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.
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.
Corresponding
Members: Changdon Kee (KOREA)
Single-based real-time
kinematic GPS positioning systems over medium-range, e.g. 10-50km have been
investigated. The distance dependent errors, e.g. ionosphere and troposphere,
have been included into the functional model. The capability of long-range RTK
system has been reported to extend to 35km from Leica and 40km from Thales
Navigation.
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/). In order to characterize the
ionosphere’s vertical profiles and subsequently further improve the ionosphere
modeling accuracy, a three-dimensional ionosphere modeling method has also
recently been developed based on tomography techniques. Preliminary research
results based on carrier smoothed code observations have indicated that over
90% ionosphere delays in GPS measurements could be recovered by the proposed 3D
tomographic model. 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. Also numerical
weather prediction has proven to contribute to the estimation of the
tropospheric delay.
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.
Another new development is the carrier phase-based positioning system
without requiring base receiver. It differs from current RTK systems since the
positioning is based on the processing of un-differenced carrier phase
observations from a single receiver. Although it does require the support of
precise GPS orbit and clock data, it doesn’t requires the use of any base stations
so that no longer limited by the vicinity requirement of a rover receiver to
the base receiver as the case in current RTK positioning. The results have already demonstrated
position accuracy at 10cm-level after the convergence of the float ambiguities
or fixing of the integer ambiguities. Fast un-differenced ambiguity convergence
and resolution is a challenge to develop this type of high precision
positioning systems and it requires strong collaborations among international
researchers in the field.
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 which the
user does not require calibrated templates.
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-RTKTM 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.
The stochastic behaviours of the residuals in un-differenced carrier
phase observations using single GPS receiver without a base receiver has been investigated.
The correlation analysis results indicated high correlations among the receiver
clock, the height position component and the tropospheric parameter. The residual error influence on the point
determination has also been assessed and different stochastic processes have
been implemented for positioning under different environments from static to
highly dynamic situation.
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. Moreover an inverse integer Cholesky decorrelation method and the
Lenstra, Lenstra and Lovasz (LLL) method have also been proposed. 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-RTKTM 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.
Fast
ambiguity convergence and resolution for high precision single GPS receiver
positioning system has been investigated. Since un-difference carrier phase
contains various residual errors including a non-zero initial phase bias, the
ambiguity resolution problem becomes much more difficult compared to the
traditional double difference ambiguity resolution. A pseudo ambiguity fixing
algorithm has been developed based on a partial ambiguity search and fixing
strategy and more research is currently underway.
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.
The high precision
positioning system using one dual frequency GPS receiver without base receiver
has been developed, in which the precise orbit and precise satellite clock are
required. The commercial products or development reports have been released
from NAVCOM, Thales Goesolution and Fugro. However the long converge time to
10cm centimeter is an obstacle for some applications and
With the new development of
GPS modernization, Galileo and Glonass systems, the wide area error modelling
for precise satellite positioning will be significantly improved.