communications channel. Data capacity on the current

LDC can allow for a network of several dozen reference stations per Eurofix-

modulated transmitter, depending on the rate at which corrections are

broadcast.


Figure 3-3 – Changes in ASF for Loran are analogous to changes in atmospheric delay for GPS, and can be mitigated by a differential service

in much the same way.

The GLAs are currently involved in the process of designing such a differential-

Loran network to cover their service area, and will conduct an ASF

measurement campaign to cover the entrances and approach channels to all

the major ports of the British Isles. In addition to investigating the requirement

for ASFs in other confluence zones, where vessels come together and

negotiate navigation channels such as the Dover Strait. The rest of this report

details the efforts made to establish Best-Practice for ASF measurement and

processing, and the work of the candidate in this regard.

3.4 ASF Measurement

The measurement of signal delay to produce ASF maps and differential

corrections is not a trivial matter. For many years the development of reliable

equipment to measure ASF remained elusive, and at least two organisations

tried and failed to produce a reliable measurement unit for NELS. The


inventively titled ASF Measurement System developed by Reelektronika

(www.reelektronika.nl) in the Netherlands is currently the best all-in-one unit for

measuring ASF, tested by the GLAs. The conceptual method for making precise

measurements is detailed below, and the operation of the Reelektronika device

is described.

In order to measure ASF two things are necessary, a user must know precisely

where they are and precisely when they are. When these are known it is

possible to calculate exactly when each group of Loran pulses is expected to

arrive, any delay in arrival may be ascribed to ASF. The way this is calculated is

as follows.

The location of each Loran transmitter is known in the WGS84 reference frame,

as the location of each mast has been surveyed using GPS and published.

From the user’s location, the distance ρ to the transmitter can be calculated

either using Vincenty’s algorithm [15], or an equivalently accurate geodetic

technique. The expected Time-of-Flight (TOF) can then be found by applying

the PF and SF delays, as described in Section 3.1.

( )PFe

nTOF SFc

ρ ρ= + (1.6)

The expected Time-of-Emission (TOE) of each GRI is precisely defined relative

to UTC. The Loran Epoch of midnight (00:00:00) 1st January 1958 is defined as

the point when all Loran Master Stations are deemed to have ‘begun

transmitting’. In reality this means that by counting an integer number of a

Chain’s GRI (for example 67310μs for the Lessay Chain) since the Loran Epoch

it is possible to calculate the next TOE for any signal exactly. If the Time-of-

Arrival (TOA) that is actually measured by the user can also be related to UTC,

by knowing the exact time of the measurement, then the observed TOF can be

calculated. The ASF is thus the difference between the measured and the

expected TOF, as shown in (1.8).

mTOF TOA TOE= − (1.7)

m eASF TOF TOF= − (1.8)

http://www.reelektronika.nl/�


3.5 ASF Measurement Equipment

The ASF measurement unit contains the following equipment:

• Reelektronika LORADD eLoran receiver

• NovAtel OEM-4 GPS receiver

• Temex SRO Rubidium Oscillator

• Custom FPGA-based Timing Measurement Processor for time-tagging

data

• eLoran Simulator signal-generator

• A PC platform

The equipment architecture is detailed in Figure 3-4.

Figure 3-4 – ASF Measurement Unit architecture. Courtesy Reelektronika.

The unit determines its ground-truth position using a radio-beacon DGPS

corrected position derived from the GPS receiver. Using this ground truth

position, together with knowledge of the locations of the transmitters, Vincenty’s


distance algorithm and the PF and SF equations from (1.6) the unit then

calculates an all-seawater Expected Time of Flight (TOFe).

The most challenging aspect of ASF measurement is establishing the time-

frame and obtaining UTC-referenced TOA measurements. The unit establishes

a time-frame by using the GPS-disciplined Rubidium Oscillator as a master

clock. As shown in Figure 3-4 the clock output drives three key pieces of

hardware; the eLoran receiver, the timing measurement processor, and the

eLoran signal simulator. Each of these is discussed next.

1) The eLoran receiver uses an Analogue-to-Digital Converter (ADC) to

digitise the input from the Loran antenna. These samples are then fed to

a digital processing platform which performs the signal acquisition and

tracking to provide signal Time-Of-Arrival (TOA) measurements. The

ADC sampling is driven by the master clock signal. All TOA

measurements are related to a common reference point called Sample-

Count Zero (SC0), this is the time of the master clock at the point when

signal sampling began when the receiver was first powered up.

2) The Timing Measurement Processor generates a time-tag by measuring

the leading edge of a One-Pulse-Per-Second (1PPS) strobe relative to

SC0 of the master clock. A time-tag can be generated for either the

1PPS output from the Rubidium Clock (referred to as Time-Tag1), or the

GPS 1PPS output directly from the GPS receiver (referred to as Time-

Tag2). This effectively gives an accurate measurement of each UTC-

second relative to SC0, and provides a UTC time-stamp for the Loran

TOA measurements.

3) The eLoran Signal Simulator is used to calibrate out any remaining

timing delays, which may exist between reception of the Loran signal at

the antenna and digitisation at the LORADD receiver’s ADC front-end.

These delays are due to temperature variations in the H-field antenna,

and variations in the amount of front-end filtering performed by the

LORADD receiver. The simulator generates a Loran signal, on a GRI of

78230μs, which is injected directly into the antenna and tracked by the

receiver in the usual way.


The TOA measured by the LORADD receiver is the difference between the time

of measurement (Tm) according to the receiver’s clock, and SC0, as shown in

(1.9).

0LORADD mTOA T SC= − (1.9)

The time-tags in turn give the difference between the time of the UTC second

and SC0, as shown in (1.10) and (1.11).

1 0SROTAG UTC SC= − (1.10)

2 0GPSTAG UTC SC= − (1.11)

The TOA, as output by the receiver can then be related to the time of the actual

UTC second, by subtracting either time-tag offset, thus,

UTC LORADDTOA TOA TAG= − (1.12)

Substituting (1.9) and either of the time-tags (1.10) or (1.11) into (1.12) gives:

( )0 ( 0)UTC mTOA T SC UTC SC= − − − (1.13)

UTC mTOA T UTC= − (1.14)

Each TOA measurement is now known relative to the exact time of the UTC

second. However there exists a slight delay between the signal arriving at the

antenna (true TOA) and the signal being measured by the receiver. This delay

is variable and is composed of several components:

• The response-time of the H-field antenna’s ferrite core to the signal’s

magnetic field, here termed the Antenna Delay (ΔA). This is variable and

highly dependent on the temperature of the antenna.

• The Cable Delay (ΔC) as the signal travels from the antenna to the

receiver is a constant offset and does not change over time.


• The Processing Delay (ΔP) in the front-end filtering and analogue-digital

conversion. This delay may change depending on how much filtering

and pre-processing of the signals is needed.

To find the true time-of-arrival, these delays must be removed from the UTC-

referenced TOA measurement in (1.14), thus:

true UTCTOA TOA A C P= −∆ −∆ −∆ (1.15)

By creating a precisely timed simulated signal and injecting it into the antenna,

the Simulator Delay (SD) can be accurately measured. This is equal to the

antenna and processing delay, plus two times the cable delay (once up to the

antenna and back),

2in outSIM SIM A P C= + ∆ + ∆ + ∆ (1.16)

in outSD SIM SIM= − (1.17)

2SD A P C= ∆ + ∆ + ∆ (1.18)

True UTC referenced TOA can then be found from (1.15) by substituting

TOAUTC as given in (1.12), and applying the simulator delay (SD) from (1.18).

true LORADDTOA TOA TAG SD C= − − + ∆ (1.19)

It is assumed that the speed at which the signals travel along the antenna cable

is constant, so the Cable Delay (ΔC) can be found by knowing the exact length

of antenna cable used. Further information about the unit is available from the

manufacturers. Figure 3-5 shows a diagram summarising the establishment of

an accurate common time-frame relative to SC0.


