CORS and a Future Geodetic Framework for

Western Australia

Technical Documentation

July 2006

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Table of Contents

List of acronyms 3 Scope of this document 4 1. Assessment of accuracy of online static positioning services in a global context 6 1.1 Introduction 6 1.2 Issues with existing online GPS processing services 8 1.3 Nature of this study 9 1.4 Online GPS processing services freely available in 2006 9 1.5 Data and analysis methodology 12 1.6 Results 14 1.6.1 24 hour observation period 14 1.6.1.1 Pre-analysis 14 1.6.1.2 Coordinate repeatability at individual stations for solutions from individual processing centres 16 1.6.1.3 Coordinate accuracy at individual stations for solutions from individual processing centres 19 1.6.1.4 Comparison of solutions from different processing centres 21 1.6.2 6 hour observation period 22 1.6.2.1 Pre-analysis 22 1.6.2.2 Coordinate repeatability at individual stations for solutions from individual processing centres 23 1.6.2.3 Coordinate accuracy at individual stations for solutions from individual processing centres 23 1.6.2.4 Comparison of solutions from different processing centres 26 1.7 Discussion 26 1.8 References 28

2. Assessment of accuracy of online static positioning services in a Western Australian context 29 2.1 Introduction 29 2.2 Data and analysis 29 2.3 Results 30 2.3.1 Western Australian IGS stations 30 2.3.2 SWSZ stations 31 2.4 Discussion and conclusions 31

3. Assessment of online products for kinematic positioning applications 39 3.1 Introduction 39 3.2 Data and analysis methodology 39 3.3 Results 40 3.3.1 IGS data 40 3.3.2 Norwegian Data 41 3.3.3 Australian Data 42 3.4 Summary and Conclusions 42 3.5 Acknowledgments 43 3.6 References 43

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4. Assessment of the accuracy of the OmniSTAR Pty Ltd service in Western Australia 48 4.1 Introduction 48 4.2 Data and processing 48 4.3 Results 50 4.4 Discussion 51 4.5 References 51 4.6 Acknowledgment 51 5. Design, simulation and assessment of CORS networks for static positioning in Western Australia 55 5.1 Introduction 55 5.2 Design Parameters – theoretical background 55 5.3 References 56

6. Design, simulation and assessment of CORS networks for RTK positioning in Western Australia 57 6.1 Introduction 57 6.2 Optimal CORS network design parameters for RTK 58 6.3 Theoretical background 60 6.3.1 Internal reliability 60 6.3.2 Ambiguity Success Rate (AS) 60 6.4 References/Further reading 62

7. Impact assessment of an enhanced Western Australian CORS network on regional orbital products 64 7.1 Introduction 64 7.2 Design parameters 64 7.3 Simulations 65 7.4 Results 67 7.5 Discussion 67 8. Simulation software 80

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List of acronyms AUSPOS GA automated web-based positioning service CORS Continuously Operating Reference Station CSRS Canadian Spatial Reference System CSRS-PP Canadian Spatial Reference System Precise Point Positioning service DGPS Differential GPS DLI Department of Land Information, Western Australia GA Geoscience Australia GDA Geocentric Datum of Australia GNSS Global Navigation Satellite Systems GPS Global Positioning System IERS International Earth Rotation Service IGS International GNSS Service ITRF International Terrestrial Reference Frame JPL Jet Propulsion Laboratory NOAA National Oceanographic & Atmospheric Administration, USA NRTK Network Real Time Kinematic GPS OPUS On-line Positioning User Service (USA system) OSI Ordnance Survey Ireland PDOP Position Dilution of Precision PPP Precise Point Positioning RINEX Receiver Independent Exchange format – for exchange of GNSS data RTK Real Time Kinematic SWSZ South West Seismic Zone VRS Virtual Reference Station WADGPS Wide Area Differential GPS

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Scope of this document

This document provides a summary of the data, methodology and analysis undertaken as part

of the workplan detailed in the Proposed Technical Study document on ‘CORS and a Future

Geodetic Framework for Western Australia’ and should be read as an accompanying document

to the final report from that Technical Study.

The Proposed Technical Study was developed under the following Terms of Reference (TOR),

in order to develop a future strategy for GPS CORS networks in Western Australia:

1. What CORS options are currently available and how good are they for Western

Australia?

2. What are the uses of CORS technology beyond geodetic and survey control?

3. What is the required absolute and relative accuracy for a Western Australian CORS

network now and in the future?

4. What is the likely impact of GPS modernisation, Galileo and GLONASS on CORS

technology and how would this relate in a Western Australian context?

5. Should DLI wish to proceed with a trial CORS network in the Perth metropolitan area,

how should that trial be designed to maximise benefit to DLI in future decision

making?

The research undertaken within the constraints of the TOR comprised seven separate studies:

1. Assessment of accuracy of online static positioning services in a global context which

encompasses TOR 1 and contributes to Section 2.1.1.1 of the main report;

2. Assessment of accuracy of online static positioning services in a Western Australian context

which encompasses TORs 1 and 3 and contributes to Section 2.1.1.1 of the main report;

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3. Assessment of online products for kinematic positioning applications which encompasses

TOR 2 and contributes to Section 3.2 of the main report;

4. Assessment of the accuracy of the OmniSTAR Pty Ltd service in Western Australia which

encompasses TORs 1, 2 and 3 and contributes to Section 2.1.3 of the main report;

5. Design, simulation and assessment of CORS networks for static positioning in Western

Australia which encompasses TORs 1, 2, 3 and 4 and contributes to Sections 2.1 and 5.7 of

the main report;

6. Design, simulation and assessment of CORS networks for RTK positioning in Western

Australia which encompasses TORs 1, 2, 3 and 4 and contributes to Sections 3.3 and 5.8 of

the main report;

7. Impact assessment of an enhanced Western Australian CORS network on regional orbital

products which encompasses TORs 2 and 4and contributes to Sections 2.1 and 5.7.4 of the

main report;

The final section of this report provides a description of the simulation software developed as

part of this project and its operation.

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1. Assessment of accuracy of online static positioning services in a global

context

1.1 Introduction

The advent of online GPS processing services over the past decade has been possible due to

the increasing availability of GPS data through global, regional and national Continuously

Operating Reference Station (CORS) networks, and to the free availability of the associated

geodetic products (eg precise orbits, earth orientation parameters, satellite clock information,

regional atmospheric products) required to deliver such services.

Online GPS processing services are free and can greatly simplify the process of realising high

precision coordinates in a recognized (eg International Terrestrial Reference Frame (ITRF))

datum. Indeed, it is now possible for a user with a dual frequency geodetic GPS receiver to

compute high precision ITRF coordinates for any point on Earth by observing just a few hours

of data and having a good internet connection.

Online processing represents a paradigm shift compared to traditional GPS processing

methodology for realisation of high precision coordinates which places substantially more

emphasis on the users themselves. The traditional technique involves users setting up a

reference GPS receiver on a ground mark whose coordinates were known a priori and

observing a GPS baseline formed by setting up a second receiver at an unknown position.

Often, for quality control purposes, a geodetic network is formed, comprising a number of

known and unknown points, connected by a number of baselines. The network design would

be the responsibility of the user, as would the processing and analysis of the GPS data

constituting the baselines and the network adjustment to compute the final coordinates and

their associated precision and accuracy.

Modern CORS networks remove the issue of network design from the user’s domain. Instead,

data from permanent GPS networks are available, thus enabling a user to simply add in an

unknown point to the existing network. From an operational point of view, this approach

represents a significant saving in time and costs to the user. The need for a second ‘reference’

receiver is eliminated, as is the necessity of physically occupying a wide array of reference

marks, greatly reducing the time required to collect sufficient data to compute accurate

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coordinates in the required datum. Essentially, all the relevant information is pre-supplied by

the CORS network.

Prior to 1999, notwithstanding the increasing availability of GPS data from CORS networks,

the onus was still on users to process data themselves. The complexity of GPS data processing

and analysis, particularly for baselines longer than 10-20 km, which was the maximum length

of baselines for commercial processing software packages to operate reliably, meant that

longer baseline processing was the domain of those users familiar with and with access to the

so-called ‘scientific’ GPS processing software packages (eg Bernese, Gamit, GIPSY). The

advanced models and processing techniques applied by these packages enabled processing of

baselines of hundreds or even thousands of kilometers in length in large geodetic networks.

Unfortunately, since CORS receivers were often greater than 20km from a user, high precision

positioning using CORS data was not generally available to the non-scientific user.

Since 1999, a number of developments have made CORS technology more accessible. First,

commercial processing software have incorporated many of the models and techniques

pioneered in the scientific packages, thus enabling longer baseline processing and allowing a

user to form much longer baselines to CORS sites than was previously possible. Second, the

global densification of CORS networks has resulted in the number of regions covered by dense

CORS networks greatly increasing. The combination of these two developments has meant that

it is now much easier for users (in some regions) to make use of CORS data in conjunction

with commercial GPS processing software for high precision datum realization. However, in

this case, data processing is still the responsibility of the user, which represents a time and

manpower overhead. A third development, that of online processing services based on

scientific software packages, has provided users with the opportunity to completely unburden

themselves of a requirement for any GPS processing capability.

The principle of online GPS processing services is straightforward. A user uploads a data file

(typically in RINEX format) to a processing server which is running a scientific GPS data

processing package. This package has access to data from the International GNSS Service

(IGS) global network of GPS CORS receivers (and possibly data from other GPS CORS

receivers) and IGS products (eg satellite clock files, precise ephemeris etc), combining this

information with the uploaded user data to compute a coordinate solution for the user’s

unknown point. Results and some quality control indicators are returned to the user by email.

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The ease with which users can collect and process data to realise high precision GPS

coordinates in ITRF (or some other local datum) represents a major contribution to the transfer

of positioning technology from the scientific to the broader community. Currently, there are

some limitations. Online systems require at least 1 hour (in some cases more) of input GPS

data, solution quality can be compromised by the speed in which IGS products are available

and internet connection and server processing speed can delay the speed at which results are

returned to the user. However, such limitations will be overcome with next generation

hardware and processing software. It is conceivable that near real-time high precision online

processing will become available over the next decade. Such services are likely to become the

mainstay of geodetic infrastructure, both nationally and internationally, well into the 21st

century.

1.2 Issues with existing online GPS processing services

The convenience and perceived reliability of online processing services has led to their

increasing use within the positioning industry. Today, most national geodetic datums are

realisations, in some way, of ITRF. Online processing services provide users with a method of

quickly realising ITRF coordinates without recourse to nationally maintained geodetic ground

marks, nor, in some situations, even national or regional densifications of CORS networks.

Therefore, by definition, online GPS processing services to some extent circumvent national

controls and standards for datum realisation. Therefore, national survey organizations are faced

with the prospect of users deriving their own coordinates in ITRF (or more precisely in one

realisation of ITRF represented by the sub-network of CORS sites chosen by the online

processing service) and using their coordinates and transformation parameters to define

position in the national geodetic datum.

Such a situation would be acceptable, indeed, preferable, if online processing services were

regulated to some standard and the solutions provided represented some form of guaranteed

quality. Unfortunately, with the current technology, this is not the case. Whilst online

processing services use processing software derived from similar mathematical algorithms and

models, these can differ significantly in application and particularly in quality control

procedures, often computing different results for the same data sets. Furthermore, services

differ in the amount of output quality control information they supply to the user. Finally, and

perhaps most significantly, all services are dependent on the quality of the data supplied to

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them by the user. By their very nature, online GPS processing services emphasise the long held

belief amongst many positioning professionals that GPS is a black box technology.

Interpretation of feedback from online processing services still requires expert knowledge in

GPS data analysis. Therefore the situation has arisen that anyone with a GPS receiver and an

internet connection can send data to online processing services and receive a result. However,

whether or not that result is acceptable requires a user to be much more discerning.

1.3 Nature of this study

This study aims to assess the four globally available online GPS processing services from the

point of view of a user or organisation wishing to make use of such a service for datum

realization on a regular basis. Similar comparison studies have been conducted previously,

most notably by Ghoddousi-Fard and Dare (2005). Previous studies have, however, been

somewhat limited in the amount of data analysed (for example Ghoddousi-Fard and Dare

(ibid.) analyse only a single day of data). This is not, perhaps, unsurprising, given the time

required to upload data files to different online processing services some of which do not offer

batch processing services as yet, but has not allowed a statistically significant comparison

analysis to be performed. This study attempts to address this point to some extent.

