International Journal of Electronics and Electrical Engineering Vol. 2, No. 3, September, 2014
Analysis and Mitigation of Tropospheric Error
Effect on GPS Positioning Using Real GPS Data
Tahir Saleem and Mohammad Usman
Department of Electronic Engineering, International Islamic University Islamabad Pakistan
Email: {tahir.phdee41, musman} @iiu.edu.pk
Abstract—The GPS (Global Positioning System) is used for
navigation and positioning purposes by a diverse set of
users. The navigation solution provided by a commercial
GPS receiver is subject to errors contributed by various
sources. These sources of errors in GPS navigation (e.g.
satellite clock, receiver clock, atmospheric and multipath
errors etc.) induce biases in the measurement of pseudo
range and degrade system accuracy. In the current
research endeavor the atmospheric and troposphere error
sources and its impact on GPS position accuracy is
critically analyzed. In this regard a tropospheric error
correction model is simulated on real captured GPS data
and results are analyzed.
antenna array and advance receivers having suitable
tracking algorithms, such as, narrow correlator spacing,
Multipath Elimination Technology (MET) and Multipath
Estimating Delay Lock Loops (MEDLL). According to
Lachapelle [2] MEDLL has the most effective method at
reducing multipath error as compared to other methods
described earlier.
II. ESTIMATION OF GPS POSITION
For estimating user position coordinates a term, called
pseudorange is frequently used. It is basically the
distance measurement between satellite and receiver,
including combined effect of all error sources [3]. By
measuring the time of arrival (TOA) of the signal, the
user’s distance (range) from each of the satellite is
calculated. By combining the range from a minimum of
3 satellites, the user position can be calculated in three
dimensions. The basic pseudorange measurement
equation can be given as [4]:
Index Terms—troposphere, GPS, mitigation, navigation,
Hopfield model
I.
INTRODUCTION
The Global Positioning System (GPS) is a space-based
global navigation satellite system maintained by U.S
Department of Defense. There are a total of 32 GPS
satellites in which 24 satellites are currently operational
divided into six orbits and each orbit has four satellites.
The system is designed in such way that at least five
satellites are visible at any point on the earth's surface
having a clear view of the sky.
Due to the tremendous accuracy potential of this
system, and the latest improvements in receiver
technology, the GPS (Global Positioning Systems) has
revolutionized navigation and position location for more
than a decade [1]. However GPS signal suffers from
inherent imprecision due to a variety of error sources.
The combined effects of these errors during signal
propagation result in the degradation of positioning
accuracy as calculated by the GPS receiver. The
commonly held belief is that GPS is accurate to ± X
meters, where X is often viewed as acceptable for the
purpose of the system under consideration. Fortunately,
there are several methods to address these errors and
improve the positioning accuracy. For example
differential correction technique is often used to combat
the satellite and receiver clock errors. Similarly
Multipath errors can be reduced to a greater extent by
selecting a suitable observation site, using special type of
(1)
where, is the measured pseudo range (m), is the
geometric range (m), an orbital error (m), speed of
light (m/s),
satellite clock error (s),
receiver
clock error (s),
ionospheric error (m),
tropospheric error (m), and receiver code noise plus
multipath (m).
The signals transmitted by the GPS satellites are used
to measure the Time of Arrival (TOA) at the receiver.
Since the propagation speed (the speed of light) is known,
the distance (geometric range) can be calculated from the
delay.
GPS Satellite
r=s-u
user
s
u
Earth
Figure 1. Definition of the User-to-Satellite vector r
The position of the satellite, , is known from satellite
ephemeris data broadcasts (ECEF coordinates). If a user
Manuscript received January 17, 2014; revised February 27, 2014.
©2014 Engineering and Technology Publishing
doi: 10.12720/ijeee.2.3.249-253
)
(
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International Journal of Electronics and Electrical Engineering Vol. 2, No. 3, September, 2014
is located at position , the user-to-satellite vector
then be written as shown in Fig. 1.
Table I depicts the average numerical values of both
components of the troposphere delay related to different
elevation angles.
The dry delay is mainly caused by the O2 and N2 gases
present in the atmosphere and it can be modeled only up
to1% or better. On the other hand the wet delay which
causes up to 10-20% of the total delay is difficult to
model. The wet delay is due to the presence of water
vapors in the atmosphere. Mathematically the
tropospheric delay T can be represented as
can
(2)
III. GPS ERROR SOURCES
As depicted in eq. 1, there are a number of possible
sources of errors which can degrade the accuracy of
position computed and hence adversely affect the
performance of a GPS receiver. These error sources can
be mainly categorized into two groups, system wide
errors and specific operating environment or specific
GPS receiver errors. System wide errors include
selective availability (S/A), ephemeris error, satellite
clock error, troposphere and ionosphere error. We shall
only discuss the troposphere error effect in the paper.
System wide errors and their impact which can be
reduced partially or completely eliminated by means of
differential correction technique are summarized in the
following Fig. 2.
∫
(
)
(3)
where is the refractive index of the atmospheric gases
and is the difference between the curved and freespace paths.
