## SPECIAL
STUDY GROUP 1.179:

## "WIDE AREA MODELLING FOR
PRECISE SATELLITE POSITIONING"

**
**

**Introduction**

Precise
satellite positioning requires that carrier phase data be used and
that the integer ambiguities associated with the carrier phase
measurements be resolved in some way. However, the distance from the
user receiver to the nearest reference receiver may range from a few
kilometres to hundreds of kilometres. As the receiver separation
increases, the problems of accounting for distance-dependent biases
increase, and reliable ambiguity resolution for carrier phase-based
satellite positioning becomes an even greater challenge.

'Wide
area modelling' for precise satellite positioning requires either long
observation spans to estimate all biases in the functional model, or
multiple reference stations. For the first approach, all error
sources, such as orbit bias, atmospheric parameters, receiver
inter-channel biases, along with the user’s trajectory, should be
estimated simultaneously. This is the approach used
for geodetic static positioning (e.g., IGS-based site coordinate
determination, and precise GPS orbit determination). The second
approach provides more opportunities to either estimate the different
biases individually and then apply interpolated biases (at the user
location) to the measurements, *or* generate a so-called 'virtual
reference station', by using the data from a multiple reference
station network. Some of the concepts have been studied in the past by
previous IAG SSGs, both separately and in combination, and with
respect to various applications. In 1999 the IAG established SSG
1.1.79 to focus on investigations of the GPS functional model, the
stochastic model, and ambiguity resolution procedures. The
website of the Special Study Group 1.179 is http://www.gmat.unsw.edu.au/snap/gps/iag_section1/ssg1179.htm.

**Objectives
of the SSG 1.179**

1.
Error
modelling through the improvement of functional models for
medium-range, and long-range high precision satellite positioning
using multiple reference stations, including:

·
multipath
mitigation algorithms,

·
troposphere
model refinement,

·
regional
ionosphere modelling algorithms,

·
orbit
bias modelling,

·
parametric
modelling algorithms (for each error source), and

·
integer
bias estimation and validation, e.g. cycle slip detection/repair and
ambiguity resolution.

2.
Error
modelling through stochastic model refinement, including:

·
correlation
analysis of carrier phase measurements from satellite positioning
systems,

·
stochastic
modelling algorithms suitable for post-processing applications, and

·
stochastic
modelling algorithms suitable for real-time applications.

3.
The
continued study of ambiguity resolution techniques in order to
develop:

·
more
efficient means of searching integer ambiguities, and

·
validation
procedures for ambiguity resolution.

4.
The
application of these improvements to:

·
short-range
satellite positioning applications,

·
differential
correction generation from multiple reference GNSS receiver network,
in support of medium-range high precision navigation,

·
precise
long-range GPS kinematic positioning, and

·
sub-centimetre
engineering applications, e.g. construction deformation monitoring,
volcano monitoring, etc.

**Members
and Corresponding Members
**

**
**

Members:
Shaowei Han (Chair, USA), Oscar Colombo (USA), Paul Cross (UK), Paul
de Jonge (U.S.A), Hans-Jürgen Euler (SWITZERLAND), Yanming Feng
(AUSTRALIA), Yang Gao (CANADA), Yongil Kim (KOREA), Donghyun Kim
(CANADA), Dennis Odijk (THE NETHERLANDS), Günter Seeber (GERMANY),
Dariusz Lapucha (USA), Jingnan Liu (CHINA), Nigel Penna (AUSTRALIA),
Rock Santerre (CANADA), Julia Talaya (SPAIN), Jinling Wang
(AUSTRALIA), Xinhua Qin (USA), Peiliang Xu (JAPAN).

Corresponding
Members: Changdon Kee (KOREA)

**Activities
of the SSG1.17**9

** Error
Modelling Through Improvement of Functional Models**

Error
modelling through the improvement of functional models for
medium-range, and long-range high precision satellite positioning
using multiple reference stations includes the study of topics such as
multipath mitigation, troposphere modelling, regional ionosphere
modelling, and orbit bias modelling. These biases could be estimated
individually through some special approaches, or by setting different
parameters in the functional model for the different error biases.