Section 1.4 describes each of the four services, including detailed information on the expected

accuracies supplied by the operators of these services, their operational constraints and

differences in the processing algorithms and models used. Section 1.5 describes the data

analysed and methodology used for this study whilst section 1.6 presents results in terms of

quality control indicators and solution reliability. Results are discussed and some conclusions

drawn in section 1.7.

1.4 Online GPS processing services freely available in 2006

At the time of writing five online GPS processing services are freely available to users over the

internet, four of which, AUSPOS, Auto-GIPSY, SCOUT and CSRS-PPP are considered in this

study. The fifth service, OPUS, is available solely in North America and will be considered

only in the context of the results from a recently published study by Soler et al (2006).

Three of the five services are operated by government organisations responsible for national

datum definition and realisation and are offered to users as part of the remit of these

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organisations in supporting spatial infrastructure on a national basis. AUSPOS is operated by

Geoscience Australia (Dawson et al, 2002), formerly the Australian Land Information Group

(AUSLIG); CSRS-PPP is operated by the Geodetic Survey Division of Natural Resources

Canada as part of the Canadian Spatial Reference System (CSRS); OPUS (On-line Positioning

Users Service) is run by the National Geodetic Survey, which is a programme office of the

National Oceanic and Atmospheric Administration (NOAA) of the United States. The

remaining two processing services, SCOUT, operated by Scripps Orbit and Permanent Array

Centre, and Auto-GIPSY, operated by JPL (Jet Propulsion Laboratory) are run by scientific

research organisations in the United States. As a result, SCOUT and Auto-GIPSY offer

coordinate results in ITRF whilst AUSPOS, CSRS-PPP and OPUS also supply users with

coordinates in the national geodetic reference frame, that is, GDA (Geocentric Datum of

Australia) 94 for Australia and NAD (North American Datum) 83 for Canada and the United

States.

The processing services themselves have much in common in terms of user data input and

interface (data are uploaded to a central server in RINEX format) and in the way information is

supplied back to the user, in the form of emails or report files. Detailed information on these

systems is widely available (eg Ghoddousi-Fard and Dare, 2006; Soler et al (2006) and the

websites of the systems themselves) and therefore this section will highlight some of the more

notable differences only.

All five services use processing engines based on different ‘scientific’ geodetic GPS data

processing packages. AUSPOS uses MICROCOSM (Martin, 2000), although it is soon to be

changed to Bernese (Hugentobler et al 2001); SCOUT uses GAMIT (King and Bock, 2005);

auto-GIPSY uses GIPSY (Zumberge et al, 1997) ; OPUS uses PAGES1 and CRC-PPP uses the

in-house NRCan-PPP software (Heroux et al 1993, 2001). Whilst all geodetic GPS processing

software packages are based on the same fundamental mathematical principles, they tend to

differ substantially in their application. Such differences can occur at the base processor level,

at the modeling level and in data quality control and rejection algorithms. For example, NRCan

PPP and auto-GIPSY use precise point positioning methods (eg Kouba and Heroux, 2001),

which do not require definition of reference stations and baselines, whilst the other processing

softwares use the traditional baseline processing approach (eg Teunissen and Kleusberg,

1996); at the modeling level whilst most geodetic processing software apply IERS standards,

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local variations do occur, such as the non-applications of ocean tide loading models in the

current AUSPOS service. The net result is that whilst different processing services make use

of the same IERS standards and IGS products, output coordinates can often differ. Furthermore

the quality control information supplied to the user varies between services. Therefore, for

practical purposes, it is important to quantify not only the internal repeatability of individual

services, but also the agreement in results between services when asked to process identical

data.

Clearly, the quality of output from online GPS processing services is highly dependent on the

quality of the data supplied to a service by the user. GPS data can vary greatly in quality, due

to the myriad of errors which can contaminate the phase and pseudorange observations, from

local site variations which result in the presence of increased multipath error, to regional

ionospheric and tropospheric disturbances. Additionally, the length of data span observed

remains critical for high accuracy geodetic positioning. Since many of these factors are outside

the control of processing service providers, it is necessary for providers to be deliberately

vague about the likely quality of the results achievable with their service. For example,

statements on the auto-GIPSY website (http://milhouse.jpl.nasa.gov/ag/agfaq.html) “you could

expect daily repeatabilities of a few mm in horizontal components and about a cm in the

vertical for data from a stationary site with a geodetic-quality receiver” (emphasis added) and

the AUSPOS website (http://www.ga.gov.au/geodesy/sgc/wwwgps/faq1.jsp) “Typically, a

good quality geodetic receiver and antenna, with 24 hours of data using the IGS final orbit

product, should give results to better than 10mm horizontally and 10-20mm in the vertical”

(emphasis added) are typical of the accuracies quoted. Indeed, most service providers give

explicit disclaimers to emphasise that users use these services at their own risk. For example,

AUSPOS states: “Geoscience Australia does not warrant that this service a) is error free; b)

meets the customer’s requirements.” whilst CSRC-PPP does not claim “effectiveness,

completeness, accuracy, or fitness for a particular purpose.” for its service. In reality, it is

practically impossible for any service provider to provide a user with a realistic accuracy

estimate for a solution. Accuracy estimates for GPS reductions obtained by formal error

propagation are notoriously optimistic (http://www.ngs.noaa.gov/OPUS/Using_OPUS.html)

and although scaling of formal errors is routinely applied by geodetic processing software, the

resultant error estimates can only be treated as approximate indicators. See, for example,

1 http://www.ngs.noaa.gov/GRD/GPS/DOC/toc.html

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Kashani et al (2004) for a discussion of differences in the formal error treatment in the GAMIT

and Bernese processing packages.

The geodetic GPS processing packages which serve online processing services routinely

achieve centimetre-level accuracy or better when used for scientific processing. The quality of

results from online processing services therefore depends predominantly on the quality of the

data and receiver information (eg antenna type) supplied by the user, the length of the

observation span of data supplied by the user and, for the baseline dependent software, the

proximity of the unknown site to CORS stations used by that service. From an operational

point of view, users prefer to observe shorter spans of data. However, users usually would like

to think of their output coordinates as being accurate. Therefore, it is beneficial to test the

accuracy of online processing services, inter-compare these services and to test them with

various input observation data spans. The study presented subsequently provides such an

analysis.

1.5 Data and analysis methodology

Six IGS stations were selected to provide a balanced geographical sample, in terms of latitude

and distance from nearby reference stations (figure 1.1). Two stations, KELY and MAW1, are

situated at high latitudes in the northern and southern hemispheres respectively; two stations,

MALI and DARW are situated at equatorial latitudes; and two stations, MATE and SANT are

situated at mid-latitudes in the northern and southern hemispheres respectively. Stations were

also selected such that they had identical antenna types.

The main restrictions on this type of study are the limitations on batch processing imposed on

users by processing centres. Therefore, processing a statistically significant number of station

solutions can be a laborious and time consuming process. Initially, 31 days of data observed

between Julian days 095 to 125 in 2004 (in the form of 186 24 hour RINEX files) were

submitted to each processing service for each station. Therefore, 186 coordinate solutions

were available from the 24 hour observation sessions at the six stations for each processing

service, resulting in a total of 744 solutions.

Each 24 hour file of RINEX data from each station was subsequently split into 4 non-

overlapping 6 hour segments. The resultant 576 files were resubmitted to AUSPOS, auto-

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GIPSY and CSRS-PPP, giving a total 2232 coordinate solutions. Unfortunately, some

problems were experienced at the time with uploading data to SCOUT and therefore no results

are available from 6 hour sessions for that processing service.

Analysis comprised (for 24 hour and 6 hour data sets):

1) Solution rejection based on formal coordinate errors supplied by processing centres;

2) Coordinate repeatability at individual stations for solutions from individual processing

centres;

3) Coordinate accuracy at individual stations for solutions from individual processing

centres (ie comparison of solutions with known IGS ITRF2000 station coordinates at

epoch of observation);

4) Comparison of solutions from different processing centres.

Finally, a comparison of statistics from the 24 and 6 hour data sets was undertaken.

Figure 1.1 Six IGS stations used in the global online processing service study

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1.6 Results

1.6.1 24 hour observation period

1.6.1.1 Pre-analysis

Coordinate solutions (reduction for antenna height being applied where necessary) were

tabulated from each station for the processed solutions from each service. In addition, output

standard deviations of each coordinate component were recorded and the square root of the

sum of the squares of the standard deviations of each component (effectively the square root of

the trace of the covariance matrix of the estimated parameters and subsequently abbreviated to

SQTCV) was estimated for each solution. The mean SQTCV was estimated for each station

from the solutions from each processing service. Therefore, each station has 4 associated mean

SQTCV, tabulated in table 1.1. Additionally, a mean SQTCV was estimated for all 186

solutions from a particular processing service (SQTCVALL). It may be remarked that these

values, tabulated in table 1, vary between processing centres, with SCOUT having the highest

estimate (0.0153m) and CSRS-PPP the lowest (0.0083m).

AUSPOS x Auto-GIPSY x CSRS-PPP x SCOUT x

DARW 0.0112 0 0.0083 1 0.0074 0 0.0166 0

MALI 0.0074 0 0.0118 1 0.0091 2 0.0182 0

MAW1 0.0093 0 0.0095 1 0.0078 0 0.0125 0

KELY 0.0038 0 0.0079 13 0.0085 1 0.0137 0

MATE 0.0041 10 0.0083 2 0.0071 1 0.0106 0

SANT 0.0239 0 0.0081 0 0.0064 0 0.0202 0

SQTCVALL 0.0112 5.4 0.0120 9.7 0.0083 2.2 0.0153 0

Table 1.1 SQTCV (metres) at each of 6 stations computed by submitting 31 24 hour

observation files to each of the four processing services. Columns labelled ‘x’ represent the

number of solutions deleted. The final number in the ‘x’ columns is the % of solutions deleted

from all the solutions submitted to a particular processing centre.

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A number of solution outliers are apparent in the dataset and criteria are required to ascertain

as to where specific solutions should be accepted or rejected for subsequent analysis. With 31

solutions for each station and each processing service, is it straightforward to detect outliers in

the coordinate solutions visually. However, users of online processing services are unlikely to

process more than a few solutions at any one time for any particular station and have to rely on

the quality control indicators supplied in solution files to be able to detect serious errors.

Therefore, in this study, it was deemed that solutions could only be rejected if quality

indicators clearly indicated the presence of a problem. To apply the same quality control

measure to all processing services, solutions whose SQTCV was greater than three times the

SQTCVALL for a specific processing service were rejected. This approach simulates a user

having a general feeling from experience the magnitude of formal coordinates errors expected

from an acceptable solution from a positioning service. As can be seen from table 1.1 (and

highlighted by Kashani et al, 2004), SQTCVALL varies between processing services. The

number of solutions removed under the aforementioned criteria is given in table 1 and range

from 0 (SCOUT) to 9.7% (auto-GIPSY).

It is stressed that although the SQTCV values given in table 1.1 have units of metres, their

magnitude has little meaning in an absolute sense and hence may only be used to highlight the

differences in the estimation of statistical quality control indicators by different processing

services. For the same processing service, the SQTCV term can be used to provide some

relativity between station solutions. Therefore it can be deduced from table 1.1 that the

AUSPOS solutions for SANT are substantially more uncertain than the equivalent at KELY. A

similar conclusion may be drawn for SCOUT. It is interesting to note, however, that the

quality indicators from auto-GIPSY and CSRS-PPP solutions for SANT do not suggest that

solutions at that station are any worse than the other stations. Indeed, according to table 1.1,

the solutions at SANT for auto-GIPSY and CSRS-PPP should be marginally more reliable than

the solutions for the other stations.

The issue of how well the quality indicators supplied by online processing services provide a

real indication to a user of solution quality will be explored further in the following section.