During the last several decades, number of models
(Hopfield model, Saastamoinen model, etc) have been
developed and reported in scientific literature by
researchers for estimation and correction of the delay
induced by the troposphere in the GPS signal. However,
much research has gone into the creation and testing of
tropospheric refraction models to compute the
refractivity N along the path of signal travel. Among
these models the Hopfield model is most commonly used.
A. Hopfield Model
Hopfield [7] developed a dual quadratic zenith model
of the refractivity with different and separate quadratics
for the dry and wet atmospheric profiles. He described
that refractivity is function of height above the surface
assuming single polytrophic layer. The following
formula is adopted by the model:
Figure 2. System wide errors and their impact
IV. TROPOSPHERIC ERROR
(
Troposphere is the initial part of atmosphere and
ranges up to 16 km in altitude from the surface of the
earth, although the neutral atmosphere extends up to 60
km [5]. The Troposphere affects the GPS signals which
are in fact electromagnetic waves, to a significant level.
As a result the GPS signals are both delayed and
refracted. The main factors which cause troposphere
delay include temperature, pressure and humidity. The
delay also varies with the height of the user position as
the type of terrain below the signal path can affect the
delay. According to Hopfield [6], there are two
components of troposphere delay, namely wet delay and
dry delay. The dry component which comprises of about
80 to 90% of the total delay is easier to determine as
compared to the wet component.
A.
Elevation
angle in
degree
900
Dry
component
(in meters)
2.3
Wet
Component
(in meters)
0.2
Total
Delay (in
meters)
2.5
B.
200
6.7
0.6
7.3
C.
150
8.8
0.8
9.6
D.
100
12.9
1.1
14.0
E.
50
23.6
2.2
25.8
©2014 Engineering and Technology Publishing
)
(4)
)
where is the total zenith atmospheric delay
the top
height of the dry atmospheric layer,
height of the wet
atmospheric layer,
ground atmospheric pressure
(mbar),
ground temperature (T ),
ground water
vapor pressure and height of the ground level of the
observing station, the constant parameters are k1 =77.6
K/mbar, k2 = 71.6 K2/mbar and k3 = 3.747 ×105
K2/mbar.
V. SIMULATION AND RESULTS
The simulation work was carried out in the software
Matlab version 7.3 on actual acquired GPS data. The
sequence of steps carried out during the simulation
process is explained in the following subsection.
TABLE I. TROPOSPHERIC DELAY ON MEASURED RANGE
S.No
(
A. Capturing of GPS Data
The GPS data used in this project has been acquired
using custom made dual channel GPS data capturing
device [8]. The GPS data was captured in Room E44b of
Sackville street building of the University of Manchester.
A commercial off the shelf helical antenna was used. It
was mounted on a mast and pushed out of the room
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International Journal of Electronics and Electrical Engineering Vol. 2, No. 3, September, 2014
frequency as a function of time in order to keep the
signal locked and decode the navigation data.
window during measurements to have a good view of the
sky. The GPS signals were received, amplified, downconverted, and digitized into base band samples. The
base band samples are then processed using software
routines to acquire and track the direct GPS signal and to
generate the receiver position information as explained in
following sections. The software receiver can perform
signal acquisition and tracking, navigation data
extraction, code offset calculations and more importantly
the parameters can be conveniently changed and the
receiver can be adapted to suit different conditions
[9].The available satellites were limited to five on the
particular afternoon, when measurements were
performed. They were however enough to perform the
tracking and position calculations as mentioned below in
the subsection c.
B. Analysis of GPS Data
Figure 4. Acquisition results
The analysis of the data started with the generation of
two types of plots as shown in the Fig. 3. The first plot in
the figure depicts the time domain plot for 1000 samples
of data. The GPS signal is transmitted using DSSS
techniques, hence, as expected no discernible structure is
visible, despite the 4.78 MHz IF present in the frequency
domain plot.
C. Satellites Tracked
The sky plot in Fig. 5 shows which satellites were
visible and tracked when GPS data was captured. The
satellites are shown using their PRN number inside the
figure.
Figure 5. Satellite sky plot
Figure 3. Time and frequency domain plots for the actual GPS data
D. Function Tropo
This Matlab subroutine is based on Hopfield
tropospheric model [6]. The tropospheric correction
model used in the simulation was selected because it
gives best results as compared to other tropospheric
models and is used widely for tropospheric correction.
The model calculates tropospheric correction which is
used for correction of computed user position. Correction
in meters is stored in variable ddr. The range correction
ddr in m is to be subtracted from pseudo-ranges and
carrier phases. Descriptions of some important
parameters of the Tropospheric correction function
giving in Table II.
C. Acquisition and Tracking of Satellites
The first step in the simulation was to acquire the GPS
satellites from the captured data. The acquisition plot for
the captured GPS data is shown in Fig. 4. Only four
satellites have strength greater than the acquisition
threshold set at 2.5. This is an arbitrary level and can be
revised based on the circumstances. The purpose of the
acquisition process is to identify if a certain satellite is
visible or not. If the satellite is visible, the acquisition
process determines the coarse values of carrier frequency
and code phase of the satellite signals.