Absolute
field calibration of GPS antennas is based on the controlled antenna
motion of a robotic arm, and is now a mature calibration technique.
The technique can be used to calibrate all antennas in a multiple
reference station network. With (absolutely) calibrated antennas it is
possible to separate phase centre variations and multipath. An
approach for multipath calibration based on controlled antenna motion
was proposed.

Investigations into the use of 'semi-parametric least squares' for the
mitigation of systematic errors in GPS processing have been conducted.
Current focus is the lumping together of all systematic errors as a
single smoothing function, estimated over the processing session.
Initial results from a 'short' 30km baseline are encouraging, and
tests have commenced on more data sets.

An adaptive Finite-duration Impulse Response filter, based on a
least-mean-squares algorithm, has been developed to derive a
relatively noise-free time series from continuous GPS results. This
algorithm is suitable for real time applications. Numerical simulation
studies indicate that the adaptive filter is a powerful signal
decomposer, which can significantly mitigate multipath effects.

Increased
use has been made of ionospheric regional modelling to improvement
on-the-fly ambiguity resolution over long distances, as part of
initiatives within the GEOIDE project (website: www.scg.ulaval.ca/gps-rs/). Ionospheric tomography has also been used to help resolve GPS
ambiguities on-the-fly at distances of hundreds of kilometres during
increased geomagnetic activity. An approach, referred to as the
"grand solution", which estimates orbit, refraction, and
local bias error states, along with the uer's trajectory, was
proposed. The modelling and estimation of the tropospheric zenith
delay, both for more accurate real time and post-processed navigation,
and for rapid and precise meteorological updates, has been
implemented.

With
respect to Real-Time Kinematic (RTK) positioning using multiple
reference stations, the results of a survey conducted by Dr. Euler,
Chair of the RTCM SC104 Working Group "Network RTK", of
working group members found:

The expected RTK accuracy could be at sub-decimetre to
centimetre level (one sigma).

The reference station distances should be of the order of
50-70 km for centimetre accuracy, or about 200 km and above for
decimetre accuracy.

The size of a reference station area should be of the
order of 500 km x 500 km. However, target could be nationwide to
continentwide coverage.

The medium for distribution of data could be
unidirectional techniques (Broadcast like UHF, VHF, TV, DARC, etc) or
bi-directional techniques (GSM, UTMS, etc.).

The baud rates for transmission are from 2400 Baud
upwards, including 1Hz observation data.

The tolerated latency is up to 10 seconds without SA, or
up to 2 seconds with SA. However, the orbit information can be delayed
by up to 120 seconds, ionosphere by up to 10 to 60 seconds,
troposphere by up to 30 seconds. The real-time positioning output is
expected within 100 milliseconds.

The requirement for reference station equipment is
dual-frequency receivers with clear sky view.

With
regards to GPS/Glonass surveying and navigation applications using
multiple reference stations, a new method was proposed, in which the
distance-dependent biases have been separated into the
frequency-dependent errors (ionospheric bias) and
frequency-independent errors (e.g. troposphere bias and orbit bias).
The separate estimates of the two types of errors, which are generated
from the carrier phase measurements using the multiple reference
stations, can be used to model the user distance-dependent biases for
L1, L2 carrier phase and pseudo-range measurements in different ways.

**Error
Modelling Through Stochastic Model Refinement**

High
quality estimation results using least squares require the correct
selection of the functional *and* stochastic models. The
stochastic model should represent the statistical characteristics of
the modelling errors. It is dependent on the choice of observation
functional model, hence for a different choice of functional model, a
different stochastic model may be needed. For example, if the
ionospheric delay is considered an unknown parameter in the functional
model, the modelling errors will not include the residual
(double-differenced) ionospheric bias, and hence they will more likely
have random properties.

