Journal of Global Positioning Systems (2004)
Vol. 3, No. 1-2: 173-182
Performance Evaluation of Multiple Reference Station GPS RTK for a
Medium Scale Network
T.H. Diep Dao, Paul Alves and Gérard Lachapelle
Department of Geomatics Engineering, University of Calgary, Canada
Tel: [phone] Fax: [phone] Email: [e-mail]
Received: 15 November 2004 / Accepted: 3 February 2005
Abstract. Carrier phase-based differential GPS is
commonly used for high accuracy RTK positioning
because it effectively reduces the effects of spatially
corrected errors such as orbital and atmospheric errors.
The spatially correlated error reduction is a function of
the correlated errors measured by the two receivers.
Carrier phase-based single reference station (SRS)
positioning is capable of providing cm accuracy for static
positioning and dm for kinematic positioning under
normal atmospheric conditions when the inter-antenna
distance is less than approximately ten kilometres.
However, under highly localized atmospheric activity,
and/or with a longer inter-antenna distance, the residual
differential error increases and the accuracy degrades.
The University of Calgary MultiRef™ multiple reference
station (MRS) approach uses a network of GPS reference
station to model the atmospheric conditions over a
geographic region to reduce correlated measurement
errors. This approach uses a conditional least-squares
adjustment to predict the errors in the network area. This
study focuses on an evaluation of the MultiRef™
approach relative to the single reference station (SRS)
approach in the observation, position and ambiguity
domains. Long-term and short-term convergence
accuracy tests are used to assess the effectiveness of the
approach. The network used for this assessment is
located in Southern Alberta, Canada. This is a medium
scale network with baseline lengths ranging from 30 to 60
km. The results show a minor to significant improvement
of the MRS method in all domains.
Key words: Multiple reference station GPS RTK, single
reference station GPS RTK, least squares collocation,
performance evaluation
1 Introduction
Single reference station (SRS) differential GPS RTK
performs well under normal atmospheric conditions when
the inter-antenna distances are less than ten kilometres,
providing centimetre level accuracy under ideal
conditions. However, under high atmospheric conditions
or with longer inter-antenna distances, the position
solution accuracy is degraded because of the decrease in
the spatial correlation of errors, namely ionospheric,
tropospheric and satellite orbit errors. This has led to the
development of multiple reference station (MRS)
differential approaches, which attempt to model the
spatial correlated errors over a regional network and
interpolate the corrections to rover positions (e.g.
Lachapelle & Alves 2002). This paper evaluates the
performance of the University of Calgary correction-
based least-squares collocation MRS approach, namely
MultiRefTM, relative to the traditional SRS approach.
Fully evaluating the performance of a MRS approach is a
difficult task due to the numerous parameters that affect
performance, the most important ones being network
configuration, atmospheric activities, and processing
options, if one assumes the use of high performance
receivers and unobstructed satellite availability. Network
features, such as the number of reference stations and
inter-receiver distances, directly affect the performance of
the MRS approach (e.g. Alves et al 2003). If the network
scale is too big, it can be difficult to resolve the network
ambiguities over long baselines and, as a result, the
corrections may be unreliable. It is also essential that the
rover be located within the region of the network. Alves
et al (2003) have shown that a network of four reference
stations surrounding the rover is an effective
configuration and the addition of extra reference stations
does not generally further improve the performance of the
MRS approach. Different levels of atmospheric errors
result in different levels of improvement. During quiet
atmospheric conditions, the errors are fairly constant over

174 Journal of Global Positioning Systems
the network area and the SRS approach can perform very
well. Under these conditions, the MRS approach may not
yield much improvement. However, under more active
atmospheric conditions associated with highly localized
atmospheric activities, the MRS approach is expected to
offer significant improvements because the errors are
better modelled using a network of reference stations.
The use of different processing options such as L1, dual
frequency wide lane (WL) and dual frequency
ionospheric free (IF) observables will lead to different
results because of the specific advantages and
disadvantages of each individual combination.
The focus of the analysis herein is on the improvement of
the MRS approach relative to the SRS approach in the
measurement domain, the long-term position domain and
the convergence performance under both quiet and fairly
active ionospheric conditions. A specific network
configuration is used, as described in the sequel. The next
section summarizes the theory of the correction-based
least-squares collocation MRS algorithm. The testing
methodology is then presented, followed by the
presentation and discussion of the results, and
conclusions.