Figure 3-5 – TOA Timing diagram, Courtesy Reelektronika.

3.6 ASF Measurement Errors

It is important to understand how the ASF data is produced by the hardware. By

doing this it is possible to determine the accuracy of the measurements that are

made, and the possible sources of measurement error picked up along the way.

Since the GLAs have to ensure that eLoran can meet the IMO targets on

accuracy and integrity we need to know how good our ASF data is to begin

with. When fully expanded by substituting measured or known quantities (1.8)

can be represented as (1.21).

m eASF TOF TOF= − (1.20)

( ) ( )PFLORADD

nASF TOA TAG SD C TOE SFc

ρ ρ = − − + ∆ − − +

(1.21)

Following simple error-propagation laws, the error in ASF is given by:

2 22 2 2 2 2 2 2 2 2PF PFn n

ASF TOA TAG TAG SD TOE TOE c cρ ρσ σ σ δ σ σ δ σ δ= + + + + + + + (1.22)

Here σ represents the noise on a particular measurement, δ represents a bias

or offset. The terms are described in Table 5.


Error Source Magnitude Notes

2TOAσ Noise in Loran

TOA

measurement

10-25ns

(3-8m)

Depends on the signal-to-noise ratio

(SNR) of the received signals, 10-25ns

assumes 30s integration and +30dB to

0dB SNR respectively

2TAGσ Timing noise ~20ns Using the GPS 1PPS directly can

introduce extra noise into the time-

tagging, depending on the quality of the

GPS engine’s output 1PPS

2TAGδ Timing offset ~100ns Alternatively, using the SRO 1PPS can

introduce a timing bias due to clock de-

synchronisation

2SDσ Simulator

error

10ns The measurement of the Simulator TOA

depends on SNR, like any Loran signal.

The simulator is adjustable and can be

set at a high SNR (e.g. +30dB)

2TOEσ Transmitter

jitter

<10ns Time-of-emission control at the

transmitter maintains timing to within

±5ns of a bank of 3 Caesium clocks, 10ns

phase-adjustments are applied when

necessary.

2TOEδ Time-of-

emission drift

~100ns Synchronisation between Loran time and

UTC may drift over time

2ρσ Ground-truth

ranging error

3.3ns Assuming 1m accuracy for DGPS

2ρδ Ground-truth

ranging offset

~15ns If no GPS augmentation is used for the

ground-truth, a position bias of ~5m of

may affect all ASF measurements made.

Table 5 – Error sources in ASF measurement.


The ASF unit itself, by applying (1.21) only accounts for a few of the error

sources present, and as such the accuracy of its ASF output is 15-30ns (5-10m,

1σ), with potentially more than 100ns of bias. In particular the following sources

of bias remain in the raw data as output by the measurement system.

Time-Tag Errors: The default operation of the unit is to use time-tag1 (SRO

1PPS) for time synchronisation. This has the advantage of using the Rubidium

Clock to provide a stable PPS output, which is not affected by momentary GPS

outages or noise in the GPS pseudorange measurements. The disadvantage is

that during normal operation it has been observed that the clock may become

slightly misaligned to GPS and it then has to be steered gradually back into

alignment. The time-constant used to steer the clock means time-tag1 incurs a

bias error, which may be up to 100ns.

Transmitter Clock Drift: Any drift in a transmitter’s TOE will be measured as if

it were a change in ASF. This introduces time-dependent bias errors into the

ASF measurements, which may also be as much as 100ns.

Temporal ASF Variation: As with TOE drift, if the ASF values change during a

survey (due to changes in the transmission path such as rain soaking into the

earth) these changes introduce errors into the measurements made. Also

changing weather conditions between a transmitter and the measurement unit

will affect the Primary Factor (PF) delay, which is lumped in with ASF as

described in Section 3.3.

To achieve the highest level of accuracy from eLoran, the best quality ASF data

is needed. Therefore, methods have been developed by the GLAs to remove or

minimise the unaccounted for sources of error in ASF measurements. In some

cases these techniques are new or novel approaches that are not included in

the operating firmware of the ASF Measurement Unit. With optimal processing

the best possible accuracy of 15-30ns (5-10m) can be achieved with negligible

bias error.


3.7 Summary

In summary, this Chapter has described ASF as the additional Loran signal

propagation delay.

• This is due to the presence of land rather than sea-water along the

propagation path from transmitter to receiver.

• The principal cause is the relatively poor electrical conductivity of the

ground.

• ASF is not distinguishable from changes in the PF speed-of-light in the

atmosphere, so the two are often lumped together.

A brief history described the origins of measuring ASF and providing corrections

to the user.

• Look-up tables can be used to correct a Loran-C position fix, and

improve the operational accuracy of the system.

• Modern methods rely on digital tables integrated into Loran receivers.

• ASF modelling techniques were developed but suffer from the lack of

good ground-conductivity data.

• The preferred method is now to measure ASF directly, rather than rely on

modelling.

The process of measurement was explained with specific reference to the

Reelektronika unit.

• DGPS is used to provide a ground-truth position.

• A GPS-synchronised atomic oscillator is used to relate Loran TOA

measurements to UTC time

• The ASF is calculated as the difference between the expected and

measured TOA.

• Additional calibration parameters are also needed for absolute accuracy

of ASF.


It has been described how the measurement technique incurs a number of

errors due to:

• TOA-measurement variations, depending on the Loran signal SNR

• The quality of the clock synchronisation to UTC

• The presence of temporal variations in ASF, or PF variations

• Any transmitter timing drift that occurs during the survey.

It is possible to mitigate or reduce most of the measurement errors by applying

suitable processing techniques. Techniques developed by the candidate, and a

software suite written to implement them are described in the next Chapter.


4 ASF Processing

To inform the development of our ASF processing methodology, the GLAs

carried out a number of preliminary measurement campaigns to gather sample

ASF data-sets. These data-sets also serve as test and validation data. This

Chapter presents the results of two such trials.

4.1 ASF Measurement Campaigns

4.1.1 Equipment

The data gathering process is made straightforward by using the integrated

ASF Measurement System shown in Figure 4-1.

Figure 4-1 – ASF Measurement System. Courtesy Reelektronika.

Referring to the block diagram shown in Figure 3-4 the LORADD receiver within

the ASF unit communicates with the internal PC platform by passing NMEA

data over a serial-port. Data from the GPS receiver and the SRO controller are

forwarded to the LORADD receiver and also communicated over the serial

connection to the PC. Firmware within the LORADD takes in the necessary

Loran, GPS and synchronisation data and outputs the ASF measurements as

part of the stream of NMEA sentences. This data is logged to a local hard-disk,

and may also be made available to software applications running on the built-in

PC.


4.1.2 Sea Trials

A number of sea-trials have been carried out using the GLAs’ fleet of ships to

gather ASF data. Each vessel is already equipped with an eLoran H-field

antenna and an eLoran receiver as part of the GLAs’ ongoing eLoran

performance monitoring project. When the vessel is required to be used for ASF

measurements the eLoran monitoring receiver can be temporarily replaced with

an ASF Measurement System.

Preliminary survey data has been gathered to:

• Investigate the magnitude of ASF values and the typical ASF variations

seen in several parts of the UK

• Verify the assumptions made about ASF, and to validate the predictions

of the theory

• Gather typical ‘example’ ASF data-sets to inform the development of our

processing techniques

The aim of the work is to eventually produce a Best-Practice ASF Surveying

Methodology, which can be rolled out throughout the UK and Ireland as part of

providing an eLoran service. It is also the aim that the work will inform any new

European eLoran consortium on ASF measurement and processing best-

practice.

