Journal of Global Positioning Systems (2004)
Vol. 3, No. 1-2: 95-100
Performance Analysis of Precise Point Positioning Using Rea-Time
Orbit and Clock Products
Yang Gao
Department of Geomatics Engineering, University of Calgary, Calgary, AB, Canada
e-mail: [e-mail] Tel: [phone] ; Fax: [phone]
Kongzhe Chen
Department of Geomatics Engineering, University of Calgary, Calgary, AB, Canada
e-mail: [e-mail] Tel: [phone] ; Fax: [phone]
Received: 15 Nov 2004 / Accepted: 3 Feb 2005
Abstract. The real-time availability of precise GPS
satellite orbit and clock products has enabled the
development of a novel positioning methodology known
as precise point positioning (PPP). Based on the
processing of un-differenced pseudorange and carrier
phase observations from a single GPS receiver,
positioning solutions with centimeter to decimeter
accuracy can be attained globally. Such accuracy can
currently be achieved only through differential processing
of observations acquired simultaneously from at least two
receiver stations. The potential impact of PPP on the
positioning community is expected to be significant. It
brings not only great flexibility to field operations but
also reduces labor and equipment cost and simplifies
operational logistics by eliminating the need for base
stations. This paper will address issues related to precise
point positioning and perform data analysis to assess the
performance of different application solutions from PPP
using real-time precise orbit and clock corrections. They
include the discussion of an algorithm for un-differenced
data processing, error source and mitigation, and critical
elements related to real-time GPS orbit and clock
products. Numerical results will be presented to show the
positioning accuracy attained with datasets acquired from
different environments using real-time precise orbit/clock
products currently available. Features of a software
package that has been developed at the University of
Calgary for precise point positioning will also be
described.
Key words: GPS, Precise Point Positioning, Un-
differenced, Precise Orbit and Clock
1 Introduction
Current carrier phase based GPS kinematic positioning
systems are primarily based on double differencing data
processing approach which is able to provide centimetre
to decimetre accurate positional accuracy in real-time. It
has found wide applications from geodetic survey,
mapping, resources exploration, deformation monitoring
construction to aircraft landing. The differential process
however requires simultaneous observation of common
GPS satellites at both a base station (a reference site with
precisely know coordinates) and rover user stations. This
not only complicates the data acquisition process but also
reduces the applicability of the method to many other
potential applications. Since the reduction of common
errors is very much dependent on the inter-station
baseline lengths, the base and rover station separation
must be short typically in the range of about 20
kilometres. Further, the need for a base station would
increase the cost in equipment and labour and
inconsistency using different base stations.
The availability of precise GPS satellite orbit and clock
products has enabled the development of a novel
positioning methodology known as precise point
positioning (PPP). Based on the processing of un-
differenced pseudorange and carrier phase observations
from a single GPS receiver, this approach effectively
eliminates the inter-station limitations introduced by
differential GPS processing as no base station is
necessary. As a result, it offers an alternative to
differential GPS that is logistically simpler and almost as
accurate (Zumberge et al., 1997; Kouba & H¨¦roux,

96 Journal of Global Positioning Systems
2001). Although PPP does not require any base station, it
requires accurate knowledge of the GPS satellite
coordinates and the state of their clocks.
The performance of PPP for positioning determination
has been demonstrated in various papers, e.g. Zumberge
et al., 1997; Kouba & H¨¦roux, 2001; Gao and Shen,
2002; Gao et al., 2003, using post-mission precise orbit
and clock from IGS. The potential impact of PPP on the
positioning community is expected to be significant. It
brings not only great flexibility to field operations but
also reduces labor and equipment cost and simplifies
operational logistics by eliminating the need for base
stations. Following the availability of real-time precise
GPS satellite orbit and clock products from some
organizations, the interest to apply PPP to real-time
kinematic positioning is currently strong as a next
generation real-time kinematic (RTK) methodology.
This paper will address issues related to precise point
positioning and conduct data analysis to assess
performance of different application solutions from PPP
using real-time precise orbit and clock corrections. They
include the discussion of an algorithm for un-differenced
data processing, error source and mitigation, and critical
elements related to real-time GPS orbit and clock
products. Numerical results will be presented to show the
positioning accuracy attained with datasets acquired from
different environments using real-time precise orbit/clock
products currently available. Features of a software
package that has been developed at the University of
Calgary for precise point positioning will also be
described.
2 Precise Point Positioning (PPP) Method
In the following, the method of PPP is described along
with mathematical equations. With a dual-frequency GPS
receiver, the following ionosphere-free combinations can
be applied to facilitate PPP positioning using un-
differenced observations.
