Journal of Global Positioning Systems (2005)
Vol. 4, No. 1-2: 144-150
Development of Navigation Algorithm to Improve Position Accuracy
by Using Multi-DGPS Reference Stations’ PRC Informati on
Kyung Ryoo n Oh
KARI, 45 Eoeun-dong Yuseong-gu Daejeon Rep. Of Korea
e-mail: [e-mail] Tel: [phone]; Fax: [phone]
Jong Chul Kim
KARI, 45 Eoeun-dong Yuseong-gu Daejeon Rep. Of Korea
e-mail: [e-mail] Tel: [phone]; Fax: [phone]
Gi Wook Nam
KARI, 45 Eoeun-dong Yuseong-gu Daejeon Rep. Of Korea
e-mail: [e-mail] Tel: [phone]; F ax: [phone]
Received: 6 December 2004 / Accepted: 20 October 2005
Abstract. In this paper, the linearly interpolated PRC
(Pseudorange Correction) regenerating algorithm was
applied to improve the DGPS positioning accuracy at
user's position by using the various PRC information
obtained from multi-DGPS reference stations. The
unknown user's position can be calculated from the
regenerated PRC which can be expressed as the linear
combination of multi-DGPS reference station's known
position an d PRC values of common satellit e from multi-
DGPS reference stations. Two sets of 3 DGPS reference
stations were selected to compare the performance of the
linearly interpolated PRC regenerating algorithm. To test
the performance, linearly interpolated PRC regenerating
algorithm adopted multi-channel DGPS receiver was
developed. The results show that the DGPS positioning
accuracy is improved by about 40% and with the
modification of the navigation solution software of
GBAS receiver, GBAS positioning accuracy
improvement is expected without any modification of
GBAS reference station's equipment.
Key words: Multi-DGPS coverage, weighting
coefficients, Multi-PRC values, linearly in terpolated PRC
generating algorithm
1 Introduction
Since 1994, Korea Aerospace Research In stitute has been
conducting the research on the GBAS (Ground Based
Augmentation System) for precision approach and
landing of aircraft based upon the concept of CNS/ATM
(Communication Navigation Surveillance/Air Traffic
Management). As the results of this research, Korea
Government has developed a plan to install GBAS at
each domestic airport for the safety of civil airlines. If the
Government’s plan is implemented, around the
metropolitan area, especially around Seoul, multi-GBAS
environment will be established considering the
minimum GBAS service coverage as 23NM (Nautical
Mile).
The PRC information of each GPS satellite is no t varying
rapidly; it is possible to assume that the variation of PRC
information of each GPS satellite is linear. So the linearly
interpolated PRC regenerating algorithm can be applied
to improve the DGPS positioning accuracy at user's
position by using the various PRC information obtained
from multi-DGPS reference stations.
The user’s position can be calculated from the
regenerated PRC which can be expressed as the linear
combination of multi-DGPS reference station’s known
position an d PRC values of common satellit e from multi-
DGPS refer ence stations.
To test the performance of the linearly interpolated PRC
regenerating algorithm, maritime DGPS reference

Oh et al.: Development of Navigation Algorithm to Improve Position Accuracy 145
stations’ PRC data were used in RTCM format. 11
maritime DGPS reference stations and 1 inland DGPS
reference station are in service since 1999. Two sets of 3
DGPS reference stations are selected to compare the
performance of the linearly interpolated PRC
regenerating algorithm. The DGPS positioning accuracy
was dramati ca ll y improved by about 40%.
Even though common PRC was extracted from the
RTCM format, the suggested PRC regenerating algorithm
in this paper can be applied to improve the DGPS
positioning accuracy in GBAS for civil aviation.
With the change of the navigation solution software of
the GBAS receiver, GBAS positioning accuracy
improvement is expected without any modification of
GBAS reference station’s equipment.
Palmido
Sochongdo
Cho jin
Ochongdo
Chumundo
Marad
o
Sohuksando
Yongdo
Changgigot
Ullungd o
Chumunjin
Daejeon
Dead-zone Area
Mu Joo
Fig. 1 MOMAF DGPS reference stations in Ko rea (Jun. 2004)
2 Maritime DGPS reference stations in Korea
Korean Government, Ministry of Maritime Affairs and
Fisheries (MOMAF), has started DGPS service from
1999 by the IMO (International Maritime Organization)
recommendation of using GNSS in maritime navigation.