4.1.3 ASF-Unit Calibration at Lowestoft

An important early trial involved the measurement of ASF data from Lowestoft,

the Eastern most point in England. This was done in order to obtain a

calibration reading from the ASF Unit, and therefore verify the accuracy of its

output. As described in Section 3.5, it is very important that all timing delays are

precisely calibrated in order to establish the exact UTC time of each Loran

measurement. Any unaccounted delays or biases can introduce errors into the

measured ASF. The only way to check that the ASF measurements it is

providing are correct is to go to a place of known ASF.

By definition ASF is zero for an all sea-water path. At Lowestoft the propagation

path from the Loran transmitter at Sylt, in Germany, is entirely sea-water, with

the exception of a few hundred meters of shoreline near the transmitter. It was


important to be able to obtain a consistent ‘zero’ reading from the unit to be

confident of its calibration and operation.

Figure 4-2 – The eLoran propagation path from the transmitter at Sylt to Lowestoft. ASF is, by definition, equal to zero for an all-seawater path.

Several hours of static ASF calibration data were gathered from Lowestoft. The

results of this are discussed later on, in Section 4.2.1.

4.1.4 eLoran Assessment in the Orkney Islands

Amongst the trials conducted was a comprehensive study of eLoran around the

Orkney Islands off the north coast of Scotland. It is known that the ASF value at

a point depends on the propagation path of the signal from the transmitter and,

importantly, the ground conductivity of any land along that path. The belief was

that in archipelago terrain like the Orkneys, with many small islands and the

resulting complicated coastline, that a moving vessel would encounter fast

changes in ASF due to rapid variations in the coastline.

The data gathered by the GLAs included two ‘sample’ ASF data sets following

the two approach channels in to Kirkwall harbour on the Orkney Mainland. Plots

of these data sets are shown in Figure 4-3 and Figure 4-4.


Figure 4-3 – Data Set 1: Anthorn ASF for the Eastern approaches to Kirkwall harbour and a limited survey of Shapinsay Sound

Figure 4-4 – Data Set 2: Anthorn ASF for the Northern channel to Kirkwall and a survey of the outer approaches to Shapinsay Sound


The ASF value is indicated by the colour-bar on the right-hand-side of the

figures. It can be seen that the highest values (2.25μs) are found in the harbour

and the lowest (1.8μs) are found in the Eastern approaches to Shapinsay

Sound. The Anthorn transmitter itself is located due south of the Orkneys, and

the variations in the data reflect the differences in propagation-path taken by the

signal. For example the Eastern approaches have a low ASF as the signal does

not pass over any of the Orkney Mainland, and so accumulates less of a delay.

The routes followed to collect these two data sets were designed to provide a

good base to study the effectiveness of the ASF data processing techniques

developed by the candidate.

4.1.5 GPS Jamming Trial in Newcastle

In late November and early December 2009 the GLAs conducted a number of

demonstrations of the effect the denial of the GPS service has on a typical

modern ship’s bridge. Located onboard the THV Galatea was a GPS jamming

device, owned and operated for the GLAs by the Defence Science and

Technology Laboratories (DSTL). Guests from within the Shipping Industry and

the Government were invited onboard the ship to observe first-hand the effect of

GPS Jamming. In particular this trial focused on the effects on navigation

equipment and the ability to safely navigate without GPS.

As part of this demonstration, a live eLoran trial was carried out. In preparation,

ASF data was measured on the approach to the harbour on the River Tyne. The

ASF data for the Anthorn signal is shown in Figure 4-5. These measurements

demonstrate one of the predictions of ASF theory - the Coastal Recovery Effect.

As the signal passes over land it accumulates an ASF as the surface-wave is

delayed by the poor ground conductivity. The part of the wave-front propagating

higher in the atmosphere is not delayed as much as it is not in close contact

with the ground. When this delayed signal reaches the sea, some of the delay is

recovered as the surface-wave begins to catch up again with the rest of the

wave-front.


Figure 4-5 – Anthorn ASF data measured along the approach channel to the berth at Newcastle on the River Tyne

This effect is quite easily demonstrated by the Tyne data Figure 4-5 above, as

the ASF at Newcastle is about 1.1μs, and falls away to 900ns when travelling

away from the coast. The direction to the Anthorn transmitter indicates that this

change cannot be ascribed to a reduction in land-path along the propagation

route, as was the case in the Orkneys (Figure 4-3 and Figure 4-4).

For the rest of this chapter, the data-gathering trials described above will be

used to provide examples, with the assumption that all of the processing

methods are applicable to any ASF measurement campaign or harbour survey.

4.2 ASF Error Mitigation and Minimisation

Two key techniques have been developed to mitigate the largest error terms

present in the raw measurements, as described in Table 5. These are described

in the following sub-sections.

4.2.1 Local Clock De-Synchronisation

As described in Section 3.5, the Rubidium clock within the ASF unit is used to

provide a stable time source to drive the signal measurement and time-


synchronisation hardware. This has an advantage over using the GPS time-

source directly in that the timing measurements are ‘smoothed out’ by the Rb

clock. Because of this smoothing the timing measurements are not affected by

GPS pseudo-range measurement noise, or interrupted by any momentary loss

of GPS. It has been observed, however, that the time-constant of the control

loop used to steer the Rb clock to the GPS 1PPS source can cause the clock to

take a long time to ‘settle down’. This can introduce errors of up to 100ns. Some

synchronisation measurements were made during the calibration trial at

Lowestoft and these are shown in Figure 4-6 and Figure 4-7.

Figure 4-6 – ASF Measurements for Sylt 6731Z made at Lowestoft, a constant value close to zero is expected.

Figure 4-7 – Difference between the atomic clock 1PPS and GPS-derived UTC.

The results indicate that the drift in ASF value measured for Sylt was equal, and

opposite to the drift of the Rb. clock from UTC, which ran to 100ns during the


experiment. Processing this offset out is straightforward. The smoothed clock-

offset data can be applied as a correction to the measured ASF data. This

technique is preferred over using the GPS synchronisation data directly, as it

adds no additional noise to the ASF data, and can be applied in real time during

an ASF survey, as shown in Figure 4-8.

Figure 4-8 – ASF for Sylt. When corrected for the clock drift the value remains constant at about 50ns, with a standard-deviation of 15ns

4.2.2 Removal of Temporal Variations

When conducting a survey, a roving ASF unit will measure both temporal and

spatial variations of ASF. The temporal variations may be due to genuine

changes in ASF, such as freeze/thaw changes in the propagation path, rain

soaking into the earth; or the effects of passing weather-fronts. Weather-fronts

change the atmospheric pressure and moisture content, which actually affect

the Primary Factor (PF) delay but manifest as changes in the ASF

measurement. Also, any drift in the Loran transmitter’s TOE will be interpreted

as a change in ASF. It is necessary to remove these temporal components so

that the spatial variations in ASF can be isolated and published for eventual

upload into a user’s eLoran receiver.

The removal of temporal variations may be performed by using a second ASF

unit employed as a static reference receiver. Because the reference receiver

remains static it will not see any spatial variation in ASF, and will record only the

temporal component. Data log files can be taken from the roving receiver and


the reference receiver, and then processed together to subtract the temporal

variations observed by the reference receiver.

Mathematically we can describe the ASF data recorded by the rover as a

function of position and time. We can decompose this into two functions: a

temporal component (T) that depends only on time; and a spatial component,

(S) that depends only on position. In addition we have some measurement

noise as described in Section 3.6.