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1.6.1.2 Coordinate repeatability at individual stations for solutions from individual

processing centres

Day to day coordinate repeatability is a good indicator of the true precision of the station

solutions from each individual processing centre. The standard deviation of the x, y and z

components were computed for the 31 solutions from each processing service at each station.

Solution outliers were removed prior to the analysis as per section 1.6.1.1.

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station Processing service σx (m) σy (m) σz (m)

DARW AUSPOS 0.0086 0.0248 0.0083

Auto-GIPSY 0.0387 0.0440 0.0145

CSRS-PPP 0.0072 0.0073 0.0030

SCOUT 0.0111 0.0095 0.0088

MALI AUSPOS 0.0162 0.0395 0.0166

Auto-GIPSY 0.0102 0.0090 0.0078

CSRS-PPP 0.0134 0.0125 0.0069

SCOUT 0.0514 0.0337 0.0232

MAW1 AUSPOS 0.0060 0.0115 0.0121

Auto-GIPSY 0.0067 0.0022 0.0052

CSRS-PPP 0.0040 0.0043 0.0072

SCOUT 0.0039 0.0029 0.0065

KELY AUSPOS 0.0083 0.0105 0.0268

Auto-GIPSY 0.0054 0.0038 0.0056

CSRS-PPP 0.0059 0.0096 0.0061

SCOUT 0.0069 0.0139 0.0101

MATE AUSPOS 0.0138 0.0062 0.0716

Auto-GIPSY 0.0048 0.0033 0.0060

CSRS-PPP 0.0229 0.0049 0.0044

SCOUT 0.0064 0.0058 0.0053

SANT AUSPOS 0.0126 0.0084 0.0049

Auto-GIPSY 0.0202 0.0679 0.0481

CSRS-PPP 0.0054 0.0053 0.0044

SCOUT 0.0093 0.0082 0.0054

Table 1.2 Day-to-day coordinate repeatability for solutions from each processing service for

each of the 6 stations.

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From table 1.2, it can be seen that, overall, coordinate repeatability is at the 1-2cm level, with

processing services often achieving sub-cm repeatability in all components. Some irregularities

are present throughout table 1.2. The largest repeatability, 7.16cm in the y component of the

AUSPOS solution at MATE, is somewhat surprising given that the other 3 processing services

give sub-cm repeatabilities (with the exception of the x component for CSRS-PPP). The same

can be said for the 6.79cm in the x component of the auto-GIPSY solution at SANT. On closer

inspection, this anomaly is caused by two outlying solutions in the auto-GIPSY SANT data set

which, however, could not be removed by the criteria set in section 1.6.1. Similarly, figure 1.2

shows how the formal error on the z coordinate from the AUSPOS solution at MATE does not

model the coordinate variation. Elsewhere, equatorial MALI is the noisiest station overall,

although auto-GIPSY solutions are at the cm level. The SCOUT solution at MALI is

significantly worse than the SCOUT solutions at all other stations. At DARW, the other

equatorial site, both AUSPOS and auto-GIPSY give relatively noisy results but SCOUT and,

even more so, CSRS-PPP give relatively good repeatabilities. Solutions from high-latitude

stations MAW1 and KELY are uniformly at the cm level or better, although the AUSPOS

solutions are slightly worse, whilst at mid-latitudes, MATE provides the worst CSRS-PPP

result (in the x component).

-0.1000

-0.0500

0.0000

0.0500

0.1000

0.1500

0.2000

100 105 110 115 120 125

julian day

met

res sigma z

z coordinate

Figure 1.2 Variation in z coordinate and formal error on the z coordinate for AUSPOS 24

hour solutions at MATE

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The overall impression gained from table 1.2 is a lack of uniformity between the solutions

from the different processing services. All performed at about the same level overall (and

generally slightly better than quoted precisions) although they do not perform consistently for

the six stations. It might be expected to find some correlation between solution quality at the

same station for different processing services, since a common factor for all solutions is that

the same GPS data sets were submitted for each station to each processing service. However,

this is not the case in table 1.2, which emphasises that while solutions are generally ‘good’ (ie

at the 1-2cm level), solutions can be much worse. Furthermore, in isolated instances it would

be difficult to estimate from the quality control information supplied by processing services

whether or not an individual solution was within this specification.

1.6.1.3 Coordinate accuracy at individual stations for solutions from individual

processing centres

Coordinate accuracy is somewhat more problematic for online processing services, being

directly dependent on the quality of the antenna information supplied by a user and the antenna

models applied by the processing engine. The means of all 31 final solution coordinates for

each station and each processing service (outlying solutions having been removed) were

compared with the station ITRF coordinates at epoch 2004.301, ie the central epoch of the 1

month data set. These results are displayed in table 1.3.

Given the uncertainties in ITRF coordinates and velocities and possible antenna and phase

centre issues, it is not unsurprising that the coordinates solutions shown in table 1.3 are

somewhat worse that the coordinate repeatabilities presented in table 1.2. Again, a lack of

consistency is noticeable between solutions from different centres. For example, CSRS-PPP

has the solution closest to the ITRF solution at SANT but the ‘worst’ solution at DARW,

whereas SCOUT has a relatively good solution at DARW but is somewhat farther from the

ITRF solution at SANT. Taking the entire 186 solution data set (with outliers removed), the

mean and standard deviations in relation to the ITRF coordinates in the x, y and z components

are -0.002 ± 0.024 m, 0.011 ± 0.037 and -0.009 ± 0.038 respectively. Therefore, it can be seen

that, in spite of local variations between solutions at different stations and processing services,

solutions are generally centred about the ITRF coordinates at the 2-4cm level.

20

station Processing service dx (m) dy (m) dz (m)

DARW AUSPOS -0.0283 0.0168 -0.0236

Auto-GIPSY 0.0275 -0.0417 -0.0027

CSRS-PPP 0.0554 -0.0731 0.0064

SCOUT 0.0202 -0.0114 0.0256

MALI AUSPOS -0.0138 0.0625 -0.0202

Auto-GIPSY -0.0097 0.0378 -0.0176

CSRS-PPP -0.0087 0.0353 -0.0137

SCOUT -0.0057 0.1175 0.0288

MAW1 AUSPOS -0.0079 -0.0224 0.0181

Auto-GIPSY 0.0052 -0.0006 -0.0399

CSRS-PPP -0.0093 -0.0244 0.0374

SCOUT -0.0283 0.0168 -0.0236

KELY AUSPOS 0.0275 -0.0417 -0.0027

Auto-GIPSY 0.0554 -0.0731 0.0064

CSRS-PPP 0.0202 -0.0114 0.0256

SCOUT -0.0138 0.0625 -0.0202

MATE AUSPOS -0.0097 0.0378 -0.0176

Auto-GIPSY -0.0087 0.0353 -0.0137

CSRS-PPP -0.0057 0.1175 0.0288

SCOUT -0.0079 -0.0224 0.0181

SANT AUSPOS 0.0052 -0.0006 -0.0399

Auto-GIPSY -0.0093 -0.0244 0.0374

CSRS-PPP 0.0119 -0.0104 -0.0044

SCOUT -0.0308 0.0233 -0.0710

Table 1.3 Coordinate accuracy relative to ITRF@ 2004.301 for solutions from each

processing service for each of the 6 stations.

21

1.6.1.4 Comparison of solutions from different processing centres.

Inter-processing service solutions are compared in two ways. First, the mean coordinate

repeatability, ie the mean of all components of the repeatabilities presented in table 1.2, was

computed from each solution of the 186 data sets submitted to each processing service. Again,

outlying solutions were omitted from the analysis. These values can be found in the second

column of table 1.4. Second, the mean and standard deviation of the differences between

solution coordinates and ITRF coordinates as presented in table 1.3 was computed from all

solutions and all coordinate components from each individual processing service. These values

are given in columns 3 and 4 of table 1.4.

Processing service Mean repeatability (m) Mean Accuracy (m) Standard dev (m)

AUSPOS 0.0170 -0.0049 0.0379

Auto-GIPSY 0.0149 -0.0050 0.0315

CSRS-PPP 0.0075 0.0008 0.0341

SCOUT 0.0123 0.0100 0.0340

Table 1.4 Mean repeatability, mean accuracy (relative to ITRF) and standard deviation of

mean accuracy for the 186 24 hour solutions submitted to each processing service.

It can be seen in table 1.4 that the Canadian CSRS-PPP service gave the most consistently

repeatable solutions overall, with AUSPOS being the least repeatable. However, all services

provided solutions that were generally repeatable at better than the 2cm level. Solutions from

all processing centres are centred closely around the ITRF coordinates, with, again, CSRS-PPP

coming out nominally as ‘best’. The scatter around the ‘true’ ITRF coordinate is in the order

of 3-4cm for each processing service, with AUSPOS having marginally the highest standard

deviation and auto-GIPSY the smallest.

22

1.6.2 6 hour observation period

1.6.2.1 Pre-analysis

Pre-analysis was performed as described in section 1.6.1.1. As shown in table 1.5, A small

number of solutions were deleted based the predefined selection criteria. As might be expected,

formal errors from the processing services were marginally higher for the shorter observation

spans though the values for the stations in table 1.5 are strongly correlated to those from table

1.1 since both the 6 and 24 hour analyses have used fundamentally the same data.

AUSPOS x Auto-GIPSY x CSRS-PPP x

DARW 0.0112 4 0.0035 0 0.0172 6

MALI 0.0074 0 0.0086 0 0.0735 0

MAW1 0.0093 0 0.0091 0 0.0076 0

KELY 0.0038 0 0.0117 1 0.0179 0

MATE 0.0041 0 0.0099 0 0.0182 0

SANT 0.0239 0 0.0607 0 0.0201 0

SQTCVALL 0.0172 2.1 0.0197 0.5 0.0258 3.2

Table 1.5 SQTCV (metres) at each of 6 stations computed by submitting 186 6 hour

observation files to each of the three processing services. Columns labelled ‘x’ represent the

number of solutions deleted. The final number in the ‘x’ columns is the % of solutions deleted

from all the solutions submitted to a particular processing centre.

23

1.6.2.2 Coordinate repeatability at individual stations for solutions from individual

processing centres

The standard deviations of the x, y and z components were computed for the 186 solutions

from each processing service at each station. Solution outliers were removed prior to the

analysis as per section 1.6.1.1.

In comparison with the 24 hour solutions in table 1.2, more variability can be seen in the

coordinate solutions in the 6 hour solutions. This is particularly evident at MALI, MATE and

to some extent SANT, although AUSPOS and auto-GIPSY are more affected than CSRS-PPP.

1.6.2.3 Coordinate accuracy at individual stations for solutions from individual

processing centres

The means of all 186 final solution coordinates for each station and each processing service

(outlying solutions having been removed) were compared with ITRF at epoch 2004.301, ie the

central epoch of the 1 month data set. These results are displayed in table 1.6.

As with coordinate repeatability, coordinate accuracy is more variable in the 6 hour solutions

than in the 24 hour solutions, although more so for AUSPOS and auto-GIPSY than CSRS-PPP.

24

station Processing service σx (m) σy (m) σz (m)

DARW AUSPOS 0.0107 0.0217 0.0130

Auto-GIPSY 0.0043 0.0145 0.0035

CSRS-PPP 0.0084 0.0076 0.0042

MALI AUSPOS 0.0292 0.0249 0.0188

Auto-GIPSY 0.0358 0.0321 0.0086

CSRS-PPP 0.0084 0.0099 0.0081

MAW1 AUSPOS 0.0099 0.0156 0.0583

Auto-GIPSY 0.0073 0.0063 0.0091

CSRS-PPP 0.0050 0.0056 0.0075

KELY AUSPOS 0.0079 0.0140 0.0133

Auto-GIPSY 0.0047 0.0130 0.0117

CSRS-PPP 0.0048 0.0054 0.0058

MATE AUSPOS 0.0981 0.0227 0.0924

Auto-GIPSY 0.0166 0.0070 0.0099

CSRS-PPP 0.0096 0.0083 0.0085

SANT AUSPOS 0.0162 0.0491 0.0094

Auto-GIPSY 0.0225 0.0182 0.0607

CSRS-PPP 0.0089 0.0063 0.0050

Table 1.6 Day-to-day coordinate repeatability for solutions from each processing service for

each of the 6 stations.