The parameters i.e. carrier frequency and code phase
are further refined by the tracking process. The main
purpose of tracking algorithms is to refine the coarse
values of code phase and frequency, and keep track of
these as the signal properties change over time. Thus the
tracking code runs continuously to follow the changes in
©2014 Engineering and Technology Publishing
E. Position before and after Tropospheric Correction
User position was computed before and after
atmospheric i.e. troposphere error correction and effect
of the error was noted which can be seen from the Fig. 6
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International Journal of Electronics and Electrical Engineering Vol. 2, No. 3, September, 2014
TABLE II. DESCRIPTION OF IMPORTANT PARAMETERS OF TROPO
FUNCTION
to Fig. 8. Difference in latitude value was noted and also
a significant variation can be seen in coordinates in UTM
system from these figures. Results for 70 ms
(millisecond) out of 500 ms (millisecond) data are shown
in the Fig. 6 to Fig. 8.
Description
S/N
Parameter
1.
sinel
sin of elevation angle of satellite.
2.
hsta
Height of station in km.
3.
p
4.
tkel
5.
6.
hum
hp
7.
htkel
8.
hhum
Atmospheric pressure in mb at height hp.
Surface temperature in degrees Kelvin at
height htkel.
Humidity in % at height hhum.
Height of pressure measurement in km.
Height of temperature measurement in
km.
Height of humidity measurement in km.
VI. CONCLUSION
This paper has demonstrated the impact of
tropospheric effect on GPS positioning. As shown in the
simulation and results section, the tropospheric error can
degrade the GPS receiver accuracy up to significant level
if the error is not compensated properly. Further research
can be carried out by capturing more GPS data and
analyzing the results.
Figure 6. East coordinate variations with and without tropospheric
correction
ACKNOWLEDGMENT
The authors would like to thank Higher Education
Commission (HEC), Pakistan for the financial support of
this work.
REFERENCES
[1] E. D. Kaplan and C. J. Hegarty, Understanding GPS Principles
and Application, 2nd ed. Artech House Publishers London, 2005,
ch 1.
[2] G. Lachapelle, A. Bruton, J. Henriksen, M. E. Cannon, and C.
McMillan, “Evaluation of high performance multipath reduction
technologies for precise DGPS shipborne positioning,” The
Hydrographic Journal, no. 82, pp. 11-17, October 1996.
[3] L. Baroni and H. K. Kuga, “Analysis of navigational algorithms for a
real time differential GPS system,” in Proc. 18th International
Congress of Mechanical Engineering, Ouro Preto, MG, November 611, 2005.
[4] D. Wells, et al. Guide to GPS Positioning, 2nd ed. Canadian GPS
Associates, 1987.
[5] C. Satirapod and P. Chalermwattanachai, “Impact of different
tropospheric models on GPS baseline accuracy: Case study in
Thailand,” Journal of Global Positioning Systems, vol. 4, no. 1-2, pp.
36-40, 2005.
[6] H. S. Hopfield, “Tropospheric effects on electromagnetically measured
range: Prediction from surface weather data,” Radio Science, vol. 6, no.
3, 1971.
[7] H. S. Hopfield, “Two–quadratic tropospheric refractivity profile for
correction satellite data,” Journal of Geophysical Research, vol. 74,
no. 18, pp. 4487 – 4499, 1969.
[8] M. Usman and D. W. Armitage, “Acquisition of reflected GPS
signals for remote sensing applications,” in Proc. ICAST,
Islamabad, Pakistan, 29-30 November, 2008,
[9] K. Borre, D. M. A., N. Bertelson, et al., “A software defined GPS and
Galileo receiver, a single frequency approach,” Birkhauser, 2006.
Figure 7. North coordinate variations with and without tropospheric
correction
Figure 8. Uping coordinate variations with and without tropospheric
correction
©2014 Engineering and Technology Publishing
252
International Journal of Electronics and Electrical Engineering Vol. 2, No. 3, September, 2014
Tahir Saleem was born in KPK, Pakistan. He
received the BS degree in Information Technology
from Kohat University in 2006 and the M.S.E
degree in Electronic Engineering from International
Islamic
university
Islamabad
(IIUI)
in
2010.Currently he is Ph.D scholar at IIUI in
Electronic Engineering. His research interests focus
on satellite communication and synthetic Aperture Radar (SAR) signal
processing.
©2014 Engineering and Technology Publishing
Mohammad Usman was born in Punjab, Pakistan.
He received the B.Sc degree in Electrical
Engineering from UET, Lahore in 1993, M.S.E and
Ph.D degrees in Electrical Engineering with
specialization in Imaging and Signal processing
from The University of Manchester, Manchester,
UK, in 2005 and 2009 respectively. Currently he is
adjunct faculty member since 2009 at IIUI. His
research interests focus on GPS and synthetic Aperture Radar (SAR)
signal processing.
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