2 Correction-Based Least-Squares Collocation
Algorithm
MRS algorithms are divided into two main categories,
namely the correction-based and tightly coupled
approaches. The correction-based approach uses
observations obtained at the reference stations to estimate
the spatially correlated network errors and then
interpolates these “corrections” to the rover position.
Numerous correction-based algorithms have been
developed using different approaches to interpolate the
corrections to the rover. These include the linear
combination algorithm (Han & Rizos 1996), the linear
interpolation algorithms (Gao et al 1997, Wanninger
1995), the Partial Derivative algorithm (Wübbena 1996)
and the least-squares collocation algorithm (Raquet
1998). Dai et al (2004) compared their performance and
concluded that they are more or less equal. The major
advantage of the correction-based approach is that, once
the corrections are generated and applied to the carrier
phase observables, existing standard single reference
station algorithms and software can be used to process the
corrected carrier phase observables. If this constraint is
removed however, a tightly coupled approach that uses
all observations obtained both at the reference stations
and at the rover in one filter can yield superior results
(Alves et al 2004).
The correction-based least-squares collocation approach,
used in MultiRef™ optimally estimates the network
corrections, based on the known coordinates of the
reference stations, assuming that the network ambiguities
are resolved (Raquet 1998, Alves et al 2003). It then uses
the covariance properties of the errors to predict the
estimated reference station double differential errors to
the location of the rover with the condition of minimizing
the sum of the differential error variances (Raquet 1998).
The correlated errors are spatially modelled over the
network region while the uncorrelated errors are filtered
out. A stochastic ionospheric modeling is used to
estimate the dual frequency slant ionospheric delays. The
correction vector l
ˆ
δat each reference station, and that at
the approximated rover position, denoted as r
l
ˆ
δ, are
computed as (Raquet 1998)
)NBl()BBC(BCl
ˆ1T
l
T
l∇∆−=δ − (1)
)NBl()BBC(BCl
ˆ1T
l
T
l,lr r
∇∆−=δ − (2)
where l
C is the covariance matrix of the reference
station observations, l,lr Cis the covariance matrix
between the rover observations and the reference station
observations, )
l
l
(B ∂
∇
∆
∂
=is the double difference
matrix, l is the vector of measurement-minus-true range
observables computed from the true coordinates of the
reference stations,
λ
is the carrier wavelength, and
N
∇
∆
is the vector of double difference ambiguities
between reference stations.
The signal covariance function used to define the
covariance matrices represents the stochastic behaviour
of the correlated errors that affect the measurements. It
therefore theoretically plays an important role on the
effectiveness of the MRS approach. Ideally, the
covariance function coefficients should be estimated
adaptively using real-time data (Fortes 2002, Alves
2004). However, previous results have shown that the
MultiRefTM corrections are not very sensitive to the
covariance function itself under a medium level of
ionospheric activity (Fortes 2002). The covariance
function used herein is a function of satellite elevations
and inter-reference receiver distances.
The corrections are applied to the observations of one
reference station, which is called the primary reference
station, in the form of single difference between the
station and the rover. These corrected observations are
then used at the rover in single reference station mode.

Dao et al: Performance Evaluation of Multiple Reference Station GPS RTK for a Medium Scale Network 175
3 Testing Methodology
The MultiRefTM software was evaluated in post mission
(but assuming real-time operation) using data collected
with five stations of the Southern Alberta Network (SAN)
located in Southern Alberta. The network configuration is
shown in Figure 1. Stations AIRD, COCH, STRA and
BLDM acted as reference stations. In the tests described
herein, the UOFC station located in the middle of the
network acted as rover. This is a medium scale network
with baseline lengths ranging from 30 to 60 kilometres.
The AIRD station, located 24 kilometres away from
UOFC, was chosen as the primary reference station. Two
dual-frequency 24-hour data sets with a 1 second data
rate collected on 24 May 2004 and 6 April 2004 were
used for testing. The ionosphere was normal and
relatively active, respectively, during these two days,
with a double difference effect of up to 5 ppm on the
active day.