()
IFIFtropIF Pdmdcdt
ff
PfPf
P ερ ++++=
−
⋅−⋅
=2
2
2
1
2
2
21
2
1 (1)
)( m
ff
NcfNcf
dcdt
ff
ff
IFIFtrop
IF
Φ++
−
−
+++=
−
Φ⋅−Φ⋅
=Φ
εδρ
2
2
2
1
2211
2
2
2
1
2
2
21
2
1
(2)
where i P is the measured pseudorange on Li (m); i
Φ
is
the measured carrier phase on Li (m); ρ is the true
geometric range (m); c is the speed of light (m/s); dt is
the receiver clock error (s);trop d is the tropospheric delay
(m); i
fis the frequency of Li (m); i N is the integer phase
ambiguity on Li (cycle); i dm is the multipath effect in the
measured pseudorange on Li (m);i m
δ
is the multipath
effect in the measured carrier phase on Li (m) and (.)
ε
is
the measurement noise (m).
Satellite orbit and clock errors are not present in equation
(1) and (2) since they can be removed by the use of
precise orbit and clock products. The remaining receiver
clock and tropospheric delays in equations (1) and (2) are
to be estimated in PPP. A choke-ring antenna should be
used in the presence of significant multipath.
The estimation of tropospheric gradients is beneficial for
both GPS positioning and tropospheric delay estimation
(Bar-sever et al., 1998). The following equation can be
used to model the tropospheric effect (McCarthy and
Petit, 2003):
)]asin(G)acos(G)[e(m
D)e(mD)e(md
ENg
wzwhzhtrop
++
+
=
(3)
where hz
D,wz
D are the zenith hydrostatic and wet delay;
N
G,E
G are the horizontal delay gradient in north and
east direct; )e(mh is the hydrostatic mapping function;
)e(mw is the wet mapping function and )e(mg is the
gradient mapping function;e
,
a are the azimuth and
elevation angles.
In this research the following gradient mapping function
has been used (Chen and Herring, 1997):
00320
1
.)etan()esin(
)e(mg+ = (4)
and the Saastamoinen model has been applied to model
the zenith hydrostatic delay (McCarthy and Petit, 2003):
H.cos.
P.
Dhz 00028020026601
00227680 0
−−
=
φ
(5)
where 0 P is the pressure in millibars;
φ
is the latitude
and H is the height above the geoid (km).
The unknown vector in the PPP processing include three
position coordinate parameters, a receiver clock offset
parameter, a wet zenith tropospheric delay parameter, two
tropospheric gradient parameters and float ambiguity
terms in ionosphere-free combinations (equal to the
number of satellites used in estimation).

Gao and Chen: Performance Analysis of PPP Using Rea-Time Orbit and Clock 97
3 Real-Time Precise GPS Orbits and Clocks
List in Table 1 is the source of precise orbit and clock
products from IGS and other organizations. We notice
that only JPL and NRCan are currently providing real-
time precise orbit and clock data, known as IGDG and
GPS•C respectively. The precise orbit and clock data
from JPL is generated based on data from a network
consisting of about 70 globally distributed reference
stations and their accuracy are about 20 cm for orbits and
0.5 ns for clocks. Its latency is about 4 seconds and the
date interval is 1 second (Muellerschoen, 2003). The
precise orbit and clock data from NRCan is generated
based on data from a network consisting of about 20
globally distributed reference stations with accuracy for
orbits about 10 cm and clocks about 1 ns respectively.
Still under development, the data latency for NRCan’s
precise orbit and clock is at the level of several hours and
the update interval is 2 seconds (Héroux, 2004).
JPL real-time precise orbit and clock data is now
available for commercial applications and will be used in
this paper to assess the performance of different
application solutions from PPP. JPL IGDG real-time
precise orbit and clock corrections were acquired over
Internet from a JPL server at a rate of 1 Hz.
Tab. 1 Precise orbit and clock accuracy
(unit: cm for orbit and ns for clock)
Sources Accuracy Latency Update Interval
Orbit Clock Orbit Clock
IGS Final <5 <0.1 13 days Weekly 15 min 5 min
IGS Rapid <5 0.1 17
hours Daily 15 min 5 min
IGS
UltraEST <5 0.2 3 hours 12 hours 15 min 15 min
IGS
UltraPRD 10 5 None 12 hours 15 min 15 min
IGDG
(Global) 20 0.5 ~4 sec 1 sec 29 sec 1 sec
GPS•C
(Global) 20 1 ~8 hours 2 sec 20 sec 2 sec
4 Numerical Results and Analysis
In the following, data processing and analysis are
conducted to assess performance of different application
solutions from PPP using JPL real-time precise orbit and
clock corrections. Results in different positioning modes
and other application solutions including receiver clock
offset and water vapor estimates are presented.