( ) ( ) ( ),rover roverASF x t S x T t ε= + + (1.23)

The functions S and T are assumed to be continuous and slowly-varying. The

temporal variations are not expected to change rapidly over time, and the

spatial variation is expected to be a smoothly-varying function of position. The

static receiver will measure only the temporal component of the variation:

( ) ( )0reference refASF t ASF T t ε= + + (1.24)

With the correct choice of nominal value (ASF0) it is assumed that the temporal

variations T are the same between two receivers if the baseline between them

is short, say less than 20km or so. To correct for the temporal variations the two

data series’ are aligned in time and subtracted:

( ) ( ) ( ) 0rover reference rover refASF ASF S x T t T t ASF ε ε− = + − − + + (1.25)

( ) 0rover reference rover refASF ASF S x ASF ε ε− = − + + (1.26)

The effect of this is to leave only the function S relative to the nominal value at

the reference station. This operation does also have the effect of increasing the

noise level in the measurements. Equation (1.26) is the basis for the operation

of the differential-Loran service. A nominal value of ASF0 is measured on one

day at the reference station site and kept fixed for the lifetime of the station. The

differential broadcast then consists of timely updates of the function T, which is


assumed to vary slowly over time. As described in Section 3.3 the differential

broadcasts are made on the Loran Data Channel modulated onto the Loran

pulses themselves via Eurofix. The GLAs operate a Eurofix-equipped eLoran

station at Anthorn, in Cumbria. The Eurofix transmitting equipment is accessible

via a Virtual Private Network (VPN) from any GLA computer with Internet

access and knowledge of the keys appropriate to the VPN. During a survey it is

possible to operate the ‘reference’ ASF unit as a fully-functional differential-

Loran Reference Station and broadcast its differential corrections over Eurofix

in real-time.

With the corrections broadcast on the LDC it is possible to remove the temporal

ASF variations on-the-fly as an ASF survey is in operation. This removes the

need for any post-mission processing and crucially can be used to assess the

quality of the ASF measurements while the survey is still ongoing. There is a

practical consideration to the advantage of knowing how good the data is during

the survey and while still onboard a survey vessel. Generally it will be easier

(and cheaper) to make additional measurements during a current survey than to

re-schedule a repeat survey at a later date to fill in any gaps.

4.2.3 Setting up a Differential-Loran Reference Station

Since the differential reference-station infrastructure is not currently in place,

any Loran survey or trial requires its own station to be installed before the

survey begins. The GLAs are able to deploy a temporary reference station at

short notice, using their Mobile Measurement Unit, affectionately known as the

‘Burger Van’. The photograph in Figure 4-9, below, shows the van deployed as

a reference station for the Orkney Islands trial.

The van is fitted with an eLoran antenna (centre of the picture, top), and a

survey-grade NovAtel GPS antenna (centre) for reception of the eLoran and

GPS signals. An eLoran ASF unit measures the Loran signals, and generates

differential corrections, which are broadcast via a Sailor 250™ satellite

broadband Internet connection (the radome on the far right) to the transmitter at

Anthorn.


Figure 4-9 - The Burger Van mobile differential-Loran Reference Station + Willing Volunteer.

Before the corrections can be used, the site needs to have its position

surveyed. A 24-hour DGPS survey is carried out to determine the precise

location of the antenna, and a similar Loran survey is done to provide nominal

ASF values at the Reference Station. The Reference Station can then generate

its differential corrections by calculating the difference between the measured

ASF and these nominal values.

4.2.4 Processing Differential-Corrections

ASF measurements contain a certain amount of error and, as we have seen,

applying a set of static ASF measurements as temporal corrections to the data

collected during a dynamic survey increases the errors in the dynamic data

(1.26). Typically differential-Loran corrections are averaged over a moving

integration window to reduce the noise in the data and thus the errors. The

length of the integration window is a trade-off: too short a window and the

station broadcasts too much noise in the corrections; too long a window and the


corrections will lag the temporal changes in ASF. The GLAs have found that a

median-filter over a rolling window of 5 minutes, with new corrections broadcast

every 30 seconds is a good setup for a reference station.

4.2.5 Other Error Sources and Conclusion

It can now be seen that by applying corrections to the measured data, many of

the known error sources that we identified in Chapter 3 can be mitigated or

greatly reduced as shown below in Table 6.

The only significant source of error that remains is due to the measurement of

the Loran signal Times-of-Arrival (TOA). This error is dependent on the signal-

to-noise ratio of the signal being measured and as such cannot be mitigated

without raising the power of the transmitting station, or through integration

(averaging) of the received signal. The GLAs typically use a 30-second

integration time for ASF measurements, which can mitigate some of the

measurement noise in the raw TOA measurements. However, we have to strike

a compromise between too much integration and too much lag appearing in the

spatial ASF data compared to the change in coastline/terrain over the route of

the survey.

The result is ASF measurements, which are accurate to 15-30ns, with little or

no bias offset. However, this means that 5-10m of error still remains in the raw

ASF measurements, which is a significant proportion of our error budget.

Further processing is needed to create a data format suitable for use by the

user. The goal is to produce a set of ASF measurements, which will contribute

as little as possible to the error budget of eLoran position-fixing. Any remaining

error must be estimated and published alongside the ASF data so it can be

accounted for within the user’s receiver.


Error Source Magnitude Mitigated By

2TOAσ Noise in Loran

TOA

measurements

10-25ns Can be improved by using a longer

integration time

2TAGσ Timing noise <10ns Use Time-tag 1 (SRO 1PPS) for UTC

synchronisation

2TAGδ Timing offset <10ns Processing the clock-offset out using

exponential-averaging

2SDσ Simulator error 10ns N/A

2TOEσ Transmitter jitter <10ns Short-term transmitter noise will remain

as part of the 10-25ns measurement

noise.

2TOEδ Time-of-

emission drift

<10ns Processed out with temporal

corrections, some amount of spatial de-

correlation is expected to remain,

however.

2ρσ Ground-truth

ranging error

3ns Slight gains can be made by using a

better ground-truth system such as RTK

GPS, but the error savings are minimal

for the extra cost and effort.

2ρδ Ground-truth

offset

<1ns Using DGPS for ground-truth accuracy

Table 6 – Mitigation of timing errors in ASF measurement

4.3 Producing an ASF Grid

The proposed method for providing the mariner with spatial ASF data is to

create a database of geographically located values, which is pre-loaded into


their eLoran receiver. The proposed data format is a ‘grid’ of spot values of ASF

at regular spacing throughout the harbour and approach channel area for each

Loran transmitter. These grids will also be assigned a particular reference

station ID so that the correct set of differential-corrections can be used in

conjunction with them.

Experimental work in the USA [14] has indicated that 500m grid spacing for the

values is an optimal figure to be able to describe typical spatial variations

accurately. For ease of use the grid lines follow the WGS84 lines of Latitude

and Longitude. In latitude we use a 0.005 degree spacing and the longitudinal

values are scaled appropriately depending on the latitude (for example, 0.01

degrees longitude in the Orkneys at 59°N, gives a longitudinal grid spacing of

560m or so).

4.3.1 The Basic ASF Grid

The simplest database which can be produced is termed the ‘Basic’ grid, and is

produced thusly:

• A lattice of cells, or elements, at 0.005 degree spacing is produced. The

co-ordinates of the outer edges of the lattice are determined by the

extent of the surveyed data north, south, east and west

• The value for each cell is then assigned as the mean of all of the

surveyed data that lies within that cell

• Any empty cells within the grid are assigned the median value of the

entire data set for a given transmitter

This type of grid is currently the preferred database format implemented within

the commercial eLoran receivers available. This is because the format is easy

to use, the operation is as so:

• The receiver looks up the ASF values, one per eLoran transmitter, for the

cell within which it is currently located based on a sea-water only position

computation

• Differential-corrections are then applied to these ASF values from the

appropriate Reference Station


• The ASF corrections are then applied to the measured signal Time-of-

Arrival (TOA) values and a final ASF corrected eLoran position-solution

is then found

An example of a Basic grid is shown in Figure 4-10.

Figure 4-10– Basic ASF grid of the data in Figure 4-3 at 500m spacing.