The
SIGMA-D
model has been developed for stochastic modelling of GPS signal
diffraction errors in high precision GPS surveys. The basic
information used in the SIGMA-D
model is the measured carrier-to-noise power-density ratio (C/N0).
Using the C/N0 data and a template technique, the proper variances are
derived for all phase observations. Thus the quality of the measured
phase is automatically assessed and if phase observations are
suspected of being contaminated by diffraction effects they are
downweighted in the least-squares adjustment. An extended weight model
for GPS phase observations was also proposed.

Mathematical
and statistical modelling has also been investigated. Using a
multipath estimation method based on the signal-to-noise ratio and an
elevation-dependent stochastic model, the height accuracy of a typical
RTK session has been improved by approximately 44% and the fidelity of
quality measures has been increased.

A stochastic assessment procedure has been developed to take into account
the heteroscedastic, space- and time-correlated error structure of the
GPS measurements. Test results indicate that by applying the
stochastic assessment procedure developed , the reliability of the
estimated positioning results is improved. In addition, the quality of
ambiguity resolution can be more realistically evaluated.

Magellan's
new product Instant-RTK^{TM} has reportedly overcome the
functional and stochastic modelling problem through empirical
knowledge and a real-time learning procedure which can used to adapt
the model when the environment is changing.

On
the other hand, the stochastic modelling approach has been applied to
the parameters in the functional model. For example, the residual
ionospheric delay after applying ionospheric delay corrections could
be accounted for through processing the residual ionospheric delay
correction as stochastic observables.
The stochastic model to be applied for the corrections could be
provided by multiple reference stations. First results show indeed an
enormous improvement in the success rate of ambiguity resolution.

**Continued
Study of Ambiguity Resolution Techniques**

GPS
ambiguity resolution (AR) techniques have been intensively
investigated. The integer ambiguity searching techniques have been
dramatically improved over the last decade, especially by the
contribution of the LAMBDA method. However, it has to be recognised
that all search algorithms are likely to result in identical integer
ambiguity candidates under comparable setups, e.g. using like search
windows/volumes and similar parameters. Continued study is now focused
on AR in integrated systems: GPS, Glonass, pseudolite or other
systems, and more powerful validation criteria to ensure correct
ambiguity resolution.

For
example, Magellan's new product Instant-RTK^{TM} appears to
have successfully addressed the functional and stochastic modelling
problem through empirical knowledge and a real-time learning
procedure. A series of validation criteria have been implemented, in
addition to the commonly used ratio test, which can be adapted based
on the reliability requirements, number of satellites, observation
time and baseline length. The Instant-RTK validation criteria have
successfully traded off the requirements of observation span on the
one hand, and RTK solution reliability on the other. Moreover, the
algorithm to detect, identify and adapt the outliers to guard against
incorrect integer ambiguity determination has been implemented, and
the success rate of AR has been increased significantly.

Leica
Geosystems' System 500 has implemented a repeated search processing
technique to shorten ambiguity initialisation time and to improve AR
reliability, especially in difficult environments. This method repeats
its internal determination of the integer ambiguity using
significantly shorter observation times. Once the AR algorithm has
verified that they are identical, the system can output its
coordinates.

On the theoretical side, a method was proposed to evaluate the
probabilities of correct integer estimation based on the variance
matrix of the (real-valued) least-squares ambiguities. These success
rates are given for the ambiguity estimator that follows from integer
bootstrapping. Although less optimal than integer least-squares,
integer bootstrapping provides useful and easy-to-compute
approximations to the integer least-squares solution. In a similar
manner, the bootstrapped success rates provide bounds for the
probability of correct integer least-squares estimation.

**New
Development and Future Trends**

In
the next few years, more commercial system will be developed to
generate corrections from multiple reference stations for surveying
and precise navigation applications. RTCM SC104 Working Group
"Network RTK" will propose a new format to transmit
correction information from multiple reference station networks. This
is not only beneficial to RTK systems, but also to single-frequency,
low-cost GPS systems. Moreover, once the additional civilian frequency
is transmitted by Block IIF satellites, the wide area error modelling
for precise satellite positioning will be significantly improved.

**
**