The processing includes two steps: The first step is
running the MultiRefTM software using observations
collected from the above four reference stations to
generate network corrections. As the result, single
difference corrections for observations obtained at AIRD
are estimated using equations (1) and (2). In the second
step, the corrected AIRD observations, along with the
raw UOFC observations, are used in a single baseline
processing to estimate the UOFC position solutions, the
so-called MRS solutions. It is assumed that MultiRefTM
requires a certain time, e.g. 2 hours in these tests, for
initialization. The uncorrected AIRD observations are
also used in parallel to obtain the traditional SRS position
solutions for comparisons. An external commercial
software package, GrafNav Version 7.01, developed by
Waypoint Consulting Inc. is used for the single baseline
processing to provide independence. The software is
capable of epoch-by-epoch carrier phase based
differential processing using single frequency L1 and
dual frequency observations. Ionospheric-Free (IF) model
is used with dual frequency. In order to obtain the IF
ambiguities, the Wide Lane (WL) ambiguities are
resolved first and followed by the L1 and then L2
ambiguities. The processing options were setup to
attempt resolving ambiguities after 11.6 minutes using
single frequency L1 observations and after 4.6 minutes
using dual frequency observations. The ionosphere model
for single frequency processing option, which is the
satellite broadcast Klobuchar model, was not used. A 15
degrees elevation cut off was used.
Figure 1. Minimal Southern Alberta Network (MSAN) Configuration
4 Results and Analysis
4.1 Double Difference Network Corrections
In order to obtain an approximate measure of the
ionospheric activity in the region on these days, the local
ionospheric K values are shown in Table 1 for three-hour
intervals through out the 24-hour data sets. These values
are calculated based on observations of the magnetic field
fluctuations obtained at the MEA magnetometer station,
which is located approximately 300 kilometres away
from the UOFC station. Local K values theoretically
range from 0 (quiet) to 9 (extreme). A more active
ionosphere was observed during night-time, from 17:00
to 08:00 local time (00:00 - 15:00 UTC) than during
daytime, from 08:00 to 17:00 local time (15:00 – 24:00
UTC) on both days. On 24 May 2004, the ionosphere was
normal during night-time. Local K values of 3 to 4 were
observed. On 6 April 2004, local K values of 5 to 6 were
observed, indicating a more active ionosphere. A quiet
ionospheric condition was experienced during daytime on
both days with local K values of 2 to 3.
Double difference network corrections for different
combined observables are shown in Figures 2 and 3 for
24 May 2004 and 6 April 2004, respectively. These are
also the estimated double difference errors between
AIRD and UOFC. The RMS values are shown in red
separately for the active and quiet ionospheric periods of
these two days. For 24 May 2004, the RMS double
difference corrections on L1, L2 and WL observables
during the active ionosphere period are 3.3 cm (1.4 ppm),
5.4 cm (2.2 ppm) and 4.5 cm (1.8 ppm), respectively.
Over the baseline length of 24 km, these values are
reasonable. The GF (Geometric-Free) corrections are 2.3
centimetres representing ionospheric errors of
approximately 1 ppm. These corrections are smaller
during the quiet ionosphere period but not significantly.

176 Journal of Global Positioning Systems
The IF (Ionospheric-Free) corrections are small and
constant throughout the day, with a magnitude of 1 cm.
These corrections are mainly due to the tropospheric
residuals and noise.
Table 1: The local K values obtained at MEA geomagnetic station
located in Edmonton (approximately 300 km away from UOFC station)
Hour of
day
(UTC
time)
0
-
3
3
-
6
6
-
9
9
-
12
12
-
15
15
-
18
18
-
21
21
-
24
May 24,
2004
3 1 4 3 4 2 2 2
April 6,
2004
6 4 5 5 5 2 2 3
The network corrections are larger on 6 April 2004. This
is expected due to the more active ionosphere as
discussed. The estimated RMS value, for all errors on L1
observations, is 9.8 cm or 4 ppm over the 24 km baseline.
The GF corrections are 6.6 cm, equivalent to 3 ppm over
24 km baseline. These are mainly caused by the
ionosphere, which is fairly active. During daytime (quiet
ionosphere), the corrections are again smaller than the
ones obtained during night-time (more active ionosphere)
but are larger than the ones obtained during daytime on
24 May 2004. The correction variation correlates well
with the variation in the local K indices. The IF
corrections, with a magnitude of approximately 1.1 cm
for the entire day, show that the tropospheric residuals
were consistent.