It is often necessary to enlarge the area covered by the ASF survey, as in the

case of Figure 4-10 where the surveyed approach channel is rather narrow. A

‘nearest-neighbour’ extrapolation technique has been investigated by the GLAs.

It is assumed that spatial ASF values at sea vary smoothly, and as such will not

differ much from one cell to its neighbour. This assumption allows for the

extension of the surveyed data by 500m with potentially only marginal loss of

accuracy. Compare Figure 4-11 with Figure 4-10.


Figure 4-11 – Extrapolation of the ASF grid shown in Figure 4-10

The advantage for this type of ASF database is that by averaging all the data

within each 500m cell, the data presented in the grid is more accurate than the

raw data because of the noise reducing property of the process of averaging.

The disadvantages of the Basic grid method are that there are discontinuities at

each cell boundary; sudden ‘jumps’ in position have been observed as a

receiver moves from one cell to another when using this type of grid.

This could potentially be worrying for a mariner who would observe sudden

changes in their position or course. Also, the issue may increase the difficulty of

integrating eLoran with another source of position, such as GPS.

Additionally, the Basic grid does not account for the spatial distribution of the

measurements within each cell. The ASF values surveyed are only truly

applicable at one particular location within each cell, and by averaging all the

measurements within 500m, a lot of the spatial variation information is lost. The

discontinuity issue becomes apparent by observing a 3D isometric view of the

above grid:


Figure 4-12 – Basic Grid shown in a 3D isometric view to highlight the discontinuities at cell boundaries.

A solution to the problem of the discontinuities is to interpolate the values from

one cell to the next in order to provide a smooth cell transition. This method will

also reflect the true nature of ASF more accurately, as the phenomena is

assumed to be a continuous and smoothly varying function of position.

4.3.2 The Interpolated ASF Grid

A two-dimensional interpolation method, which has been investigated by the

candidate for the GLAs, is now described. At a particular location (X), given by

the co-ordinates (x, y), the geographical position of the receiver within a

particular ASF grid cell can be expressed in terms of two parameters α and β.

The position (x, y) will have to be provided by a seed position either from an

estimated fix or the last available eLoran fix.


( )

( )( )

( 1) ( )x x i

x i x iα

−=

+ − (1.27)

( )

( )( )

( 1) ( )y y j

y j y jβ

−=

+ − (1.28)

Here x(i) and y(i) are the WGS84 co-ordinates of the grid cell, within which the

receiver is currently located. The parameters (α, β) are then used to perform a

two dimensional interpolation between the four nearest grid elements C1-C4:

The ASF value at location X is given by the Interpolation Equation:

( ) ( ) ( )1 1 1 3 1 2 4ASF C C C Cα β β α β β× = − ⋅ − ⋅ + ⋅ + ⋅ − ⋅ + ⋅ (1.29)

Viewing this equation, in a 3D isometric view again, shows that essentially a

small surface element is fitted to each grid cell. The elements will not be flat, but


due to the two-dimensional interpolation will be curved and look more like

‘Pringles’ crisps as shown in Figure 4-13.

Figure 4-13 – Example surface generated by interpolating a single grid cell, the differences at each vertex have been exaggerated for

demonstration. A circle has been drawn on the surface to show how the surface element is curved.

Figure 4-14 – ‘Pringles’ Crisps demonstrate the same mathematical shape. They are also Hyperbolic Paraboloids


When creating the grid in the first place, the question of assigning values to the

cell vertices is how to find the best fit of these curved surface elements to the

raw data. For the Basic grid we could just take the mean of the survey data

within a cell, but for an Interpolated grid the method becomes more

mathematically involved.

A method first developed by G. Johnson and his team in the US [17] is to

reverse the Interpolation Equation (1.29) by performing a least-squares fit of the

data. The parameters which are to be fitted by least-squares are the ASF

values at the vertices of the grid (Figure 4-15), which are arranged into a vector

(1.30).

Figure 4-15 – ASF cell vertices for a grid n cells in Longitude, and m cells in Latitude

[ ]1, 2, 3, , , 1, 2, , , *asf C C C Cn Cn Cn Cm n= + + (1.30)

The observations used to fit these parameters are the ASF measurements

made during the survey. As the survey vessel’s track passes through a grid cell,

then each measurement is an observation of its position (α, β) and ASF value.

Figure 4-16 shows the “kth” observation, and the four surrounding cell vertices:


Figure 4-16 – kth observation and four surrounding cell vertices.

The Interpolation Equation (1.29) gives the “kth” row of the design matrix,

according to the location of the parameters (Ck) in the asf vector (1.30).

( ) ( )( ) ( ) ( ), 0,0,0, , 1 1 , 1 , , 1 , , ,0,0,0A k α β α β α β αβ= − − − − (1.31)

The “kth” entry into the observation vector is the raw ASF measurement made at

the point Xk:

( ) Xkl k ASF= (1.32)

The result is a sparse design matrix, the values of C1 – Cm*n are found by least

squares:

( ) 1T Tasf A A A l−

= × × × (1.33)

As described in Table 6, the quality of the measurement depends on the SNR of

the received signal. An alternate method is to perform weighted Least-Squares

fit, where a higher weighting is given to measurements with a higher SNR:

( ) 1T Ta sf A W A A W l−

= × × × × × (1.34)


There exists an issue with the accuracy of this inversion method, which is

related to how observable the value on each vertex is. The cells where the data

is poorly distributed (located all to one side of the cell, or in one corner only) will

have any linear trend in the data extrapolated beyond the data’s extent, and can

lead to very large grid values (spikes). This spikiness can be seen in Figure

4-17 in a reverse-interpolated grid, which has been created from our sample

data in Figure 4-3.

Figure 4-17 A 3D image of a reverse-interpolated ASF grid, showing ‘spikes’.

It is highly unlikely that the grid above represents the true ASF variation in

Shapinsay Sound. The inversion method, although mathematically precise does

not provide plausible results, we already know that the spatial variation of ASF

should be quite smoothly varying. A technique is needed to prevent these

‘spikes’ from corrupting an ASF database.

The technique favoured by the team in the USA was to bound the survey area

by taking measurements at additional points, often on land using a static

receiver, or to remove any ‘implausible’ cells by eye. Both these methods were

impractical as they involved some extra work and attention when processing the

data.


The Candidate has developed a different technique for the GLAs. The addition

of ‘sensible’ data points surrounding the raw data can be used to prevent the

reverse-interpolation method from shooting off to unreasonable values. As the

‘spikiness’ problem does not appear in the Basic gridding technique, the mean

of each cell is therefore a good choice for these ‘sensible’ boundary points.

Figure 4-18 – The addition of ‘sensible’ boundary points to raw ASF data, this bounds the inversion technique and prevents ‘spiky’ ASF grids like

Figure 4-17

Figure 4-19 – Extrapolated boundary points added to the raw data.


Since the number of added points is quite low (usually less than 5% of the total

amount of raw data), this additional data is not expected to significantly affect

the grid values. The boundary points can also be extrapolated further to

increase the stability of the edges of the grid, as shown in Figure 4-19.

The advantage of the GLAs’ boundary-conditions method is that it can be

automated, and does not require additional work or further data-gathering. The

result of the GLAs’ reverse-interpolation method is a grid where the ASF used

by the receiver changes gradually across each cell and there are no jumps or

discontinuities at cell boundaries, and the data is sensible and plausible

throughout, as shown in Figure 4-20

Figure 4-20 – Gradual cell transitions are obtained by Interpolating an ASF grid, the grid is kept ‘sensible’ by the application of boundary data derived

from the ‘Basic’ Grid.

Once the data has been processed into a convenient representation, it is

important to be able to assess the contribution of this processing to the overall


ASF error budget. A number of self-consistency checks are available to assess

the quality of the ASF grid, and additional data gathering can be performed to

verify the grid accuracy.