P3 Software
A software package called P3 has been developed at the
University of Calgary for precise point positioning that
runs on Microsoft Windows operating system family. The
software is able to output solutions of different
application parameters including position, zenith
tropospheric delay and receiver clock offset estimates.
Processing can be done in post mission or in real-time,
and the program can be run in either static or kinematic
mode. Backward processing is supported to reduce errors
associated with solution convergence. A sample
screenshot of the software during processing is shown in
Fig. 1.
Fig. 1 P3 interface
Static Control Survey
In this test, one day of GPS data acquired on August 4,
2004 at IGS station ALGO was processed. The data from
a IGS station was selected because the coordinates of all
IGS stations are precisely determined everyday with
respect to ITRF2000 which is also the reference frame
that has been used by JPL in the generation of real-time
orbit and clock corrections. The GPS data at ALGO and
the station coordinates were downloaded from the IGS
website while the JPL real-time corrections were
retrieved from JPL server. The position results are shown
in Figure 2 and the accuracy statistics is given in Table 2.
It is seen that the coordinate estimates could converge to
centimetre level within 20 minutes. After the
convergence, all position coordinate components are
accurate at sub-centimetre level. The results in Table 1
indicate that PPP is capable of providing real-time
centimetre level accuracy for static control survey.
Tab. 2 Static positioning accuracy
RMS (m) BIAS (m) STD (m)
Latitude 0.009 0.008 0.003
Longitude 0.010 0.003 0.009
Height 0.007 0.000 0.007

98 Journal of Global Positioning Systems
Fig. 2 Static positioning errors
Vehicle Kinematic Positioning
In this test, a kinematic positioning with a vehicle was
conducted on September 30th, 2003. The vehicle was
driven along the highway at a speed of 80 km/h near
Springbank, Alberta. In order to establish a reference
trajectory for the vehicle, a reference receiver was set up
at one control point of the Springbank baseline network
so double difference data processing could be performed
to establish a reference for accuracy assessment. Both the
control point and vehicle used a Javad Legacy dual-
frequency receiver with the same type of antenna. A
CDPD radio was used to receive JPL IGDG real-time
precise orbit and clock corrections via the Internet. The
sample rate of the two GPS receivers was set to 1 Hz. The
PPP solutions are obtained using P3 software while the
double difference solutions are obtained using a
commercial software package from Waypoint Consulting
Inc. With a relatively short baseline length (about 7km),
the ambiguity-fixed results were available and can be
served as the ground-truth to assess the positioning
accuracy of PPP solutions.
The positioning differences between PPP and double
difference solutions are shown in Figure 3 and the
accuracy statistics is given in Table 2. They indicate that
centimetre accurate positioning results have been
obtained in real-time using precise point positioning
method.
Tab. 3 Vehicle kinematic positioning accuracy
RMS (m) BIAS (m) STD (m)
Latitude 0.009 0.008 0.003
Longitude 0.010 0.003 0.009
Height 0.007 0.000 0.007
Fig. 3 Vehicle trajectory and positioning errors
Airborne Kinematic Positioning
The airborne dataset was collected on August 28, 2004 at
40 kilometers north of Halifax, Nova Scotia. A Novatel
GPS receiver (Black Diamond) and antenna (model 512)
were set up on a helicopter. Another Novatel DL-4
receiver and antenna with ground plane were served as
base station. The sample rate of the two GPS receivers
was 1 Hz. The helicopter was typically flying at an
altitude of 250 meters above ground level at 50 knots.
The distance between the rover and base is less than 10
kilometers. The double-differenced with ambiguity-fixed
trajectory is served as ground-truth.
As shown in Figure 4 and Table 4, centimetre accurate
positioning results have been achieved in using real-time
precise orbit and clock products and point positioning
method.
Tab. 4 Aircraft positioning accuracy
RMS (m) BIAS (m) STD (m)
Latitude 0.009 0.008 0.003
Longitude 0.010 0.003 0.009
Height 0.007 0.000 0.007

Gao and Chen: Performance Analysis of PPP Using Rea-Time Orbit and Clock 99
Fig. 4 Aircraft trajectory and positioning errors
Receiver Clock Estimation
In addition position determination, PPP can also output
receiver clock offset solution which has the potential to
support precise timing applications. Since JPL IGDG
corrections are generated using a high-precision clock at
IGS station AMC2 (equipped with a hydrogen maser
external frequency) as the reference clock
(Muellerschoen, 2003), we can assess the accuracy of
receiver clock offset estimation from our PPP by
processing the GPS data from AMC2. The resultant
receiver clock estimates from PPP solutions for AMC2
station should theoretically equal zero using JPL IGDG
precise orbit and clock corrections and the variations in
the solutions directly reflect the quality of the clock
solutions from PPP.