25

station Processing service dx (m) dy (m) dy (m)

DARW AUSPOS -0.067 0.008 0.024

Auto-GIPSY 0.011 0.008 0.033

CSRS-PPP 0.015 -0.077 0.061

MALI AUSPOS 0.139 0.194 -0.015

Auto-GIPSY -0.007 0.063 -0.003

CSRS-PPP -0.023 0.046 0.011

MAW1 AUSPOS 0.005 0.000 -0.027

Auto-GIPSY 0.003 0.008 -0.071

CSRS-PPP -0.008 -0.028 0.034

KELY AUSPOS 0.002 -0.036 0.119

Auto-GIPSY -0.027 -0.027 0.110

CSRS-PPP -0.050 0.026 -0.066

MATE AUSPOS 0.076 0.048 0.138

Auto-GIPSY 0.107 0.054 0.121

CSRS-PPP -0.017 0.040 0.023

SANT AUSPOS 0.040 -0.073 -0.066

Auto-GIPSY 0.042 0.015 -0.010

CSRS-PPP 0.020 0.013 0.031

Table 1.7 Coordinate accuracy relative to ITRF@ 2004.301 for solutions from each

processing service for each of the 6 stations.

26

1.6.2.4 Comparison of solutions from different processing centres.

Inter-processing service solutions are compared as per section 1.6.1.4. First, the mean

coordinate repeatability, ie the mean of all components of the repeatabilities presented in table

1.5, was computed from each solution of the 744 data sets submitted to each processing

service. Again, outlying solutions were omitted from the analysis. These values can be found

in the second column of table 1.8. Second, the mean and standard deviation of the differences

between solution coordinates and ITRF coordinates as presented in table 1.7 was computed

from all solutions and all coordinate components from each individual processing service.

These values are given in columns 3 and 4 of table 1.8.

It can be seen from table 1.8 that the AUSPOS solutions are significantly worse than a)

solutions from the other processing centres, both in terms of precision and accuracy, and b) the

equivalent 24 hour AUSPOS solutions. Auto-GIPSY is marginally worse in precision but 2cm

worse in accuracy whilst CSRS-PPP shows no degradation in repeatability and only a slightly

weaker accuracy than the equivalent 24 hour solutions.

Processing service Mean repeatability (m) Mean Accuracy (m) Standard dev (m)

AUSPOS 0.0292 0.0280 0.0776

Auto-GIPSY 0.0159 0.0024 0.0513

CSRS-PPP 0.0071 0.0003 0.0390

Table 1.8 Mean repeatability, mean accuracy (relative to ITRF) and standard deviation of

mean accuracy for the 744 6 hour solutions submitted to each processing service

1.7 Discussion

As the processed data span shortens, online processing services become more vulnerable to

errors in the data and solution quality degrades. Perhaps the most surprising aspect of the

results from the data set discussed in this study is the different behaviour of solutions from

different processing services at 6 and 24 hour observation spans. The degradation of the

AUSPOS solutions was significant, that of auto-GIPSY and CRSR-PPP solutions less so.

Another noticeable aspect of the results from this data set is the wide variability of results from

different processing centres (and their associated quality control indicators) when processing

identical data. Whilst solutions with 24 hour data are generally repeatable at the 1-2cm level

27

and accurate (in terms of ITRF coordinate recovery) at the 3-4 cm level, individual daily

solutions can vary substantially between processing centres. Such differences are accentuated

as processing time decreases.

It may be concluded that whilst online processing generally offer solutions at a 1-2cm level of

accuracy, it is very difficult to be able to state that any isolated individual solution, such as

may be generated by a user submitting a single data file to retrieve ITRF coordinates of a

known points, is within that range. Therefore, significant uncertainty lies with these types of

solutions and clearly online processing services could be improved in terms of quality control

and reliability.

A user who seriously requires ITRF coordinates of unknown points at the 1-2cm level is still

more likely to achieve this goal by using traditional baseline observation techniques. If forced

to use online processing services, it would seem advisable to observe multiple sessions for as

long as possible and process the data through all available processing services in order to get a

realistic quality estimate of the final coordinate.

Finally, some comment must be made on the degradation of the AUSPOS service when using

6 hour data spans. This is likely due to the long baselines required for processing the 6 IGS

sites chosen for this study. AUSPOS is unlikely to exhibit such a degradation if data submitted

is close to IGS CORS. This can be seen in the next section. When using a baseline processing

engine (rather than PPP), it is therefore advantageous to have a dense regional network of

CORS if users wish to reduce occupation time. This has been demonstrated in tests by Soler et

al (2006) on the OPUS system which relies on the dense CORS network covering North

America for its reference stations. For 5 test sites where 3 reference stations were within

300km of each test site, rms errors of 0.8, 2.1 and 3.4cm were achieved for over 1500 2 hour

solutions. However, observation spans of less than 2 hours drastically increased the

uncertainties. It may therefore be concluded that a dense CORS network in WA which

ensured baseline were kept below 300km would be able to achieve a similar level of accuracy

with AUSPOS.

28

1.8 References Dawson J, R Govind and J Manning (2002) The AUSLIG online GPS processing system.

(AUSPOS), Geoscience Australia. http://www.ga.gov.au/image_cache /GA 5057.pdf

Hugentobler U, Schaer S and Fridez P (2001). Bernese GPS Software Version 4.2 User

Manual, Astronomical Institute, University of Bern, Switzerland.

Kashani I, ΖP Wielgosz and DA. Grejner-Brzezinska (2004). On the reliability of the VCV

Matrix: A case study based on GAMIT and Bernese GPS Software. GPS Solutions, 8:193-

199. DOI 10.1007/s10291-004-0103-9.

King, R. W., and Y. Bock (2005). Documentation for the GAMIT GPS processing software

release 10.2, Mass. Inst. of Technol., Cambridge.

Kouba J and P Heroux (2001). Precise point positioning using IGS orbits and clock products.

GPS Solutions, 5 (2), 12-28.

Martin, T.V., 2000, “MicroCosm, Vols. 1-4”, Van Martin Systems, inc.

Soler T, P Michalak, ND Weston, RA Snay and RH Foote (2006). Accuracy of OPUS

solutions for 1- to 4-h observing sessions. GPS Solutions. 10: 45-55. DOI 10.1007 /s10291-

005-0007-3.

Zumberge, J.F., M.B. Heflin, D.C. Jefferson, M.M. Watkins, and F.H. Webb (1997), Precise

point positioning for the efficient and robust analysis of GPS data from large networks, J.

Geophys. Res., 102(B3), 5005-5017.

29

2. Assessment of accuracy of online static positioning services in a Western Australian

context

2.1 Introduction

In addition to the study outlined in section 1 of this report, a study of online processing

services was conducted in a Western Australian context, the rationale being that atmospheric

conditions and the number of available reference stations in the State present a relatively

unique scenario. The global study in section 1 showed some inter-station variations and a more

detailed study highlighting the capabilities of the online services in the State is appropriate.

2.2 Data and analysis

Due to time constraints on the project only two online processing services were considered,

namely CSRS-PPP and AUSPOS. CSRS-PPP represents the genre of precise point positioning

(PPP) services and performed consistently well in the global tests. Furthermore, it is the

service which is philosophically closest to the AUSPOS service in terms of raison d’etre, being

a government service designed to support users for datum realisation. AUSPOS, being the

local service, was chosen for obvious reasons.

Section 2.3.1 provides results from a regional study using data from 4 IGS CORS stations in

Western Australia (1 week of data, 1st January 2005 – 7th January 2005), these being PERT,

NNOR, YARR and KARR (figure 2.1). For each station and each day solutions were

computed for 1 hour, 2 hour, 4 hour, 8 hour, 16 hour and 24 hour observation sessions. The

coordinate solutions were compared with ITRF coordinates at that epoch. Unlike the analysis

in section 1, no outlier rejection criteria were applied, the sample size already being rather

small and, furthermore, short data span solutions were expected to be somewhat variable.

Section 2.3.2 provides results from data collected from four selected sites in the south-west of

Western Australia. These stations are part of the same data set used for the OmniSTAR study

in section 4 and more details about the data can be found in section 4.2 and figure 4.1.

30

Figure 2.1 Four Western Australian IGS stations used in this study

2.3 Results

2.3.1 Western Australian IGS stations

Table 2.1 summarises the differences between CSRS-PPP and AUSPOS online services’

resultant coordinates and the ITRF coordinates for four IGS stations shown in figure 2.1 based

on one week of 6 hour and 24 hour data sets. Therefore, for each station, 7 24 hour solutions

were available and 28 6 hour solutions were available. Tables 2.2a and 2.2b are the equivalent

of table 1.4 for the 6 and 24 hour CSRS-PPP and AUSPOS solutions respectively.

In comparison with table 1.4, the 24 hour solutions are marginally worse in precision for this

data sample, although the solutions are in better agreement with the ITRF coordinates ie they

display a slightly better accuracy. As with the global data set, the precision (repeatability) of

this limited sample of AUSPOS data is worse than for CSRS-PPP. However, this is to be

expected given the long baselines AUSPOS must form in Western Australia. Furthermore,

since this test used IGS sites which could not themselves be used in the final solutions,

31

baseline lengths for these AUSPOS solutions are longer than would usually be required for

regular users in WA.

Figures 2.2a, 2.2b, 2.2c and 2.2d show variations in solutions for the 4 WA IGS stations for

varying input observation spans for the AUSPOS positioning service. Most notably, the

solutions are stable beyond an observation span of 4 hours but are widely variable for short

observations spans.

2.3.2 SWSZ Stations

Table 2.3 summarises the differences between CSRS-PPP and AUSPOS online services’

resultant coordinates and the ITRF coordinates for four SWSZ stations SZ01, SZ20, SZ33 and

SZ48, based on two weeks of 6 hour and 24 hour data sets. Therefore, for each station, 14 24

hour solutions were available and 56 6 hour solutions were available. Tables 2.4a and 2.4b are

the equivalent of tables 2.2a and 2.2b for the 6 and 24 CSRS-PPP and AUSPOS solutions

respectively.

Compared with the global data set presented in section 1 and the WA IGS data set analysis in

section 2.3.1, the solutions at the SWSZ sites are less noisy. Furthermore, the AUSPOS

solutions exhibit less scatter than the CSRS stations, demonstrating cm level repeatability and

accuracy.

Figures 2.3a, 2.3b, 2.3c and 2.3d show variations in solutions for the 4 WA IGS stations for

varying input observation spans for the AUSPOS positioning service. Most notably, the

solutions are stable beyond an observation span of 4 hours but demonstrate a greater stability

than the IGS data set over short observations spans.

2.4 Discussion and conclusions

Western Australia has a particularly sparse network of IGS CORS stations meaning that online

processing services which use baseline processing engines will tend to produce slightly worse

results than PPP services which are not baseline dependent. This fact is exhibited in the results

from section 2.3.1. However, if baseline lengths are kept relatively short, say less than a few

hundred kilometres, baseline processing services can produce better results than the PPP

services, most probably because differencing process deals more successfully with atmospheric

error in baseline processing than the modelling/estimation strategy used in PPP. Therefore,

32

although only stations at YARR, NNOR and PERT were available for the AUSPOS

processing, for SWSZ stations results came out better than for CSRS-PPP. This suggests that a

densified CORS network across WA, in combination with AUSPOS, could provide a high

accuracy service for datum realisation. Since atmospheric error between a base station and a

reference station decorrelates beyond about 300km, it may be suggested that CORS stations

should not be located more than 300km apart in any densified network in WA if benefits from

AUSPOS baseline processing are to be derived.

Length of data span is an important practical issue for users wishing to utilise online

processing services. Reducing a length of data span required is important if such services are to

become more widely used. Results from this study and that present in section 1 show the

limitations of online processing services with short data spans. However, the SWSZ data show

that shorter data spans can yield acceptable results if baselines are kept relatively short for

AUSPOS. Clearly, shortening data spans to achieve the same level of accuracy and

repeatability with online services as with 24 hour data sets will require improvements in data,

processing algorithms and analysis techniques in the future. However, with the current

technology, inclusion of a densified CORS network in WA would likely reduce the

observation time required to achieve 1-2cm accuracy across most of the State.