4.3.3 Error Statistics

As a first step, the standard errors on the grid values can be found. In what

follows we will show a method for both the Basic Grid and the Interpolated Grid.

For the Basic grid, propagation of error laws gives the error on the mean value

for each cell as:

{ }2 2 2 20 1 2

1NN

σ σ σ σ= + + + (1.35)

Where N is the number of data points measured in that cell, and σn is the

standard-deviation of the “nth” data point.

As described in Table 6, the error on each measurement is largely due to the

SNR of the received signals. If the SNR is fairly constant during a survey, we

can assume that the measurement error σ will remain constant. The multiplier

N1 then gives us a measure of the normalised variance for each grid element,

which can be used as a simple assessment of data quality, as shown in Figure

4-21.

Figure 4-21 – Normalised Errors for a Basic ASF grid.


‘Good’ data, which is well surveyed, has a value of N1 which approaches zero.

For the Basic Grid, the area around Kirkwall Harbour itself is shown to be the

‘best’ surveyed cell in the grid, as it contains the largest number of data points.

This cell is shown in bright green near the south-west corner of the grid. Any

ASF cell only surveyed by a single measurement would have a value of 1,

designated ‘Poor’. Un-surveyed cells are shown in blue. The colour-scheme is

quite intuitive for assessing data-quality quickly by eye; it can be seen for

instance that there are a number of poorly surveyed cells in red and orange

which require further surveying.

For the Interpolated grid, estimating the errors requires using the matrix

formulation. The grid-element covariance matrix is given by (1.36):

( ) 1TijC A W A

−= × × (1.36)

Where W is the matrix of weightings for each data point, given by:

21

21 2

2

0 00 0

0 0 N

W

σσ

σ

−

=

(1.37)

If we can assume measurement noise is the same for all measurements, we

have that:

2NW Iσ −= ⋅ (1.38)

And the grid covariance matrix is given by (1.39):

( ) 12 TijC A Aσ

−= ⋅ × (1.39)


Neglecting the off-diagonal co-variances (which are rather hard to visualise!) the

normalised, diagonal form ( 2iiC σ ) can be used. This gives a normalised

standard error on each cell vertex; the standard error at any point on the grid

will be given by the interpolated values at each vertex by applying propagation-

of-error laws to the Interpolation Equation (1.29)

Figure 4-22 – Normalised Standard Errors for an interpolated ASF grid, visualised as an interpolation of the errors on each cell vertex.

Missing (un-surveyed) data has been given a nominal value of -5 (in blue) to

differentiate it from the ‘good’ data. The colour-scheme shown is similar to that

used in Figure 4-21, but it can be seen that the standard errors for an

Interpolated grid are larger and may be greater than 1. Ideal standard errors

approach 0 (green), any value greater than 1 is poorer than the noise in the raw

data, so is considered ‘bad’. It becomes clearer now that the Inverse

Interpolation method works better in the centre of a surveyed area. The red

elements are those with very poor accuracy, which displayed the ‘spiky’

behaviour when not constrained by any boundary points as in Figure 4-17.

In contrast to the Basic grid shown in Figure 4-21, the cells to the western side

of Figure 4-22, near Kirkwall Harbour, demonstrate the highest standard errors.


This is an area crossed by only a single survey-track, (see Figure 4-3) and

demonstrates the importance of making repeat-tracks over an area to

thoroughly survey the ASF variations across the width of an approach channel.

4.3.4 Standard Deviation of Residuals

The residuals between the raw data points and the values of the grid can give

an indication of the ‘goodness of fit’ of the grid to the raw data. This technique

does have limited usefulness for assessing an Interpolated grid, as the Least-

Squares fitting minimises the squares of the residuals by definition so will

always report a very good fit to the data. A plot of the residuals of the grid in

Figure 4-20 is shown in Figure 4-23 , note that the extrapolated cells do not

contain any raw data so give zero residual:

Figure 4-23 – A plot of residuals from the gridded data, the scale is in micro-seconds.

The residuals can be used as a good indicator of where the data fits the grid

well, and where there is probably insufficient data. We can use the noise in the

ASF measurements (in this case, σ = 28ns for the data in Figure 4-23) as a

measure of goodness of fit. In Figure 4-23 above, the colour scale goes from 0


to 56ns (2σ), with ideally fitting data shown in green at 28ns (1σ). Residuals that

are too high suggest a poor fit between the raw data and the gridded values.

This may be due to an incorrect choice of grid spacing (500m in this case) or

erroneous measured data. The important indicator is where the residuals are

too low, indicating the gridded values may be tracking the noise in the data and

more measurements are needed for that cell.

Ideally an ‘all green’ indicator for both Standard Error and Residuals will indicate

that the grid cell has been surveyed to the right level of accuracy. To improve

the ‘usability’ of these two quality indicators it would be better if they could be

combined into a single error-statistic, so that individual cells can be either

accepted; rejected; or re-surveyed as appropriate.

4.3.5 Summary of ASF Processing

Raw ASF measurements contain a number of biases and errors, as described

in Table 5. A number of techniques have been developed to minimise these

errors and provide the best ASF measurements possible:

• The Rubidium Oscillator is used to provide the most stable UTC-

synchronisation and time-tagging.

• Real-time processing of the clock de-synchronisation removes any drift

from UTC

• Differential corrections are applied to measured ASF data to correct for

ASF variations, PF variations and transmitter timing drift.

• These differential-corrections are smoothed using a 5-minute rolling-

window median filter to minimise the amount of noise broadcast.

Once the data has been gathered, a grid of ASF values is created from the raw

data.

• These gridded values can be interpolated between nearby cells for

smooth cell transitions.

• An Inverse-Interpolation algorithm is used to create the grid suitable for

this Interpolation method.


• This algorithm is bounded by ‘sensible’ data-points to keep the grid

values plausible.

The final grid, once produced can be assessed using two parameters.

• The residuals of the raw data from the grid indicate how well it fits the

data, and can indicate where additional measurements need to be made.

• The ‘geometry’ of the Inversion technique indicates how reliable the

value on each ASF grid vertex is. ‘Poor’ geometry indicates low accuracy

in the gridded values.

It has been proposed that a single ASF grid error-statistic be produced from

these two quality indicators, preferably relating the quality of the ASF data to an

error-bound or Integrity indicator.

4.4 GLA eLoran Position-Solution Algorithm

The true test of an ASF grid is when it is used to generate ASF-corrected

position solutions in an eLoran receiver. If a repeat sailing through the survey

area is performed, gathering Loran time-of-arrival (TOA) data, then ASF-

corrected eLoran position solutions can be generated. The closeness of these

fixes to the DGPS ‘ground-truth’ indicates how well eLoran is performing, and

indicates the quality of the ASF data gathered.

As mentioned earlier (Section 4.3 – Basic Grid) current eLoran receivers offer

limited support for uploading an ASF grid, and offer no method of performing

post-mission processing to assess the quality of different ASF grids. For this

reason the candidate has written an eLoran positioning-solution algorithm for

the GLAs’ use. The purpose of this algorithm is to take measured TOA data

from a receiver operating without ASF data, to apply ASF and differential

corrections, and re-compute the Loran fixes.

The algorithm is based on a GPS-like pseudo-range solution of all available

TOA measurements using Least-Squares; this solution is iterated to arrive at a

‘best’ eLoran fix. The operation of the algorithm is described next.


An Assumed Position (AP) or seed position (x0, y0) is used as a first guess

about the location of the receiver. From this position, the pseudo-range

measurements to each Loran transmitter are calculated, the pseudo-range

equation for the “ith” transmitter is given as the expected TOA at the AP:

( ) PFi i i i i i

nTOA SF D D ASF vc

δ ε= + ⋅ + + + + (1.40)

Di is the arc distance along a great circle path from the AP to the transmitter,

with Primary and Secondary factor corrections applied as in (1.6). The ASF

value is obtained from the ASF grid by interpolation at the AP (1.29); δi is the

differential correction received over Eurofix;ε is the unknown clock-offset and

iv is the residual, also unknown.