MOMAF will extend its DGPS infra structure into the
inland to establish nationwide DGPS (NDGPS) system
by 2006. (Jong Chul Kim, 2002)
In 2004, the first inland DGPS reference station of
MOMAF start to provide DGPS service (See the right of
Figure 2). 5 more inland DGPS reference stations will be
constructed by 2006 to get rid of the dead zone area as
shown in Figure 1. So the multiple coverage area will be
increased.
3 Navigation solution usi n g multiDGPS information
Due to the characteristics of the GBAS, somewhat
extensive network of DGPS reference stations need to be
established. In the GBAS coverage, it is possible to
receive valid corrections from a number of stations.
Within a multiple DGPS referen ce station solu tion , all th e
pseudo-range corrections received from pre-selected
reference stations are used to position the mobile station.
There are a number of different approaches to providing
such a solution.
Fig. 2 MOMAF DGPS service coverage (left) and Muju DGPS s e rvice
coverage (right)
z Position domain approach (See the left of Figure 3):
This is the simplest approach which computes an
independent position using each reference station
from which corrections are received. The resultant
positions are later combined by taking a weighted
average.
z Centroid approach (See the middle of Figure 3 ): The
pseudo-range corrections from all reference stations
are combined to form one correction for each
satellite in view. This correction should fit the
centroid of the area defined by the reference stations
that are used. Additional directional corrections can
also be developed by examining the correlation
between the composite centroid corrections and
those at particular reference stations. The pseudo-
range corrections for the centroid can be generated

146 Journal of Global Positioning Systems
either at a land-based hub or at the mobile station
itself. T he advan tage of the fo rmer is that the mobile
station needs only to receive one set of pseudo-range
corrections.
z All-in-view approach (See the right o f Figure 3): All
the pseudo-range corrections received from the
reference stations are incorporated into one
positioning solution with no pre-processing (except
for validity checks). For instance, the correction for
satellite PRN 12 may be received from 4 different
reference stations and will be used separately to
correct the pseudo-range observed at the mobile
station from PRN 12 - thus adding 4 observations to
the system.
Fig. 3 The positioning methods us ing multi-DGPS references
Fig. 4 Linear interpolation of the PRC from two DG P S Reference stations
3.1 Developing the linearly interpolated P RC
regenerat i n g al g o r i t h m
In developing the linearly interpolated PRC regenerating
algorithm, there are some basic assumptions:
a. The user only uses the common in view
satellites to calculate hhe positions for both
sides of the user and reference stations.
b. At least, 4 common satellites exist between the
user and reference stations.
c. The variation of the correction data of a
satellite is small enough to assume that the
characteristic of the PRC variation for each
satellite is linear.
 PRC linear interpolating Algorithm:
In Figure 4, the user will be at user1 or user2, 3 location
between DGPS reference station x and station y. The
DGPS correction(PRCx,i , PRCy,i, i=1,2,..n) value of
common satellite is not the same, so there is a gradient of
the DGPS correction value for the common satellite
between the DGPS reference stations. If the user can use
this gradient information, more precise position
information is achievable. (Loomis et al., 1995)
The unknown user’s position (longitude, latitude) can be
calculated from the regenerated PRC which can be
expressed as the linear combination of multi-DGPS
reference station’s known positions and the PRC values
of the common satellite from the multi-DGPS reference
stations. (Hong, 1990)
The unknown user’s position can be expressed by using
the relative geometry information of the stations. (van
Essen et al., 1997)

Oh et al.: Development of Navigation Algorithm to Improve Position Accuracy 147
Fig. 5 Geometry relation betw ee n t he user and DGPS reference station’s
locations
nni
n
iixaxaxaxaxax ++++== ∑
=
...
332211
1 (1)
nni
n
iiyayayayayay ++++== ∑ =
...