Figure 2. Double difference network corrections for all satellites pairs
for 24 May 2004
Figure 3. Double difference network corrections for all satellites pairs
for 6 April 2004
The network ambiguities were resolved approximately 90
% of the time on both days. This suggests that the
ionospheric model was effective in estimating the double
difference slant ionospheric effects even under fairly
active conditions. The network corrections can be
considered reliable with such high percentage of fixed
ambiguities.
4.2 MRS Improvement in Observation Domain
Figures 4 and 5 show the AIRD-UOCF double difference
observable misclosures for 24 May 2004 and 6 April
2004, respectively. Both AIRD station and UOFC station
were fixed to their true coordinates for this analysis. The
misclosures calculated using the raw uncorrected AIRD
observations (SRS) are shown in red while the ones using
the corrected AIRD observations (MRS) are shown in
blue. A table at the bottom of each figure gives a
summary of the statistics.
The misclosures are generally larger for 4 April 2004.
This is due to the higher ionospheric error experienced on
that day. The MRS approach yields improvement relative
to SRS approach with the use of L1, L2, WL and GF
observables for both data sets. Higher level of
improvement is observed under higher ionospheric
condition. For example, MRS approach reduced the RMS
of the misclosures by 45 % for 6 April (high ionosphere)
compared to 35 % for 24 May 2004 (normal ionosphere).
However, MRS does not yield any improvement for IF
observables under either condition. This is because the
largest error, ionosphere, is eliminated in this case while
the double difference troposphere residuals and satellite
orbit error are small over the distance of 24 km.

Dao et al: Performance Evaluation of Multiple Reference Station GPS RTK for a Medium Scale Network 177
RMS (cm) SRS MRS Impr. (%)
C/A Code
L1 Phase
L2 Phase
WL
IF
GF
44.8
3.5
5.7
4.5
0.4
2.2
44.7
2.4
3.8
2.9
0.4
1.4
0
31
33
36
0
36
Figure 4. Double difference residuals for all satellites pairs - 24 May
2004
RMS (cm) SRS MRS Impr. (%)
C/A Code
L1 Phase
L2 Phase
WL
IF
GF
43.4
4.2
6.9
5.5
0.3
2.7
43.3
2.5
3.8
3.0
0.4
1.5
0
40
45
45
-33
44
Figure 5. Double difference residuals for all satellites pairs - 6 April
2004
4.3 Long-term Position Domain Improvement with
MRS
The single baseline AIRD-UOFC was processed to
estimate epoch-by-epoch UOFC position solutions using
the corrected and uncorrected AIRD observations. The
UOFC position errors and the ambiguity status using L1
observations for 24 May 2004 are shown in Figure 6. The
results with IF observables are shown in Figure 7. The
SRS solutions are shown in red and the MRS solutions in
blue. Statistics are given at the bottom of each figure for
both converging and steady state position errors.
RMS
(cm)
During Convergence
Position – 2 hours
Steady State
Position
E N H 3D E N H 3
D
SRS 8 16 18 26 7 5 12 15
MRS 9 6 11 15 5 4 7 9
%
Impr
-13 63 39 42 29 20 42 40
Figure 6. Position Accuracy in L1 mode after two hour network
initialization - 24 May 2004
The L1 position solutions are affected by the ionospheric
errors for both MRS and SRS cases. Compared to the
SRS approach, the MRS approach yields a significant 11
cm improvement, equivalent to 42 %, in the 3D
converging position accuracy during the first two hours.
The improvement is 6 cm, equivalent to 40 %, in the 3D
position accuracy after convergence. This shows that the
MRS approach effectively reduces the differential
ionospheric errors compared to the SRS approach under
normal atmospheric conditions. As a result, the L1
ambiguities are resolved faster in the MRS case.
The ionospheric-free (IF) position solutions shown in
Figure 7 are only affected by the tropospheric residuals,
multipath and noise. The L1 and L2 ambiguities are
therefore resolved very well in this case for both
approaches. The MRS approach performs slightly worse
by 2 to 3 cm during convergence. Both approaches offer a
similar 3D position accuracy of 3 cm after convergence.