One reason that emphasis has been placed on AUSPOS in this section of the report is that it is

accessible to DLI. No other CORS processing services are likely to include many additional

CORS sites from Western Australia in their database of available reference sites, whilst

inclusion of new CORS sites in AUSPOS would be relatively easy to negotiate.

33

CSRS-PPP AUSPOS

6hr 24hr 6hr 24hr

dx 0.020 0.010 0.069 0.062

dy 0.021 0.016 0.056 0.038

Std

(m)

dz 0.014 0.007 0.037 0.025

dx -0.006 -0.003 0.052 0.045

dy 0.011 0.009 -0.058 -0.047

KARR

Mean

(m)

dz -0.007 -0.005 0.014 0.010

dx 0.048 0.022 0.031 0.021

dy 0.037 0.028 0.057 0.041

Std

(m)

dz 0.028 0.028 0.028 0.018

dx -0.029 -0.032 0.007 0.002

dy 0.031 0.039 -0.036 -0.034

PERT

Mean

(m)

dz -0.018 -0.018 0.016 0.014

dx 0.048 0.010 0.028 0.017

dy 0.038 0.021 0.048 0.025

Std

(m)

dz 0.029 0.024 0.032 0.023

dx -0.021 -0.018 0.002 -0.003

dy 0.022 0.021 -0.024 -0.022

NNOR

Mean

(m)

dz -0.015 -0.007 0.012 0.011

dx 0.010 0.009 0.034 0.025

dy 0.014 0.010 0.043 0.026

Std

(m)

dz 0.008 0.016 0.026 0.016

dx -0.002 0.004 0.013 0.008

dy 0.007 0.012 -0.023 -0.020

YARR

Mean

(m)

dz -0.008 -0.003 0.014 0.013

Table 2.1 Statistical summary of the differences between online services’ resultant coordinates

and IRTF coordinates based on one week (01 January 2005 to 07 January 2005) of 6hr and

24hr data sets (m)

34

Processing service Mean repeatability (m) Mean Accuracy (m) Standard dev (m)

AUSPOS 0.0281 -0.0019 0.0250

CSRS-PPP 0.0168 -0.0001 0.0190

Table 2.2a Mean repeatability, mean accuracy (relative to ITRF) and standard deviation of

mean accuracy for the 7 24 hour solutions submitted to each processing service (IGS stations).

Processing service Mean repeatability (m) Mean Accuracy (m) Standard dev (m)

AUSPOS 0.0408 0.0009 0.0293

CSRS-PPP 0.0263 -0.0029 0.0178

Table 2.2b Mean repeatability, mean accuracy (relative to ITRF) and standard deviation of

mean accuracy for the 28 6 hour solutions submitted to each processing service (IGS

station)s.

KARR station

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Posi

tion

erro

r (m

)

dx dy dz

Figure 2.2a Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station KARR

35

PERT station

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Posi

tion

erro

r (m

)

dx dy dz

Figure 2.2b Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station PERT

YARR station

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Posi

tion

erro

r (m

)

dx dy dz

Figure 2.2c Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station YARR

NNOR station

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Posi

tion

erro

r (m

)

dx dy dz

Figure 2.2d Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station NNOR

36

CSRS (Canada) AUSPOS

6hr 24hr 6hr 24hr

dx 0.017 0.003 0.010 0.012

dy 0.010 0.003 0.013 0.010

Std

dz 0.012 0.006 0.008 0.006

dx 0.002 -0.001 0.011 0.012

dy 0.012 0.020 -0.021 -0.022

SZ01

Mean

dz -0.006 -0.010 0.009 0.010

dx 0.012 0.007 0.008 0.003

dy 0.016 0.007 0.013 0.005

Std

dz 0.016 0.008 0.008 0.003

dx -0.001 -0.005 -0.002 -0.003

dy 0.013 0.014 0.008 0.005

SZ20

Mean

dz -0.006 -0.008 -0.009 -0.008

dx 0.010 0.006 0.009 0.004

dy 0.015 0.006 0.012 0.008

Std

dz 0.013 0.004 0.006 0.005

dx -0.003 -0.006 -0.003 -0.002

dy 0.015 0.017 0.010 0.007

SZ33

Mean

dz -0.006 -0.009 -0.011 -0.009

dx 0.077 0.062 0.010 0.004

dy 0.014 0.004 0.014 0.009

Std

dz 0.017 0.009 0.009 0.006

dx 0.015 0.015 -0.001 0.003

dy 0.015 0.019 0.005 0.003

SZ48

Mean

dz -0.006 -0.013 -0.008 -0.006

Table 2.3 Statistical summary of the differences between online services’ resultant coordinates

and the known values for four SWSZ stations based on one week (01 May 2002 to 08 May

2002) of 6hr and 24hr data sets (m)

37

Processing service Mean repeatability (m) Mean Accuracy (m) Standard dev (m)

AUSPOS 0.0063 -0.0008 0.0096

CSRS-PPP 0.0104 0.0028 0.0130

Table 2.4a Mean repeatability, mean accuracy (relative to ITRF) and standard deviation of

mean accuracy for the 7 24 hour solutions submitted to each processing service (SWSZ

stations).

Processing service Mean repeatability (m) Mean Accuracy (m) Standard dev (m)

AUSPOS 0.0100 -0.0010 0.0100

CSRS-PPP 0.0191 0.0037 0.0095

Table 2.4 Mean repeatability, mean accuracy (relative to ITRF) and standard deviation of

mean accuracy for the 28 6 hour solutions submitted to each processing service (SWSZ

stations).

SZ01 station

-0.10

-0.05

0.00

0.05

0.10

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Posi

tion

erro

r (m

)

dx dy dz

Figure 2.3a Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station SZ01

38

SZ20 station

-0.10

-0.05

0.00

0.05

0.10

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Pos

ition

err

or (m

)

dx dy dz

Figure 2.3b Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station SZ20

SZ33 station

-0.10

-0.05

0.00

0.05

0.10

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Pos

ition

err

or (m

)

dx dy dz

Figure 2.3c Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station SZ33

SZ48 station

-0.10

-0.05

0.00

0.05

0.10

0.00 4.00 8.00 12.00 16.00 20.00 24.00

Session length (hr)

Pos

ition

err

or (m

)

dx dy dz

Figure 2.3d Position accuracy, relative to ITRF of AUSPOS solutions for varying session

lengths for station SZ48

39

3. Assessment of online products for kinematic positioning applications

3.1 Introduction

One attractive application for CORS networks is for supporting kinematic positioning which is

a major requirement for the airborne surveying industry. A Western Australian CORS network

would be able to support post-processed kinematic positioning and studies into the feasibility

of such a system have been published previously (Hu et al, 2005). However, some online

processing services already offer free post-processed kinematic data positioning services and it

is the purpose of this part of the technical study to assess the capabilities of such services.

Post-processed kinematic positioning services are offered by CSRS-PPP. GIPSY has

kinematic capability but this is not yet available in auto-GIPSY. CSRS-PPP, being a precise

point positioning engine, has the advantage that no reference stations are required and

solutions are not dependent on baseline length. Such a service is particularly attractive for

Western Australia with its current sparsity of GPS CORS. Furthermore, the kinematic option is

simple to invoke on the CSRS-PPP web interface.

3.2 Data and analysis methodology

Three data sets were used for this study. First, 24 hour 30 second RINEX files from two static

IGS stations, one in the northern hemisphere (ONSA -06 May 2002) and one in the southern

hemisphere (ALIC - 22 Jan 2003), were processed in kinematic mode using CSRS-PPP. The

results, from ostensibly high quality static sites with known coordinates, are used to provide a

benchmark by which solutions from real kinematic data can be compared.

The second data set is a two-hour dual-frequency airborne dataset from Norway. The time span

is from 07:58:00 to 09:57:30 (GPS time) on May 8th 2002, with a data collection rate of 1 Hz.

The CSRS-PPP kinematic service resultant coordinates are compared with a reference

trajectory computed from DGPS.

Finally, a third data set, from airborne kinematic tests conducted by AAMHatch in Australia

was submitted to the CSRS-PPP service. The time span was from 22 Jan 2003, 23:10:16 to 23

Jan 2003, 00:44:20 (GPS time), with a data collection rate of 1 Hz. As with the Norwegian

40

data set, the CSRS-PPP kinematic service resultant coordinates are compared with a reference

trajectory computed from DGPS.

3.3 Results

3.3.1 IGS data

In total 2880 solutions were computed at each test site, at 30 second intervals. The east, north

and height components of the kinematic solutions relative to the known ITRF coordinate can

be seen in figures 3.1 and 3.2 for ALIC and ONSA respectively. A statistical summary of the

coordinate solutions, relative to the ITRF coordinates for ALIC and ONSA, is given in table

3.1.

Coord. Comp. STD Mean (m) Max (m) Min (m)

North 0.043 0.008 0.153 -0.153

East 0.035 0.003 0.158 -0.185

ALIC

Height 0.085 0.013 0.424 -0.341

North 0.031 -0.002 0.144 -0.123

East 0.049 -0.006 0.210 -0.252

ONSA

Height 0.095 0.015 0.574 -0.769

Table 3.1 Position Error Statistics (m) for ALIC and ONSA stations: CSRS-PPP vs. ITRF

coordinates

The results for the two stations are, overall, uniform. The CSRS-PPP kinematic service yields

solutions good to better than 5 cm in the horizontal and 10cm in the vertical, resolving the

ITRF coordinates to better than 1cm in the horizontal and 2cm in the vertical.

These results strongly demonstrate the potential of post-processed precise point positioning for

kinematic solutions. However, two features are noticeable from figures 3.1 and 3.2. First, a

small number of outlying solutions appear for each station. There is no obvious explanation for

such spikes in the computed kinematic trajectory, particularly as the test data sets are from

41

stationary receivers. All outliers have been left in the analysis as no quality control indicators

could be used to justify their removal.

Second, systematic trends and biases are clearly evident in the data, indicating a vulnerability

in the processing engine to multipath and interference effects and atmospheric variations over

time. However, with both these data sets, it is difficult to specifically identify error sources in

the context of the ‘black box’ processing of an online positioning service.

It may be concluded that in ideal conditions CSRS-PPP kinematic can yield kinematic

solutions at the 5 cm level in the horizontal and 10cm level in height. However, as with all

online processing services, CSRS-PPP kinematic is vulnerable to data quality and it may be

anticipated that result would be substantially worse with real kinematic data.

3.3.2 Norwegian Data

Some 7000 solutions were computed from the 2 hour 1Hz airborne kinematic data set collected

in Norway. These were compared against the trajectory computed from DGPS for the same

data set. The east, north and height results relative to this trajectory are presented in figure 3.3;

a statistical summary is shown in table 3.2.

Coord. Comp. STD Mean Max Min North 0.047 -0.128 0.200 -0.260 East 0.048 0.116 0.223 -0.104

Height 0.110 0.006 0.498 -0.776

Table 3.2 Position Error Statistics (m) for Norway Airborne Data: CSRS_PPP vs. DGPS

It can be seen from table 3.2 that this kinematic data set gives statistical results of a similar

order of magnitude to the results from the IGS data set. However, since the DGPS trajectory is

only likely to be good to 0.5m to 1m at best, it seems likely that there is a high degree of

correlation between the DGPS and the CSRS-PPP kinematic trajectories. This is not

unsurprising, given that both solutions make use of the code pseudorange observations, whilst

CSRS-PPP makes additional use of the carrier phase. It is therefore somewhat difficult to

assess the results from this data set in a quantitative sense. However, it is possible to note in

figure 3.3 the same type of outliers and trend biases as observed in the IGS data, with some

large trends in height.

42

3.3.3 Australian Data

Results from 1.5 hours 1Hz kinematic data collected in Australia are illustrated in table 3.3 and

figure 3.4. This data set is clearly more noisy than the data sets presented previously in

sections 3.3.1 and 3.3.2, with standard deviations some 3 – 5 times greater in all three

components. Large drifts, in the order of 1m or more can be seen in figure 3.4.