332211
1 (2)
n
n
iiaaaaa ++++== ∑ =
...1 321
1 (3)
Let’s assume that the number of reference stations is r,
marks as nr, and the number of satellites in line of sight is
s, marks as ns. And each reference station observes the
same GNSS satellites, but the PRC values of specific
satellites differ from the DGPS reference stations. Then
the linearly interpolated PRC(ij
∇ ,i=1,2,...ns, j=1,2,..nr) at
the user’s spot can be expressed as:
)()( 211 yyaxxa j
i
j
iiij−+−+∇=∇ (4)
In the above equation, xi is the latitude yi is longitude
respectively in WGS-84. The parametersi
a1and i
a2 are
the coefficients of a plane which contains all the DGPS
reference station coordinates.
For the case of using 3 DGPS reference stations,
Equation 4 can be written as the following matrix format:
⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
∆∆
∆∆
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∇−∇
∇−∇
2
1
33
22
13
12
a
a
yx
yx
ii
ii
(5)
Or,
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∇−∇
∇−∇
⎥
⎦
⎤
⎢
⎣
⎡
∆∆
∆∆
=
⎥
⎦
⎤
⎢
⎣
⎡−
ii
ii
yx
yx
a
a
13
12
1
33
22
2
1 (6)
Where 1
xxx jj
−
=
∆
, 1
yyy jj −=
∆
For the case of using more than 4 DGPS reference
stations, the above equations can be written as in general
format (van Essen et al., 1997):
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
∇−∇
∇−∇
∇−∇
∇−∇
=
⎥
⎦
⎤
⎢
⎣
⎡−
ii
r
ii
ii
ii
TGG
a
a
1
14
13
12
1
2
1)(
#
(7)
Matrix G is a set of known coordinate information of the
DGPS reference stations. On the right side of Equation 7,
[ii
j1
∇−∇ ] (i=1,2,...ns, j=1,2,..nr) term value can be
determined using the measurement of PRC information
from each DGPS reference station.
With the values for a1 and a2, the linearly interpolated
PRC (ij
∇) can be determined using Equation 4.
 Generating linearly interpolated PRC :
In Figure 6, GPS time in GPS raw data and Modified Z
count in DGPS information are compared to check if the
data is time synchronized with each other or not. If data is
time synchronized, the common satellite number in the
data from the Reference Stations is checked. If the
number of common satellites is less than 4, the data will
be discarded and the next epoch data will be used.
If more than 4 common PRC data exist, the procedure
moves to next step. To get the linearly interpolated PRC
information, input the user’s position into the linearly
interpolated PRC regenerating algorithm. Then PRC
linear interpolating algorithm will regenerate the new
PRC value.
Fig. 6 Diagram of extracting c ommon PRC and generating linearly interpolate d P R C

148 Journal of Global Positioning Systems
The next procedure to get the DGPS position is explained
in Figure 7. In this procedure, the number of common
satellites is critical. If the common satellite number is
more than 4, the regenerated PRC will be input into the
DGPS navigation solution algorithm based on the carrier
smoothed algorithm (Park et al, 2003).
3.2 Analysis t he effect of the linearly interpolated
PRC
 Phase I :
In phase I analysis, the PRC information of Multi DGPS
station gathered through the landline. Each maritime
DGPS reference station stored the broadcasted DGPS
information every 5 sec. So the analysis was carried out
as a post proce ss i ng.
To analyse the effect of the linearly interpolated PRC
algorithm, three sets of DGPS reference stations
combination were used. There are 4 DGPS reference
stations in the first set, 3 in the second set, 2 in the third
set.
As a result of phase I analysis, the second set shows the
best results. Comparing the position accuracy with the
stand alone DGPS reference station, an average of 33%
improvement was achieved. Table.1 shows the results of
the analysis of the second set.
In the case of using 2 DGPS reference stations’ PRC
information, the DGPS position accuracy was 1.8m.
Other case of using 3 DGPS reference stations’ PRC
information, the DGPS positioning was 0.788m and
1.164m depending on which combination of DGPS
reference stations used. The last case of using 4 DGPS
reference stations’ PRC information, the worst result
achieved. DGPS position accuracy w a s 2.449m.
 Phase II :
In phase II analysis, one 3 channel DGPS receiver was
built to field test the performance of the linearly
interpolated PRC regenerating algorithm. The built
receiver (See Figure 10) can have up to 6 channels.
For the field test, a river side area was selected rather
than inland. By the rule of thumb, the medium wave
signal propagation characteristic around the river side is
better than that of inland.