This shows that, under quiet or normal atmospheric
conditions, the MRS and SRS approaches yield more or
less the same accuracy using IF observables, at least for
this medium scale network. This is not surprising because

178 Journal of Global Positioning Systems
there is no ionospheric impact while the tropospheric
error residuals are small in this case.
During Convergence
Position – 1 hours
Steady State
Position RMS
(cm)
RMS
(cm)
E N H 3D E N H3D
SRS 8 6 7 12 1 1 33
MRS 10 5 9 15 1 2 33
%
Impr
-25 17 -29 -25 No significant
difference
Figure 7. Position Accuracy in IF mode after 2 hour network
initialization - 24 May 2004
Similar analysis was carried out for the 6 April 2004 data
set. The UOFC position errors and the ambiguity status
using L1 observations are shown in Figure 8. The
statistics are provided for the first 15 hours of the day
during which the ionosphere was active and for the last 7
hours of the day during which the ionosphere was quiet.
The high level of ionospheric activity significantly
degrades the L1 SRS position solution accuracy to 150
cm. The MRS approach yields significant improvements
during this period, leading to a 3D position solution
accuracy of 51 cm, an improvement of 66%. However
these results still show that, during a relatively high level
of ionospheric activity, the spatial decorrelation of the
ionospheric effect is relatively rapid and the use of a
medium scale multiple reference network can only
improve the SRS method by a certain amount. The
ambiguities cannot be resolved for either cases and the
position solutions are estimated using the float
ambiguities. During the last 7 hours of the day (quiet
ionosphere), very accurate position solutions are obtained
with both SRS and MRS approaches. The 3D position
solution errors are less than 10 cm. The MRS approach
shows a small improvement of 1cm centimetre during
this period.
High Ionospheric
Activity –
First 15 hours
Low Ionospheric
Activity –
Last 7 hours
Posit
-ion
RMS
(cm) E N H 3D E N H 3D
SRS 65 88 102 150 2 3 6 7
MRS 21 18 43 51 3 2 5 6
%
Impr
68 80 58 66 -
50
33 17 14
Figure 8. Position Accuracy in L1 mode after two hour network
initialization - 6 April 2004
High Ionospheric
Activity –First 15
hours
Low Ionospheric
Activity –
Last 7 hours
Positi
-on
RMS
(cm)
E N H 3D E N H 3D
SRS 11 11 13 20 1 1 2 3
MRS 7 7 11 15 3 2 3 5
%
Impr
36 36 15 25 Not significant
Figure 9. Position Accuracy in IF mode after 2 hour network
initialization for 6 April 2004

Dao et al: Performance Evaluation of Multiple Reference Station GPS RTK for a Medium Scale Network 179
Figure 9 show the UOFC position errors when using IF
observables collected on 6 April 04. The ionospheric
error is, again, eliminated in this case, resulting in a
considerable improvement in position solution accuracy
compared to the L1 solution. During the active
ionospheric period, the SRS approach yields a 3D
position accuracy of 20 cm. These statistics are calculated
including the convergence period. The MRS approach
yields an improvement of 15 % to 36 % for all easting,
northing and height solutions, leading to a 5 cm (25 %)
improvement in the 3D position solution accuracy.
During the quiet ionospheric period, very accurate
position solutions are obtained for both approaches and
again, there is no significant difference between the two
approaches.
4.4 MRS Improvement in Solution Convergence
Each of the 24 hour data set was divided into 24 1 hour
segments, which were processed independently with
GrafNav using L1 observations for both the MRS and the
SRS approaches. MultiRefTM was setup to generate
network corrections from the beginning to the end of each
24 hour data set without being reset. The 3D UOFC
position errors for the 24 segments of 24 May 2004 are
presented in Figure 10. The SRS solutions are in red and
the MRS solutions in blue. For most of the segments, the
MRS approach convergences faster and provides more
accurate converging position solution accuracy. The
improvement is noticeable during the periods of high
ionospheric activity. Under quiet ionospheric conditions,
there is an inconsistency in MRS improvement. For
example, during the periods of 11:00-12:00 and 12:00-
13:00 (Hours 19 and 20), the MRS approach performs
worse than the SRS approach. Conversely, MRS yields
better results during periods of 07:00-08:00 and 08:00-
09:00 (Hours 15 and 16). However, the differences are
not very significant. Moreover, the low level of
ionospheric errors makes the ambiguities easier to resolve
when using the SRS approach.