The arc distance calculation and the Brunavs SF correction are not linear in the

parameters of Longitude (x) and Latitude (y), so for least-squares the equation

has to be linearised using a Taylor expansion.

( ) ( )sin cosPF PFi i i i

n nTOA T dx dy ASF vc c

α α δ ε= + ⋅ + ⋅ + + + + (1.41)

Where Ti is the expected (PF and SF corrected) TOA at the AP and αi is the

bearing to the ith transmitter. The linearised observation equation for least-

squares is thus given by:

( ) ( )sin cosPFi i i i

PF

n cTOA T ASF dx dy d vc n

δ α α ε

− − − = ⋅ + ⋅ + ⋅ +

(1.42)

The design matrix (A) is composed of bearing sines and cosines, the scale

factor in the clock-offset (3rd) column has been removed to keep the scaling of A

reasonable to help with the matrix-inversion later.


( ) ( )

( ) ( )

1 2sin cos 1

sin cos 1n n

Aα α

α α

=

(1.43)

The observation vector is given by:

1 1 1 1

n n n n

TOA T ASFb

TOA T ASF

δ

δ

− − − = − − −

(1.44)

The Least-Squares solution is given by:

( ) 1T Tz A W A A W b−

= ⋅ ⋅ ⋅ ⋅ ⋅ (1.45)

The weighting matrix W that is used is based on the SNR of each signal. The

strongest station is given a weighting of 1, and each additional station is

weighted according to (1.46):

2010iSNR S

iiW−

= (1.46)

Here S is the SNR of the strongest station. The solution z consists of updates to

the assumed position ( dx , dy ) and clock offset (ε ):

1 PF

PF

n dxz n dy

cc dε

⋅ = ⋅ ⋅

(1.47)

The assumed position ( )00 , yx is updated by the increment ( dx , dy ), and the

process is repeated. A check is performed, and if the new update is less than

1mm, then no further iterations are considered necessary, and the algorithm

outputs its position.


The accuracy of the derived eLoran position-solution can be calculated by

comparing the fixes to the DGPS ground-truth. To do this requires aligning the

eLoran and DGPS fixes in time so that their geographical separation can be

calculated. It is possible to derive a UTC time-stamp for each eLoran fix in a

number of ways. Using the ASF measurement unit, accurate Loran-to-GPS

synchronisation data is available to provide a UTC timestamp. The LORADD

unit, when used as a stand-alone receiver, will also produce adequate Loran-

derived UTC synchronisation information.

This is the basis of the GLA eLoran accuracy-assessment, and forms the core

part of our eLoran trials. The next chapter will discuss the candidate’s own suite

of custom-written software, which has been designed to oversee eLoran trials

and perform the calculations described.


5 GLA eLoran Survey Software

To aid in the data acquisition and processing described in Chapter 4, a suite of

software has been written for the GLAs by the candidate. One of the purposes

of this software is to remove the data-processing overhead, which typically

accompanies an eLoran trial. The functioning of this software is split into two

Modes: ‘Survey’; and ‘Validation’, and these are described below. The GLA

survey of the Orkney Islands is used as a demonstration of how the software

may be employed to achieve high-accuracy eLoran positioning whilst navigating

a harbour approach channel.

5.1 Survey Mode

The purpose of Survey Mode is to oversee the gathering and processing of raw

ASF data during a harbour survey. While the survey is in operation the software

performs the following functions automatically:

• The NMEA navigation data from the LORADD receiver is read in over the

ASF-unit’s serial-port and the appropriate data-fields are parsed into the

software’s data-arrays

• A text-file log of all the raw data is maintained as an additional record of

the survey

• ASF data is corrected for the local clock drift, using the data output by

the SRO controller, as shown in Figure 4-8

• The differential-corrections that are received over Eurofix are applied to

remove the temporal variations in ASF, as described in Section 4.2.2

• GPS-derived data and Loran-derived data are synchronised to a

common time frame (UTC) to aid processing and comparison of the two

navigation systems

• The appropriate data-arrays can be displayed on-screen in the form of a

simple Geographical Information System (GIS), as shown below in

Figure 5-1.


Figure 5-1 – GLA ASF Measurement software, running in Survey Mode, showing ASF data gathered for the Anthorn station in the Orkney Islands.

The software provides a Graphical User Interface (GUI) for ease of use. When

plotting data the display shows:

• Vector coastline data for the UK and Ireland (the Orkney Islands are

shown in Figure 5-1)

• The GPS track of the user’s vessel

• The current data-layer, as selected by the user (the coloured markers

represent ASF for the Anthorn signal 6731Y in Figure 5-1)

The control-panel allows the user to alter the view:

• To zoom in or out of the display (shown below in Figure 5-2)

• To scroll to different locations

• Or to snap-back to the vessel’s current location


To the right hand side of Figure 5-1 is the data-layer control, which allows the

selection of:

• Tracks of the user’s position, either GPS, eLoran (see Figure 5-2) or the

location of surveyed ASF points

• eLoran signal-specific data to be shown, such as: ASF; signal-to-noise

ratio (SNR); time-of-arrival measurements (TOA)

• A user may select which of the 14 northwest European signals’ data to

display

• Alternatively the Loran positioning error relative to DGPS (see Figure

5-2) can be shown

• The colour-scale maximum (red) and minimum (blue) can be tailored to

suit the data displayed

Figure 5-2 – Close-up of non-ASF Loran fixes sailing out of Kirkwall Harbour, colour-coded according to position accuracy. Note that without ASF corrections, 300m position errors are present and the plot seems to

show that the ship has sailed over an island!


In addition to this automatic functionality, the ‘Survey Mode’ is also used to

generate an ASF map. Clicking the ‘Create ASF Map’ icon takes all the current

ASF data and compiles an ASF grid, as described in Section 4.3

• The grid-lines of Latitude and Longitude are generated at 500m spacing

• A Basic Grid is formed to generate a ‘sensible’ ASF map (as Figure 4-11)

• The ‘sensible’ map points are extrapolated and added to the raw data to

provide the observation data to be fed into the Reverse Interpolation

algorithm.

• An Interpolated Map is produced and displayed on-screen (Figure 5-3)

• This is repeated for each transmitter in turn. The resulting maps are

compiled into a single ASCII file suitable to be uploaded into an eLoran

receiver

• Finally, the ‘Geometry’ (Figure 4-22) and ‘Residuals’ (Figure 4-23) error-

statistics are produced and displayed on-screen as an early assessment

of the ASF grid quality (see Figure 5-3)


Figure 5-3 – Survey software with the ASF Map and Interpolation Geometry windows open.

If the grid quality is not considered sufficient at this stage, then the survey may

continue. If the ASF grid is of a reasonable standard then the Survey is over

and the user may then switch the software into Validation Mode for checking the

accuracy and integrity of the grid.

5.2 Validation Mode

Validation Mode is used to assess the quality of a previously surveyed ASF

grid. The appearance and function of the software remains similar to the Survey

Mode, however, the previously surveyed ASF grid can be displayed on-screen

as an additional GIS data-layer (Figure 5-4).


Figure 5-4 - GLA ASF Measurement software running in Validation Mode. The previously surveyed ASF grid is shown as spot-values across the

harbour area.

Validation Mode allows an assessment of Loran accuracy by comparing the

receiver’s Loran position solutions against the DGPS ground-truth position

solutions. Using the receiver’s time-tagging capability, as described in Section

3.5 and illustrated in Figure 3-5, the Loran and GPS fixes can be aligned in time

and their geographical separation calculated. The fixes shown in Figure 5-2,

generated without ASF corrections demonstrate large positioning errors.