The PRC values were analysed in real situation and the
results shows (See the Table 2) that there was an
averaged 4.2% difference between the PRC values of
each GPS satellite. The PRC value changes of inbound
and outbound GPS satellites are shown in Figure 11.
Tab. 1 The position accuracy using 3 DGPS reference
stations
Multi-
Ref. Changgi got Ochong do Sochong do Chumu njin
Distance(Km) 202 127 279 214
1.164 1.959 1.607 1.223 Position Error
(m) 0.788 1.607 1.223 1.239
24.3 40.6 27.6 4.8
Improvement
(%) 41.0 51.0 35.6 36.4
Fig. 7 Scatter plot of DGPS positioning of Sochongdo (left) and
Ochongdo (right)
Fig. 8 Scatter plot of DGPS positioning of Chumunjin (left) and
Changgigot (right)
Fig. 9 Multi-Ref.s DGPS positioning accuracy; 1.164 m (left) and
0.788m (right)
Tab. 2 The maximum ga p of PRC values
SV
Ref. S. SV1 SV6 SV14 SV16 SV20 SV25
Muju -7.1951 -11.521 -11.191 -12.100 -18.858 -10.069
Ochongdo -6.9579 -12.078 -11.328 -11.218 -18.387 -10.034
Palmido -7.3114 -11.718 -11.691 -11.914 -18.574 -10.181
PRC gap 4.84(%) 4.61(%) 4.28(%) 7.29(%) 2.50(%) 1.45(%)

Oh et al.: Development of Navigation Algorithm to Improve Position Accuracy 149
Beacon
Beacon
Ant
Ant
RF
RF
signal
signal
DGPS Beacon Receiver #1 DGPS Beacon Receiver #1
DGPS Beacon Receiver #2
DGPS Beacon Receiver #2
DGPS Beacon Receiver #3 DGPS Beacon Receiver #3PRC
PRC
PRC
PRC
PRC
PRC
Regenerating Regenerating
PRC PRC
GPS
GPS
Ant
Ant
GPS Receiver
GPS Receiver GPS Raw Data GPS Raw Data
G matrix
G matrix
Ca rrier
Carrier
Sm oothing
Sm oothing
DG PS
DGPS
Positioning
Positioning
Beacon
Beacon
Ant
Ant
RF
RF
signal
signal
DGPS Beacon Receiver #1 DGPS Beacon Receiver #1 DGPS Beacon Receiver #1 DGPS Beacon Receiver #1
DGPS Beacon Receiver #2
DGPS Beacon Receiver #2
DGPS Beacon Receiver #2
DGPS Beacon Receiver #2
DGPS Beacon Receiver #3 DGPS Beacon Receiver #3 DGPS Beacon Receiver #3 DGPS Beacon Receiver #3PRC
PRC
PRC
PRC
PRC
PRC
Regenerating Regenerating
PRC PRC
GPS
GPS
Ant
Ant
GPS Receiver
GPS Receiver GPS Raw Data GPS Raw Data GPS Raw Data GPS Raw Data
G matrix
G matrix
G matrix
G matrix
Ca rrier
Carrier
Sm oothing
Sm oothing
DG PS
DGPS
Positioning
Positioning
Fig. 10 The configuration of built receiver for field test
Fig. 11 The tendency of PRC va l ue c ha n ge s
Fig. 12 Field test results of DGPS positioning of Palmido (left) and Ochon gdo (right)
Fig. 13 Field test results of DGPS positioning of Muju (left) and Multi-DGPS R.S (right)

150 Journal of Global Positioning Systems
Fig. 14 Scatter plot of the field test results of DGPS positionin g
4 Conclusion s
The linearly interpolated PRC regenerating algorithm has
been proposed in this paper, which can improve the
DGPS position accuracy by about 40% without any
changes in DGPS reference station’s system. In the phase
I study, off-lined PRC data was used. DGPS RF signals
directly from the DGPS stations are available through a
multi channel DGPS beacon receiver developed in phase
II study. The results of phase II stud y shows th at the PRC
regenerating algorithm works well.
Acknowledgement s
This study was supported by the 2004 National R&D
Program. The authors greatly appreciate the support of
Korea Research Coun cil of Public Scien ce & Technology
(KORP), Korea.
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