Coord. Comp. STD Mean Max Min

North 0.194 -0.467 0.923 -0.855

East 0.089 -0.155 0.600 -0.352

Height 0.305 0.202 1.061 -1.484

Table 3.3: Position Error Statistics (m) for Australian Airborne Data: CSRS-PPP vs. DGPS

This data set perhaps represents a more realistic scenario than the previous two. GPS antenna

mounted on aircraft are strongly susceptible to multipath and losing lock due to aircraft

dynamics. The coordinate patterns seen in figure 3.4 are as may be expected if the processing

engine has inadequately resolved loss of lock ie cycle slips in the data. Reliably resolving cycle

slips down to the 1 cycle level is still a challenge in kinematic positioning, particularly in a

noisy environment such as on an aircraft.

3.4 Summary and Conclusions

Results from the three data sets indicate that the CSRS-PPP kinematic service can deliver

kinematic solutions at the 5cm level in the horizontal and 10cm level in the vertical when good

quality data are supplied by the user. The solution quality becomes substantially worse when

what may be classed as ‘realistic’ airborne kinematic data are supplied by the user. Generally,

a solution could be expected to be accurate to the order of several decimetres but, as the

Australian data shows, some solutions are worse than 1m which is, in fact, worse than DGPS

accuracy.

Therefore it may be concluded that CSRS-PPP kinematic is a valid option for users wishing to

post-process kinematic data so long as they take extreme care in ensuring data quality.

However, from this admittedly limited dataset, the CSRS-PPP kinematic service appears to be

less precise than OMNISTAR-HP which operates in real time and is discussed in detail in the

following section. It may also be inferred that a kinematic processing service based on a

43

regional Western Australian CORS network would be able to provide more reliable results

than CSRS-PPP kinematic although further study using a controlled sample of data is required

in this area of post-processed kinematic positioning, before firm conclusions can be drawn.

3.5 Acknowledgments

The Australian kinematic data set was supplied by AAMHatch Pty Ltd. The Norwegian data

set was supplied by Dr Ola Ovstedal of the Agricultural University of Norway.

3.6 References

Hu G, D Abbey, N Castleden, W E Featherstone, C Earls, O Ovstedal and D Weihing (2005).

An approach for instantaneous ambiguity resolution for medium- to long-range multiple

reference station networks, GPS Solutions, 9:1-11, DOI: 10.1007/s10291-004-0120-8.

44

Figure 3.1 Position Error(ENh) between CSRS_PPP and ITRF coordinates at ALIC

45

Fig.3.2: Position Error (ENh) between CSRS_PPP and known coordinates at ONSA

46

Figure 3.3 Position Error between CSRS-PPP solutions and DGPS for 2 hours 1Hz Norwegian Airborne Data

47

Figure 3.4 Position Error between CSRS_PPPsolutions and DGPS for 1.5 hours 1Hz

Australian Airborne Data

48

4. Assessment of the accuracy of the OmniSTAR Pty Ltd service in Western

Australia

4.1 Introduction

The OmniSTAR system is described in section 2.1.3 of the main report. This section of the

technical report documents independent tests conducted on the OmniSTAR-HP system to

provide an independent and realistic indication of the level of accuracy of the service offered

across the State of Western Australia.

4.2 Data and processing

Data used in this study were a selection of seven points observed as part of a second epoch

GPS campaign to geodetically monitor the south-west seismic zone (SWSZ) of Western

Australia (Featherstone et al, 2004). GDA Coordinates for these points, known from the

processing of first epoch of observations in 2002 are estimated to be precise to better than 1cm

in the horizontal and 2cm in the vertical (ibid.). Static data at the selected sites (figure 4.1 and

table 4.1) were observed over multiple 24 hour sessions using geodetic receivers and antennas

at a 30 second data interval. Furthermore, sites were chosen to be stable and to be away from

GPS noise or interference sources.

OmniSTAR broadcast WADGPS corrections to users on a real time basis. These corrections

are archived at the OmniSTAR master control centre in Perth. Therefore, by applying archived

WADGPS corrections for a particular day to a file observed on that day, epoch by epoch

solutions can be computed as if the data from that file were being observed in real time. This

approach allows retrospective analysis of the quality of the OmniSTAR corrections. By

applying the archived WADGPS corrections to static data files collected at known points, an

absolute test of the accuracy and scatter of OmniSTAR-corrected data can be achieved.

WADGPS corrections were provided by OmniSTAR Pty Ltd from their OmniSTAR-HP

service for the observation periods shown in table 1. Data from the seven SWSZ stations were

processed using the software hpReplay version 4.02d, which was also supplied by OmniSTAR

Pty Ltd. It should be noted that the software uses an HP real-time processing engine which is

probably not optimised to ideally process 30 second epoch data.

49

Station Name Observation period Receiver type Antenna type

Bencubbin 90 - SZ10

05-06, 09-18 May 2004

ASHTECH UZ-12 ASH701945E_M

Corrigin 89 - SZ33

03-18 May 2004 ASHTECH UZ-12 ASH701945C_M

Gwambygine T - SZ23

05, 08, 10-14 May 2004

LEICA MC500 LEIAT504

Kellerberrin 182 - SZ20

03-18 May 2004 ASHTECH UZ-12 ASH701945E_M

Moora 228 - SZ06

05 -14 May 2004 LEICA MC500 LEIAT504

Mount Barker 316 - SZ48

03-18 May 2004 ASHTECH UZ-12 ASH701945C_M

Perth 364 - SZ12

05 -14 May 2004 LEICA MC500 LEIAT504

Table 4.1: the details of the test data from South West Seismic Zone (SWSZ) stations in 2004,

sample interval 30s

Figure 4.1: SWSZ stations used for this study and OmniSTAR Base stations in Western Australia

50

4.3 Results

The results from the analysis from the 7 stations are shown in table 4.2 and illustrated in

figures 4.2-4.8. Depending on the observation span, table 4.2 represents the statistical analysis

from between approximately 10,000 and 30,000 observation epochs per station.

Standard deviation (m) Max (m) % > 0.5m Station

Name dx dy dz dx dy dz dx dy dz

SZ10 0.086 0.094 0.086 0.106 0.360 1.061 0 0.2% 0.1%

SZ33 0.102 0.114 0.102 0.788 0.386 0.664 0.1% 1.1% 0.1%

SZ23 0.097 0.106 0.097 0.696 0.386 0.756 0.3% 0.6% 0.1%

SZ20 0.096 0.106 0.096 0.732 0.355 0.551 0.4% 0.6% 0.01%

SZ06 0.122 0.117 0.122 1.041 0.860 0.690 0.3% 0.4% 0.2%

SZ48 0.127 0.158 0.127 0.811 0.388 0.654 0.4% 6.0% 0.1%

SZ12 0.098 0.111 0.098 0.754 0.482 0.751 0.1% 0.2% 0.1%

Table 4.2: Statistical summary of the differences between OmniSTAR HP resultant

coordinates and the known values for the SWSZ stations (m)

From table 4.2, it can be seen that the scatter of OmniSTAR solutions about their known GDA

coordinates is at the 10-12cm level for each component. SZ10 has the lowest standard

deviation and SZ48, which is the furthest from an OmniSTAR reference station, the highest.

As can be seen in figures 4.2 - 4.8 some outliers exist for all stations and the percentage of

residuals for each station that are greater than 0.5m is tabulated in the final three columns of

table 4.2. The magnitude of the maximum error at each station is also given, in columns 5 to 8

of the same table. The largest error was found to be 1.061m in the z component at SZ10.

Generally, the maximum error is less than 1m and, with the exception of SZ48, the percentage

of solutions greater than 0.5m in error is less than 0.5%. For example, at SZ48, some 1800 of

the (approximately) 31,000 solutions were greater than 0.5m from the GDA coordinate in the y

component, whilst at SZ10, only 60 solutions (approximately) were outside this criteria.

51

4.4 Discussion

The results presented above support OmniSTAR’s claim of decimetre level accuracy for their

HP service. The percentage of outliers, defined in this study as solutions with one component

greater than 0.5m from the reference GDA coordinate, is statistically consistent with this level

of accuracy. Whilst SZ48 (only) shows an abnormally high rejection rate in the y component, it

is difficult to isolate a reason. It may be noted that SZ48 is farthest from an OmniSTAR base

station although this fact could simply be coincidental. Data quality could be an issue although

SW48 had no apparent site problems when its data were processed as part of the SWSZ

geodetic network.

As with the online static processing services discussed in sections 1 and 2 of this report,

OmniSTAR-HP is vulnerable to the quality of the data supplied by the user. Since this study

supplied good quality static data from geodetic quality sites and hardware, the result in table

4.2 provides an indication of the ‘best case scenario’ for OmniSTAR-HP users. It is likely that

users with more dynamic applications and with less multipath resistant hardware would

experience more variable results.

Time and data availability has limited this study to seven stations in the SWSZ. Whilst the

results presented here are a good indicator of the accuracy of the OmniSTAR-HP service,

further study would be required to confirm that the decimetre level of accuracy holds across

the entire state of Western Australia.

4.5 References W E Featherstone, N T Penna, M Leonard, D Clark, J Dawson, M C Dentith, D Darby & R

McCarthy (2004). GPS-geodetic deformation monitoring of the south-west seismic zone of

Western Australia: review, description of methodology and results from epoch-one. Journal of

the Royal Society of Western Australia, 87:1–8, 2004

4.6 Acknowledgment

The cooperation and support of Mr Mark Hardman and his operational staff at the OmniSTAR

Pty Ltd office in Perth is gratefully acknowledged.

52

Fig. 4.2 Time series of differences between OmniSTAR-HP solution coordinates and GDA

coordinates for station SZ33.

Fig. 4. Time series of differences between OmniSTAR-HP solution coordinates and GDA

coordinates for station SZ10

53

Fig. 4.4 Time series of differences between OmniSTAR-HP solution coordinates and GDA coordinates for station SZ23

Fig. 4.5 Time series of differences between OmniSTAR-HP solution coordinates and GDA

coordinates for station SZ20

Fig. 4.6 Time series of differences between OmniSTAR-HP solution coordinates and GDA

coordinates for station SZ06

Fig. 4.7 Time series of differences between OmniSTAR-HP solution coordinates and GDA

coordinates for station SZ48

54

Fig. 4.8 Time series of differences between OmniSTAR-HP solution coordinates and GDA

coordinates for station SZ12

55

5. Design, simulation and assessment of CORS networks for static

positioning in Western Australia

5.1 Introduction

This section provides the mathematical background for the case studies highlighted in sections

5.6 and 5.7 of the main report.

5.2 Design Parameters – theoretical background

In order to design a CORS network it is useful to compute some design parameters that give an

indication of the quality that can be expected from the final network solutions. This quality

will depend on:

- location of stations;

- system (GPS, GLONASS, Galileo, GPS/GLONASS, GPS/Galileo), types of

observations (code, phase), number of frequencies (double frequency or triple

frequency);

- time of measurements, observation interval, number of epochs;

- measurement scenario (single point, single baseline, network, static or kinematic).

When trying to design the best geometric configuration of a geodetic CORS network, the range

of situations can vary from the case where the possible location of the stations is so constrained

by external conditions eg site availability, that there is almost no choice for optimal site

location because there is no margin for movement, to the case where any possible location

within a region is acceptable. As the margin of choice grows, there is an increasing need for

reliable criteria to determine the most appropriate network design. Some mathematical

methods required to search for the best network design are described herewith.

The variable in this problem is the design matrix of the observations. The system of equations

for the least squares (LS) method, in its parametric form, and for any kind of observations

(pseudorange, carrier phase), can be written as

vlAx += (5.1)

where A is the design (configuration) matrix, x is the vector of unknown parameters, l is the

observation vector, v is the residual vector.

56

The variances and covariances of the estimated parameters are given by the matrix 1−= )( PAAC T

x (5.2)

Matrix xC is a function of all station positions and provisional parameters, which characterises

formally how parameter precision depends on network design. Optimisation of network design

is achieved by minimising the hypervolume of the hyperellipsoid defined by xC ; this involves

minimizing its determinant

min det( xC ) (5.3)

or the equivalent problem of maximizing the determinant of its inverse

max det( 1−xC ) (5.4)

Alternatively, the condition number of the covariance matrix reflects the sensitivity of the

solution to errors in the observations. It gives an indication of the accuracy of the solutions and

for the covariance matrix C is defined as:

( ) 1−= CCCκ (5.5)

where is a matrix norm induced by a vector norm (see eg Golub and Van Loan, 1996).