Figure 5-5 – Error statistics for non-ASF Loran positioning as a scatter-plot and Cumulative-Distribution Function (CDF), generated by the Survey

software in Validation Mode

The software also generates its own eLoran position fixes using the GLA

algorithm as described in Section 4.4. ASF data from the surveyed grid and

real-time differential corrections are applied to the raw TOA data and a track of

ASF-corrected eLoran fixes is generated. These fixes can also be plotted on-

screen as in Figure 5-6 below.


Figure 5-6 –Software running in Validation Mode showing a track of ASF-corrected eLoran fixes sailing out of Kirkwall Harbour. Note that with ASF corrections applied the ship does not appear to cut across the land as it

did in Figure 5-2!

In addition, the eLoran position-solutions generated may be converted into

‘synthetic’ NMEA $GPGGA sentences to simulate the output from a

conventional GPS receiver. The eLoran fixes may be output to a serial-port and

fed into an external ECDIS or Chart Plotter, that is expecting a GPS input. This

allows the PC running the software to function as an eLoran receiver in real-

time, and interact with other navigation equipment.

This technique was used during the GPS Jamming demonstration performed by

the GLAs in December 2009. The eLoran output was fed to PC based chart-

plotter software, which had been specially modified for the GLAs by the

software provider to enable it to accept two simultaneous inputs. When the

jamming signal was operated the LORADD continued to produce eLoran fixes,

and so a charted position was maintained when GPS was lost. This is shown in

Figure 5-8, which is repeated from [1].


Figure 5-7 – Log file of position-fixes, which was generated by converting eLoran fixes into NMEA $GPGGA sentences.

Figure 5-8 – Screenshot of chart-plotting software driven by $GPGGA data-streams from two receivers.


In Figure 5-8 the blue ship icon represents an erroneous position from a GPS

receiver under jamming conditions, and the length of the velocity vector

indicates many hundreds of knots! The green circle represents a live feed of the

eLoran position showing the correct location. The red hashed area is the GPS-

Jamming exclusion zone set up to warn mariners of the Jamming signal.

Figure 5-9 – Accuracy scatter-plot and CDF for the track of eLoran fixes shown in Figure 5-6, generated by the software’s Validation Mode.

The Validation software also computes and displays positioning-accuracy

statistics used to assess the quality of the eLoran fixes it generates.

The error-statistics in Figure 5-9 demonstrate that it was possible to attain sub-

10m accuracy from eLoran when entering Kirkwall Harbour in the Orkneys.

However, this level of accuracy has only been attained by correctly calibrating

out all of the spatial and temporal variations in signal-propagation delay using

ASFs and differential-Loran as defined for eLoran maritime navigation in such

regions.


6 Summary and Conclusions

This chapter briefly summarises the work presented in this dissertation and the

conclusions that may be drawn. The potential for future work is also identified.

6.1 Summary This dissertation reports on the work undertaken by the candidate as part of the

General Lighthouse Authorities’ work on ASF Measurement and Processing

best Practice. Users of eLoran require high-quality ASF data in order to obtain

the highest levels of accuracy from the system. The work presented here is the

current state of the art in ASF measurement and processing performed by the

GLA, to ensure that the ASF data they provide is of the highest quality.

The candidate has written a suite of measurement and processing software

which acts to oversee the surveying of ASFs. This software incorporates a

number of novel error-mitigation techniques including the real-time processing

of differential corrections, received over Eurofix. This software also acts to

create a database of ASF values in a gridded format suitable to be uploaded

into a user’s receiver. This dissertation details the work done in this regard in

developing a gridding algorithm that was first used in the USA. This algorithm

has been modified to improve the quality of its output, and also to produce a

number of validity-checks. These checks are used to monitor the progress of

the ongoing survey and will ultimately be incorporated into the published ASF

databases to inform the user of the data’s accuracy and reliability.

In addition, the candidate has written a stand-alone eLoran positioning-solution

algorithm. This takes measured Time-of-Arrival measurements; differential

corrections; and an ASF database and outputs a position in WGS’84 Latitude

and Longitude. In line with the definition of eLoran, this solution is arrived at by

‘all-in-view’ pseudo-ranging, using a Least-Squares technique. This positioning

solution is incorporated in the survey software’s Validation Mode and has been

used to demonstrate eLoran at 10m (95%) accuracy.

6.2 Conclusions - ASF Measurement Technique

By performing a comprehensive breakdown of the ASF measurement process,

we have been able to analyse the sources of errors seen in the raw data output


by the GLAs ASF measuring unit. An error-budget has been draw up, in

particular the following have been indentified as the key causes of ASF

measurement error:

• TOA measurement noise, this is dependent on SNR and is typically 15-

30ns

• Temporal variations in ASF, including variations in TOE at the Loran

transmitter

• The quality and stability of the local realisation of UTC

By focusing on the causes of these particular sources of error, an ASF

measurement Best Practice has been drawn up. The GLAs measurement

technique includes mitigating or minimising these errors in the following ways.

• Temporal corrections are removed in real-time during a survey by

making use of a differential reference station broadcasting ASF

corrections on the Loran Data Channel. This technique accounts for

changes in ASF; PF; and variations in the Loran transmitter’s TOE.

• The de-synchronisation of the local oscillator is accounted for by applying

the reported clock-offset as a correction to the ASF measurements. This

accounts for any bias errors without adding extra measurement noise.

Accurate and stable ASF measurements have been made using this technique,

and the GLA are now confident that their methods are reliable. Future work has

been identified to guarantee the GLA methods are truly Best Practice, in

particular the development of an ‘ideal’ filter used to generate differential-Loran

corrections will ensure that any noise broadcast is kept to an absolute minimum.

6.3 Conclusions - ASF Gridding Technique

We have looked at the ‘Basic’ ASF gridding technique, which assigns a value to

each cell within the grid by averaging all of the measured data that lies within

that cell. This technique is believed to be sub-optimal as it fails to account for

two features of the ASF data:


• ASF is a phenomenon which varies depending on position. The Basic

grid represents this variation quite poorly as it does not account for

spatial variations within each grid-cell.

• This variation is a smooth function of position, rapid or sharp fluctuations

in ASF are rare. The Basic grid creates discontinuities at the cell

boundaries which can lead to sudden ‘jumps’ in a users’ apparent

position.

The candidate has taken a Grid Interpolation technique first developed in the

US and has applied it to the GLAs measured data. This technique has been

found to be favourable to the Basic grid as it describes ASF variations using a

continuous ‘surface’ rather than spot-heights. This ‘surface’ accounts for the

continuous spatial variations seen in raw ASF data and also provides smooth

transitions from one cell to the next. However, the Interpolation technique has

been observed to introduce issues of its own, in particular:

• A more mathematically involved method is required to generate an ASF

grid from raw measurements, and this method requires a lot of computer

processing.

• Excessively large or unreasonable grid values can often arise from the

production of an Interpolated Grid. These values are not due to

measurement error but are intrinsic to the mathematical process used.

A novel technique to bound of these unreasonable grid values has been

developed, and allows the grid production to be fully automated. Additional

modifications by the candidate include the production of several validity-checks

which can be used mid-survey to validate the data-collection and grid-

production process. These checks have proved useful, and it is recommended

that future work should include the creation of a single error-statistic to make

use of all the GLAs knowledge of ASF measurement and processing. This

error-statistic could take the form of a data-integrity check or Horizontal-

Protection-Level, to relate the ASF grid quality to the expected level of Accuracy

and Integrity that the ASF data can guarantee to an eLoran fix.

This is the ultimate aim of the work: To guarantee that the GLAs can deliver an

eLoran service which meets or exceeds the user’s requirements for Accuracy,

Availability, Continuity and Integrity. The work done so far indicates that we can.


References

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