Figure 11 shows the averaged 3D position errors and
averaged position component errors for the 24 segments.
The MRS approach offers a significant improvement of
50 % on average for the L1 position solution accuracy
during convergence. Figure 12 shows the maximum 3D
position errors and the maximum errors in the three
position components of the 24 segments, respectively.
Improvement is observed in reducing the maximum
position solution errors during the convergence time
when the MRS approach is used.
Figure 10. Convergence Analysis: 3D position errors in L1 mode for 24
1-hour data segments - May 24, 2004
Figure 11. Convergence Analysis: Average 3D position component
errors in L1 mode of 24 1-hour data segments - May 24, 2004

180 Journal of Global Positioning Systems
Figure 12. Convergence Analysis: Maximum 3D and position
component errors in L1 mode for 24 1-hour data periods - May 24, 2004
A similar convergence analysis was carried out using the
data collected on 6 April 2004. The results are presented
in Figures 13 to 15 in a similar way to the ones for 24
May 2004. Compared to 24 May 2004, the ionosphere
was more active for the first 15 segments. As a result, a
very poor performance in convergence is obtained for the
SRS approach. The MRS approach yields much faster
convergence during these segments. Under the quiet
ionospheric period, the MRS still results in better
convergence for most of the segments in this case. On
average, approximately 60 % to 70 % improvement is
shown with the use of MRS approach. For most of the
segments, the ambiguities cannot be resolved after one
hour. Comparisons between the SRS and MRS solutions
in maximum position solution errors during convergence
are presented in Figure 15. The SRS approach suffers a
maximum error of up to several metres occurred during
period 19:00-20:00, due to the ionospheric error. The
peak is removed when the MRS approach is used, making
the latter more reliable.
Corrections generated during network initialization were
used in the first segment for each data set. Interestingly,
there is not much impact observed in both cases and the
MRS approach yields improvement from the early
beginning of the two first segments. Based on these
limited results, it would appear that background network
ambiguity convergence is not a major issue.
Figure 13. Convergence Analysis: 3D position error in L1 mode for 24
1-hour data periods -April 6, 2004
Figure 14. Convergence Analysis: Average 3D and position component
errors in L1 mode of 24 1 hour data periods - April 6, 2004

Dao et al: Performance Evaluation of Multiple Reference Station GPS RTK for a Medium Scale Network 181
Figure 15. Convergence Analysis: Maximum 3D and position
component errors in L1 mode for 24 1-hour data periods - April 6, 2004
The data sets used here have also been used by Alves and
Lachapelle (2004) to compare the performance of three
differential RTK approaches, namely SRS, MRS
correction-based least-squares collocation and MRS
tightly coupled approaches. The entire processing of the
network and rover data was carried out using MultiRef™.
Under low ionospheric conditions (24 May 2004) the
position solution accuracy obtained using the MRS
correction-based approach is the same as reported here.
Under higher ionospheric conditions, the position
accuracy is better by only a few centimetres. This shows
full compatibility between the two evaluation approaches.
5 Conclusions
The MultiRefTM correction-based approach yields minor
to significants improvements relative to the traditional
single reference station approach in the observation,
position and ambiguity resolution domains when using a
medium scale network under the atmospheric conditions
reported for these data sets. In the position domain, the
MRS approach not only offers more accurate position
solutions after convergence but also faster and more
accurate solutions during convergence. The level of
improvement, however, depends very much on the
magnitude of the atmospheric errors and on the selection
of observables. The MRS approach yields the most
improvement under active ionospheric conditions using
L1 observables due to its capability to model the spatially
correlated errors. However, this advantage is reduced in
this case when ionospheric-free observables are used or
when the atmospheric errors are constant over the region.
It remains to be seen as to whether the MRS method
would yield significantly better results for a larger scale
network when using ionospheric-free observables. More
studies on the impact of using different network
configurations and of the network initialization will be
carried out in the near future.
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