Therefore, both the determinant and condition number of the covariance matrix can be

considered as the design parameters of a network.

5.3 References

Golub and Van Loan (1996). Matrix Computations, 3rd edition. Johns Hopkins University

Press.

57

6. Design, simulation and assessment of CORS networks for RTK

positioning in Western Australia

6.1 Introduction

The optimal design configuration for a geodetic network of CORS of Global Navigation

Satellite System (GNSS) receivers is slightly different to the design of a classical geodetic

network of ground monuments (cf. Grafarend and Sanso 1985). As well as the geometrical

strength of the network and robustness against outliers, the success rate of carrier-phase GNSS

integer ambiguity resolution (AR) has to be sufficiently high, especially if the CORS network

is to support network real-time kinematic (RTK) operations. Current user expectations are

centimetric precision for a few epochs of data with single-baseline RTK over distances of ~10-

20 km or with network RTK for distances up to ~70-100 km (e.g. Wanninger 2005, Rizos

2003b). As such, a CORS network should match these expectations.

Historically, geodetic networks comprise numerous stably monumented ground marks, which

were coordinated by conventional-geodetic (but now mainly GPS-geodetic) techniques. Their

establishment really only needed to consider the classical network design criteria, as well as

the provision of a sufficiently dense coverage of ground monuments in the areas of interest.

The old considerations of station intervisibility have now largely been removed with GPS, but

now sky visibility is a consideration. Quite often, the establishment of a classical geodetic

network involved a priori simulations to determine the optimal geometry of intervisible

stations from estimates of the likely measurement precision. With the modern trend towards

CORS networks and network RTK in several countries (e.g. Ireland (Bray and Greenaway

2004), the optimal network design parameters have changed.

When designing a CORS network, say as a potential future replacement for an existing

classical geodetic network, some additional network-design factors have to be considered. As

well as the network geometry, stability and likely longevity of the albeit sparser ground

monuments, the new additional considerations include site security, uninterrupted access to

power and high-bandwidth telecommunications, ready availability of technical staff to ensure

continuous operations, clear sky visibility, and low probabilities of electrical interference and

multipath. Here we shall assume that these logistical considerations can always be solved by

appropriate site selection and/or placement of the necessary infrastructure (subject also to the

conditions imposed later).

58

The most important new consideration is the ability of the CORS network to deliver multi-

frequency (with modernised GPS and future Galileo) code-pseudorange and carrier-phase

GNSS data from a geometrical configuration that will allow near-instantaneous AR with a near

near-100% success rate for all users in the desired area of operation. As is well known,

successful AR is the key criterion for centimetric GNSS positioning. In this section, the

theoretical background behind the RTK simulations illustrated in section 5.8 of the main report

is presented.

While Australian CORS networks have been (e.g. across the State of Victoria (e.g. Penna et al.

2005) or part of Brisbane (Higgins et al. 2001)) or are currently being (Sydney (Rizos et al.

(2003a)) established, it is not clear that they have been optimised in order to deliver high AR

success rates to their users. This also applies elsewhere (cf. Bray and Greenaway 2004). As

such, the CORS infrastructure now being established might not be capable of delivering the

best-possible AR success rates for the cost of installation and maintenance. Given the

somewhat unique Western Australian scenario, it is essential to be prudent with any new

CORS network.

In this study, CORS network design for RTK is based on the following key indicators:

1. condition number and determinant of the design matrix comprising the geometry of the

CORS network, the user location and the satellite constellation (for current GPS and future

combined GPS/Galileo);

2. network reliability, in terms of its resistance to the effects of measurement blunders;

3. the likely AR success rate for GPS-only and combined GPS/Galileo constellations,

assuming uninterrupted sky visibility and low noise, multipath and interference.

6.2 Optimal CORS network design parameters for RTK

Throughout the RTK simulations, it has been assumed that all the CORS and user GNSS

receivers have an uninterrupted sky visibility above 15 degrees elevation from the local

horizon, and none are subjected to significant multipath and electrical interference. It is

acknowledged that this is unrealistic in all (notably urban) areas, but it is necessary to gain a

best-possible scenario before considering special cases. For the AR part of the simulations, we

have used a modified version of the software suite kindly provided by Verhagen (2002).

59

The key CORS network design parameters that give a ready indication of the quality that

can be expected by the user depend upon:

• the locations of CORS stations to form a geodetically robust geometry and spaced at

distances that will allow for near-instantaneous AR;

• the type of GNSS used (here, only GPS and Galileo are considered), types of observations

(code pseudorange and carrier-phase), and the number of frequencies (single, dual- or triple-

frequency);

• the sidereal time of the observations, data collection interval, number of epochs used;

• the user measurement scenario (static or kinematic; single baseline or network).

When trying to establish the best geometric configuration for either a classical or a new CORS-

based geodetic network, the range of situations can vary from the case where the possible

locations of the ground stations is so constrained by external conditions that there is almost no

choice for the most adequate location, to the case where any possible location within an area is

permitted. As the margin of choice grows, there is an increasing need for reliable criteria to

determine the most appropriate network design. Here, we shall assume that there is total

freedom for the placement of the stations.

For CORS network optimisation, a combination of existing design methods for classical

geodetic networks are coupled with simulated likely CORS AR success rates. The most

interesting observation presented later is that AR-reliable CORS network RTK positioning is

not exclusively inside the quadrilateral defined by the outer CORS stations; it may extend

beyond this quadrilateral. Moreover, there are sometimes regions within the perimeter of the

outer CORS stations that may not offer reliable AR. This latter observation seems to be not

always appreciated by those who establish CORS networks, presumably because of the

‘conventional’ thinking based on classical geodetic networks. As such, we present

consideration of the full GNSS-satellite-terrestrial network geometry. CORS network design

to avoid these ‘blind spots’ is essential for network RTK service-providers, otherwise they may

have to place additional infrastructure at a later date.

60

6.3 Theoretical background

6.3.1 Internal reliability

One useful geodetic network design parameter is the internal reliability of the CORS network,

which is the ability of that network to detect and resist against gross errors in the observations.

The internal reliability of a network depends upon its geometry (via the design matrix), the

accuracy of the observations (i.e., high precision with no gross or systematic errors), and the

total number of observations available.

The internal reliability measures a CORS network’s ability to detect outliers by the 1D

outlier test. This uses the lower bounds of detectable gross errors, which can be derived from

(e.g. Baarda 1968):

i

li r

l iσδ0

0 =∇ (6.1)

where 0δ is the lower bound for the non-centrality parameter and is a function of type I and II

errors, il

σ is the standard deviation of the i-th observation, and ir is the redundancy number of

the i-th observation.

The redundancy numbers ir of the observations are the diagonal elements of the matrix

PAPAAAIR TT 1−−= )( (6.2)

where I is the identity matrix. Typically, the redundancy numbers should be greater than 20.

As with Eq. (5.2), Eq. (6.2) does not need actual GNSS observations, but only reasonable

estimates of the observation precision together with the satellite-CORS-user geometry. Again,

this is a standard approach in conventional network design, and we acknowledge that

alternative methods exist.

6.3.2 Ambiguity Success Rate (AS)

The AR success rate (i.e., percentage of correct AR for single epoch solutions) is a most useful

CORS network design parameter (cf. Verhagen 2002) and for RTK in general. It is the

probability of successful AR under ideal conditions (i.e. with no significant systematic biases

present) at any location in the CORS network. We acknowledge that multiple epoch solutions

will give improved AR success rates, and an AR success rate of <100% does not indicate that

the network is unusable at that point, but simply likely to operate sub-optimally relative to

locations that can achieve a 100% AR success rate. Again without actual GNSS observations,

but with reasonable estimates of their precision, the likely AR success rate can be predicted for

61

a user at a particular location with respect to the CORS network for a particular satellite

constellation.

The CORS AR success rate depends on: the observation equation (cf. Eq. 5.1), the precision of

the GNSS observations, and the chosen method of AR. We shall not consider ambiguity

validation (AV) procedures (cf. Verhagen 2004), under the assumption that if the AR is

correct, the validation will prove it so. While this is a glib statement, here we are only

concerned with the ‘ideal cases’. AV will be of more use in the cases of high signal noise

(e.g., multipath) or restricted sky visibility, which are not considered here.

It is now widely acknowledged that the well-known LAMBDA method (Teunissen 1995) has

the largest success rate of all admissible AR techniques (Teunissen 1999). Therefore, the

single-epoch LAMBDA AR success rate will be used here. The AR float solution is (ibid.)

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

NNb

bNb

QQQQ

,Nb

(6.3)

where b is the 3D baseline vector, N is the float ambiguity vector, and Qb, QbN, QNb and QN are

the corresponding VCV matrices.

The LAMBDA-based AR success rate is (Teunissen 1998):

∏= ⎟

⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−

σΦ

∧

n

1iz

1)2

1(2I|i

(6.4)

where n is the number of ambiguities to be solved, and

dz)z21exp(

21)x( 2x

−π

=Φ ∫ ∞− (6.5)

The standard deviation ∧σI|izis the square root of the condition variance of the i-th ambiguity

(conditioned from the previous I=1,…, i-1 ambiguities; cf. Teunissen 1998). It can be obtained

from the diagonal matrix D after a standard LDLT decomposition of the matrix ∧z

Q , the VCV

matrix of the LAMBDA-transformed ambiguities, and z is formed by using the LAMBDA

decorrelation matrix ZT to transform the ambiguities by

ZQZQ,NZz NT

z

T == ∧

∧

(6.6)

62

where the elements of matrix ZT are all integers, and in order to be search-volume-preserving,

its determinant must be 1± .

For further details the reader is referred to Verhagen (2002).

6.4 References/Further reading Baarda W (1968) A testing procedure for use in geodetic networks, Netherlands Geodetic Commission,

Publications on Geodesy, 2(5)

Bray C, Greenaway I (2004) The OSI national network RTK solution, Proceedings of FIG Working Week,

Athens, May, http://www.fig.net/pub/athens/papers/ts11/TS11_5_Bray_Greenway.pdf

de Jong K (2002) Success rates for integrated GPS and Galileo ambiguity resolution, Revista Brasileira de

Cartografia 54: http://www2.prudente.unesp.br/rbc/_pdf_54_2002/54_01.pdf

Eckl MC, Snay RA, Soler T, Cline MW, Mader GL (2001) Accuracy of GPS-derived relative positions as a

function of interstation distance and observing-session duration, Journal of Geodesy 75(12):633-640, doi:

10.1007/s001900100204

Fotopoulos G, Cannon ME (2001) An overview of multiple-reference station methods for cm-level positioning,

GPS Solutions 4(3):1-10, doi: 10.1007/PL00012849

Grafarend EW, Sansò F (eds) (1985) Optimisation and Design of Geodetic Networks, Springer, Berlin Heidelberg

New York

Grejner-Brzezinska DA, Kashani I,Wielgosz P (2005) On accuracy and reliability of instantaneous network RTK

as a function of network geometry, station separation, and data processing strategy, GPS Solutions 9(3):212-

225, doi: 10.1007/s10291-005-0130-1

Higgins MB (2001) An Australian pilot project for a real time kinematic GPS network using the virtual reference

station concept, Proceedings of FIG Working Week, Seoul, May,

http://www.fig.net/pub/proceedings/korea/full-papers/session11/higgins.htm

Hu G, Abbey DA, Castleden N, Featherstone WE, Earls CJ, Øvstedal O, Weihing D (2005) An approach for

instantaneous ambiguity resolution for medium- to long-range multiple reference station networks, GPS

Solutions 9(1):1-11, doi: 10.1007/s10291-004-0120-8

Hu G, Khoo HS, Goh PC, Law CL (2002) Performance of Singapore Integrated Multiple Reference Station

Network (SIMRSN) for RTK positioning, GPS Solutions 6(1-2):65-71, doi: 10.1007/s10291-002-0014-6

Kwok S (2002) The Hong Kong GPS network and reference stations, Journal of Geospatial Engineering 2(2):57-

65

Penna N, Lo J, Luton G (2005) Geodetic GPS analysis of Land Victoria’s GPSnet, Journal of Spatial Science

50(1)

Rizos C (2003b) Network RTK research and implementation - a geodetic perspective, Journal of Global

Positioning Systems 1(2):144-150, http://www.gmat.unsw.edu.au/wang/jgps /v1n2/v1n2pI.pdf

Rizos C, Yan T, Omar S, Musa T, Kinlyside D (2003a) Implementing network-RTK: the SydNET CORS

infrastructure, Proceedings of the 6th International Symposium on Satellite Navigation Technology,

Melbourne, July, http://www.gmat.unsw.edu.au/snap/publications/rizos_etal2003a.pdf

63

Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS ambiguity

estimation, Journal of Geodesy 70(1-2):65–82, doi: 10.1007/BF00863419

Teunissen PJG (1998) Success probability of integer GPS ambiguity rounding and bootstrapping, Journal of

Geodesy 72(10):606-612, doi: 10.1007/s001900050199

Verhagen S (2002) Studying the performance of Global Navigation Satellite Systems: a new software tool, GPS

World 13(6):60-65

Verhagen S (2004) Integer ambiguity validation: an open problem? GPS Solutions 8(1):36-43, doi:

10.1007/s10291-004-0087-5

Wanninger L (2005) Introduction to network RTK, http://www.network-rtk.info/intro/introduction.html

64

7. Impact assessment of an enhanced Western Australian CORS network on

regional orbital products

7.1 Introduction

The inclusion of regional CORS network data in regional or global orbital solutions, such as

those generated by the IGS, is one potential benefit of installing a CORS network in Western

Australia. In this brief study, the impact of a densified West Australian CORS network on JPL

precise orbits is simulated.