In this test, the receiver clock offset was estimated as
white noise using GPS data from ACM2 station acquired
on June 12, 2004. Shown in Figure 5 are receiver clock
offset estimates at ACM2 station. Table 5 provides the
statistics of the estimation accuracy. The results indicate
that PPP is capable of providing real-time sub-
nanosecond accurate receiver clock estimates as a
promising tool for time transfer. In order to use the
estimates for clock comparisons, all instrumental biases
should be calibrated (Petit et al., 2001). Special cables
that are less temperature sensitive may be required
(Larson et al., 2000).
Fig. 5 Receiver clock offset estimates
Tab. 5 Receiver clock offset estimation accuracy
Products RMS (ns) BIAS (ns) STD (ns)
JPL IGDG 0.077 0.018 0.075
Water Vapor Estimation
In this test, a Javad JPSLEGANT antenna was set up on a
pillar on the roof of the Engineering Building at the
University of Calgary with precisely known coordinates.
JPSLEGANT is an antenna with a flat ground plane so it
can partly mitigate the multipath effects. A GPS data
acquisition at a sampling interval of 10 seconds was
conducted on September 5th 2004. For performance
analysis, a Radiometrics 1100 water vapour radiometer
(WVR) (Radiometrics Corp.) and a ParoscientificTM
MET3A meteorological sensor located on the same roof
have been applied to provide “true” precipitable water
vapor (PWV) and pressure measurements. The
radiometer was set up to make direct measurements of
line-of-sight slant water vapor to all GPS satellites. Since
the WVR tracks each satellite for approximately 40
seconds and consequently it takes about 6 minutes to
track all satellites in view in a given cycle, the PWV
measurements for each 6-minute cycle of observations
were averaged and then compared with the average value
of PPP-derived PWV estimates over the same time
period. The average PWV measurements from the
radiometer, the average PPP-derived PWV, and the
differences between them are shown in Figure 6. The
accuracy statistics were shown in Table 6.
The results indicate that the PWV difference between the
WVR truth measurements and GPS estimates is less than
1 millimetre, with very small bias at the level of about 0.3
millimeter. The results demonstrate the potential to
determine PWV to an accuracy of 1 mm in real-time
using precise orbit and clock products and PPP
methodology. This can satisfy the required accuracy for
GPS meteorological applications (Gutman and Benjamin
2001). The results are also comparable to the traditional
double-difference method, where accuracies of 1~2 mm
are achieved with very long baselines (Tregoning et al.,
1998). An advantage of the PPP approach is that no local

100 Journal of Global Positioning Systems
reference stations are required (as no differential
techniques are employed), and this method can be readily
adopted at isolated sites – e.g. in a sparse GPS network
(Gao et al., 2004).
5
15
25
WVR and GPS PWV Comparison (mm)
WVR & GPS
WVR
GPS
0 21600 43200 64800 86400
-4
0
4
GPS - WVR
18:00:0000:00:00 06:00:00 12:00:00 18:00:0
0
GPS Time
(
s
)
/ Local Time
(
HH:MM:SS
)
Fig. 6 WVR and GPS PWV comparison (Sept 5/04)
Tab. 6 PPP derived PWV accuracy
Products RMS (mm) BIAS (mm) STD (ms)
JPL IGDG 0.77 0.28 0.72
5 Conclusions
The performance of different application solutions,
including position determination under different
dynamics environments, water vapour and receiver clock
parameters estimation, using precise point positioning
methodology has been assessed using real-time precise
orbit and clock corrections. For position determination,
centimetre accuracy is obtainable which is comparable to
conventional double difference differential positioning.
For receiver clock estimates, an accuracy of sub-
nanosecond has been demonstrated by comparing to a
very accurate clock at an IGS station. The precipitable
water vapor (PWV) estimates from PPP agree with PWV
measurements from a water vapour radiometer at 1
millimeter level.
The performance analysis presented in this paper
demonstrate the potential of precise point positioning for
real-time precise positioning, time transfer and water
vapour estimation. Since no base stations are required for
precise point positioning method, it is expected that the
new method will bring greater operational flexibility
while significant reduced costs to those applications in
the future.
Acknowledgements
Financial support via a research grant from GEOIDE is
acknowledged. Susan Skone and Natalya Nicholson are
acknowledged for providing the radiometer and
meteorological data, Jet Propulsion Laboratory is
acknowledged for providing the real-time precise orbit
and clock corrections, and Paul Mrstik and Sarka Friedl
from Mosaic Mapping Systems Inc. are thanked for
providing the aircraft dataset used in the data analysis.
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