7.2 Design parameters

The position dilution of precision (PDOP) is usually computed at a point on the ground from

the relative position (and number) of the satellites in view at that point. Such a situation is

reversed during orbital computation in that a PDOP for a satellite depends on the relative

position (and number) of ground tracking stations (figure 7.1).

Figure 7.1: GPS orbit determination from IGS stations

In orbit determination, an identical set of observation equations is formed to standard GNSS

point positioning with, instead of n satellites with known coordinates being used to determine

the location of an unknown point on the surface of the Earth, n stations on the surface of the

Earth are being used to determine the unknown coordinates of a satellite.

For simulation purposes, for a single satellite, a design matrix A can be calculated using a GPS

precise ephemeris and the IGS station coordinates of stations visible at any one time. The

65

PDOP value for the determination of coordinates of that satellite at any one time can be

calculated directly from the variance-covariance matrix as below:

ZZYYXX QQQPDOP ++= (1)

where (X, Y, Z) is the position of GPS satellite, ZZYYXX QQQ ,, are the diagonal elements of the

variance-covariance matrix 1−= )( PAAQ T .

7.3 Simulations

Currently, there are eight Analysis Centre (AC) solutions contributing to the Final orbit

combinations. Each uses a different combination of IGS stations in its solutions, varying from

about 50 up to almost 200 stations. In this simulation, the 152 IGS stations used by the JPL

Analysis Centre have been taken as the basis for the orbital simulation (figure 7.1). It is notable

that only 2 stations contribute to the JPL orbital solutions in the Western Australian region.

The following assumptions regarding system specifications have been made in the simulation:

- GPS: 28 satellites (current status), dual frequency (L1 and L2) or triple frequency (L1,

L2 and L5);

- Galileo: 30 satellites, dual frequency (E1 and E5a) or triple frequency (E1, E5a and

E5b)

- Standard deviations for pseudorange and carrier phase observations are assumed as:

mPP 30021 .==σσ , mP 1005 .=σ ; mE 2001 .=σ , mbEaE 10055 .==σσ ; m0030.=φσ .

- Time interval: 300s

- Cut off angle:100.

PDOPS for both GPS and Galileo satellites have been simulated for a single day in November

2005 for the JPL ground station configuration and the same configuration with 16 additional

CORS stations situated in Western Australia included in the solution (figure 7.2). Satellites

were chosen to demonstrate the impact of the additional CORS sites on satellites situated in

different orbital planes. Therefore, simulation results are presented from GPS satellites PRN01

(plane slot F6), PRN03 (plane slot C2), PRN05 (plane slot B4), PRN10 (plane slot E3) and

Galileo satellites, PRN61 (plane slot B1), PRN71 (plane slot C1).

For each satellite, the ground track is illustrated, with the portion of the ground track to which

stations from Western Australia will contribute to the orbital solution highlighted in red,

accompanied by plots of the simulated number of tracking stations visible to each satellite over

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time and the associated PDOP over time. Again, the times when tracking stations from

Western Australia can contribute to the satellite coordinate solutions are highlighted on the

graphs in red. Plots are shown for both the JPL tracking station configuration and the enhanced

configuration for Western Australia. Finally, a graph showing the % improvement in PDOP

values of the satellites when the enhanced network is applied is given.

Figure 7.1: IGS stations (152) used by JPL analysis centre (as of Nov 2005)

Fig. 7.2: IGS stations used by JPL plus 16 additional stations in WA

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7.4 Results

Figures 7.3, 7.4, 7.5, 7.6, 7.7 and 7.8 illustrate the results from GPS satellites 1, 3, 5 and 10 and

Galileo satellites 61 and 71 respectively. It can be seen that the regional percentage

improvement in satellite PDOP can be routinely between 25 and 60% when a theoretical

densified WA CORS network of 16 stations is included in the orbital solution.

7.5 Discussion

The current philosophy at IGS Processing Centres involved in orbit computation is that it is not

the density of stations that is most important for high precision satellite orbits, but the

distribution of stations across the Earth. However, this philosophy is not borne out by actual

processing procedure, whereby a large number of sites from North America and Europe are

used in the orbital solutions whilst a sparse but evenly distributed network of sites is used

elsewhere. The question has to be asked: if station density is unimportant, why are dense

networks from Europe and North America used in orbital solutions? Coincidentally, all orbital

analysis centres are based in North America and Europe.

Once reason for limiting the number of stations included in orbital solutions is the time

required to process the large amounts of data. On this basis, processing centres such as JPL do

not include dense networks from other regions. It is unclear as to whether precise satellite

orbits are degraded in Australia relative to the rest of the world because of the sparse number

of CORS stations included in the orbital solutions and this is an area for future study.

However, the simulations presented here indicate that the inclusion of a dense WA CORS

network would at least improve the precision of precise orbits over WA. Therefore, CORS

networks in Australia could, in theory, contribute to a regional orbital solution which could be

more precise than the IGS orbital solution.

It is unlikely that much additional data from Australian reference stations will be included in

IGS orbital solutions in the near future. Therefore, it is the responsibility of the State and

National survey organisations to decide whether computing their own regional orbital products

would have national benefit. As mentioned above, further research is required in this area.

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Figure 7.3a GPS satellite track of PRN01 (Plane slot F6) on 16 Nov 2005 (JPL)

Figure 7.3b Number of visible IGS stations for PRN01 on 16 Nov 2005 (JPL)

Figure 7.3c PDOP values for PRN01 on 16 Nov 2005 (JPL)

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Figure 7.3d Number of visible IGS stations for PRN01 on 16 Nov 2005 (JPL enhanced)

Figure 7.3e PDOP values for PRN01 on 16 Nov 2005 (JPL)

Figure 7.3f % improvement of PDOP values for PRN01 on 16 Nov 2005 with JPL enhanced

configuration

70

Figure 7.4a GPS satellite track of PRN03 (Plane slot C2) on 16 Nov 2005 (JPL)

Figure 7.4b Number of visible IGS stations for PRN03 on 16 Nov 2005 (JPL)

Figure 7.4c PDOP values for PRN03 on 16 Nov 2005 (JPL)

71

Figure 7.4d Number of visible IGS stations for PRN03 on 16 Nov 2005 (JPL enhanced)

Figure 7.4e PDOP values for PRN03 on 16 Nov 2005 (JPL)

Figure 7.4f % improvement of PDOP values for PRN03 on 16 Nov 2005 with JPL enhanced

configuration

72

Figure 7.5a GPS satellite track of PRN05 (Plane slot B4) on 16 Nov 2005 (JPL)

Figure 7.5b Number of visible IGS stations for PRN05 on 16 Nov 2005 (JPL)

Figure 7.5c PDOP values for PRN05 on 16 Nov 2005 (JPL)

73

Figure 7.5d Number of visible IGS stations for PRN05 on 16 Nov 2005 (JPL enhanced)

Figure 7.5e PDOP values for PRN05 on 16 Nov 2005 (JPL)

Figure 7.5f % improvement of PDOP values for PRN05 on 16 Nov 2005 with JPL enhanced

configuration

74

Figure 7.6a GPS satellite track of PRN10 (Plane slot E3) on 16 Nov 2005 (JPL)

Figure 7.6b Number of visible IGS stations for PRN10 on 16 Nov 2005 (JPL)

Figure 7.6c PDOP values for PRN10 on 16 Nov 2005 (JPL)

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Figure 7.6d Number of visible IGS stations for PRN10on 16 Nov 2005 (JPL enhanced)

Figure 7.6e PDOP values for PRN10 on 16 Nov 2005 (JPL)

Figure 7.6f % improvement of PDOP values for PRN10 on 16 Nov 2005 with JPL enhanced

configuration

76

Figure 7.7a Galileo satellite track of PRN61 (Plane slot B1) on 16 Nov 2005 (JPL)

Figure 7.7b Number of visible IGS stations for PRN61 on 16 Nov 2005 (JPL)

Figure 7.7c PDOP values for PRN61 on 16 Nov 2005 (JPL)

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Figure 7.7d Number of visible IGS stations for PRN61 on 16 Nov 2005 (JPL enhanced)

Figure 7.7e PDOP values for PRN61 on 16 Nov 2005 (JPL)

Figure 7.4

7.7f % improvement of PDOP values for PRN61 on 16 Nov 2005 with JPL enhanced configuration

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Figure 7.8a Galileo satellite track of PRN71 (Plane slot C1) on 16 Nov 2005 (JPL)

Figure 7.8b Number of visible IGS stations for PRN71 on 16 Nov 2005 (JPL)

Figure 7.8c PDOP values for PRN71 on 16 Nov 2005 (JPL)

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Figure 7.8d Number of visible IGS stations for PRN71 on 16 Nov 2005 (JPL enhanced)

Figure 7.8e PDOP values for PRN71 on 16 Nov 2005 (JPL)

Figure 7.8f % improvement of PDOP values for PRN71 on 16 Nov 2005 with JPL enhanced

configuration

80

8. Simulation software The GPS Simulation software used in this project was originally written by Sandra Verhagen

at Delft University of Technology in the Netherlands and has been modified for the research

present in this report. A detailed description of the software operation can be found in the PDF

manual supplied with this report. The following are what have modified specially for the

project.

To run the programme it is necessary to be in the MATLAB environment2. Once in the

MATLAB, type ‘visual’ to run the main program ‘visual.m’. In the user interface, one can

choose various following options, such as:

RTK or VRS network;

ionosphere: weighted or baseline length (input 50km here); etc

In the source code of ‘visual.m’, go to line 1375 for setting up cases I-VI; from line 2589 the

set up for output plot contour maps using MATLAB is given, the result file is also output in

‘result.txt’ file which can be used for plotting figures in other software packages.

In order to run different cases of simulation, initial txt files have to be prepared and put in the

same directory as of the main program, the initial txt files include:

1) WAGeodetic.txt – for the coordinates of the existing geodetic CORS stations in WA;

2) WAUnifiedNew.txt – for the coordinates of the unified CORS network in WA;

3) WAUnified13New.txt – for the coordinates of enhanced unified CORS network in

WA;

4) WAPerth13.txt – for the coordinates of enhanced unified CORS network in WA;

5) WAPerth7.txt – for the coordinates of greater Perth Metropolitan region, 100km inter-

station distance;

6) WAPerth5.txt – for the coordinates of five station NRTK configuration for Perth

Metropolitan region;

7) yuma322.txt – GPS almanac file for the simulation date;

yumaGAL322.txt – Galileo almanac file for the simulation date.

2 www.mathworks.com