GPS Signal Degradation Modeling

GPS Signal Degradation Modeling

Changlin Ma, Gyu-In Jee, Glenn MacGougan, and Gerard Lachapelle
Department of Geomatics Engineering, the University of Calgary

S. Bloebaum
Ericsson Inc, Research Triangle Park, N.C.

G. Cox, L. Garin, J. Shewfelt
SiRF Technology Inc., San Jose, CA

BIOGRAPHY State University. He has been with Ericsson since 1990,
where he has held a variety of roles in research and
Changlin Ma is a graduate student of the department of development for cellular phones and networks.
Geomatics Engineering at the University of Calgary. He Currently, he is a Technical Manager in Ericsson Mobile
received his B.S.(1992) and M.S.(1995) in Electronics Platforms and Technologies in Research Triangle Park,
Engineering from Northwestern Polytechnical University NC where he is responsible for positioning technology
(Xi’an, China), and his first Ph.D.(1998) also in development. He has been involved with GPS for four
Electronics Engineering from Tsinghua University years and played a key role in setting GSM standards for
(Beijing, China). His current research is focused on GPS network-assisted GPS. His technical interests are hybrid
receiver technology. cellular-satellite positioning technology, speech
enhancement and compression, and multicarrier
Gyu-In Jee is a Professor in the Department of modulation and transmission systems. He holds four
Electronics Engineering at Konkuk University in Seoul, U.S. patents.
Korea. He received his Ph.D. in Systems Engineering
from Case Western Reserve University on 1989. He has Geoffrey F. Cox received his B.A. degree in
worked on several GPS related research projects; GPS Geology/Chemistry and Mathematics at the University of
receiver software design, GPS/INS integration for land Maine in 1992, M. Eng. in Geomatics Engineering from
vehicle, DGPS system development, GPS engine design the University of Calgary in 1996. His area of study at
using the Mitel chip sets, wireless location in CDMA that time was GPS Positioning and Navigation with
network, etc. His research interests include software GPS emphasis on the Foliage Effects on GPS Signals. Since
receiver, wireless positioning for E911, and GPS/INS 1996, Mr. Cox has worked in many engineering and
integration for personal navigation. business capacities ranging from WADGPS development
for Terrestrial and Aviation Precision Agricultural
Mr. Glenn MacGougan is a MSc. student in the Systems, Commercial RTK Survey and Mapping
Department of Geomatics Engineering at the University Systems. In beginning of 2000, Mr. Cox consulted for
of Calgary. In 2000 he completed a BSc. in Geomatics various companies by providing GPS related engineering
Engineering at the University of Calgary. He will and marketing services. Mr. Cox joined SiRF
complete his second degree in September 2002. Technology, Inc. in the fall of 2000 as Senior
Applications Engineer.
Dr. Gerard Lachapelle is a Professor and Head of the
Department of Geomatics Engineering where he is Lionel Garin is Lead Architect at SiRF Technology. Prior
responsible for teaching and research related to to joining SiRF he worked on Multipath Rejection
positioning, navigation, and hydrography. He has been techniques, survey quality GPS and Glonass receivers at
involved with GPS developments and applications since Ashtech and Sagem. Mr. Garin holds a MSEE from
1980. EcoleNationale Supérieure des Télécommunications.

Scott Bloebaum received the B.S. and M.S. degrees in John L. Shewfelt received a B.Sc. in Electrical
Electrical Engineering from Virginia Tech, and the Ph.D. Engineering from the University of California Santa
degree in Electrical Engineering from North Carolina Barbara in 1981. Since that time Mr. Shewfelt has been

ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 882

involved in design, development, test and integration of in this case, thus requiring a GPS receiver to be able to
complex avionics and guidance systems for various types acquire and track weak signals. Secondly, GPS signals in
of aircraft and naval platforms, including working with these serious situations can contain serious multipath
microwave radars and receivers, Jammers, UV and IR signals, which can degrade positioning accuracy
imaging systems, and GPS/INS guidance and control. In significantly.
March of 2000, Mr. Shewfelt joined SiRF Technology
Inc. as Applications Engineering Manager to facilitate To understand and perhaps solve these problems
the integration of GPS technology into embedded knowledge about the GPS signal channel is obviously a
products and platforms. prerequisite. Unfortunately, not much research has been
done in this area. Thus, the motivation for this paper was
to further such research.
ABSTRACT
This paper examines the GPS signal channel near
This paper attempts to provide some insight into the receiver antennas. Specifically, it focuses on the signal
fading properties of GPS signals. When a GPS signal fading distribution due to masking and blocking effects
gets to an antenna, it suffers from masking and blocking of surrounding objects. To do so incoming GPS signals
effects from surrounding objects. With respect to these are first divided into three categories: Clear LOS signals,
effects, GPS signals can be divided into clear LOS Shadowed signals, and Blocked signals. A statistic
signals, shadowed signals, and blocked signals. A model, Urban Three-State Fade Model (UTSFM), is
statistic model, Urban Three-State Fade Model introduced to fit the fading histogram of real data. The
(UTSFM), is discussed in this paper. Experimental fitting results describe the signal composition based on
results show that this model can describe the fading the data.
distribution of GPS signals very well. After model fitting,
the model parameters can indicate the composition of the The outline of this paper is a follows: the GPS signal
incoming signals in terms of the relative magnitude of channel is discussed, a signal classification is presented,
the three signal types. the Urban Three State Model is explained, and finally
experimental data and model fitting is discussed. Some
INTRODUCTION conclusions and discussion of ensuing research conclude
the paper.
Although GPS was first designed as a military system to
provide real time position, it is becoming a necessity in GPS SIGNAL CHANNEL
people’s daily life. GPS receivers are now being made
smaller and smaller and can be integrated into many When a GPS signal propagates from a satellite to a
devices to provide both position and time with high receiver antenna, it suffers from degradation effects, such
accuracy. Its application has already extended to many as, free space loss, refraction and absorption from the
areas, such as, earthquake detection, cellular phone atmosphere, reflection and masking from surrounding
positioning, so on and so forth. objects such as trees and buildings, jamming, and
environmental noise.
These new applications impose more serious
requirements on GPS itself. Traditionally, a GPS receiver
was required to function in an open area with a clear
view of the sky, but in new applications it is required to
work in degraded signal environments.

One typical example is the use of GPS in cellular phones
that are required to be “location Aware” for the E911
mandate in the near future ( FCC 2001). GPS is a
promising solution to this requirement since it can
provide position autonomously. However, when looking
at this problem in detail, there are many issues to address.
First, cellular phones are used in many places, not only in
open areas. This means the GPS receiver built in a
cellular phone must work well in places where there is
not much open sky, such as, urban canyons or inside a
building. From previous a study (Frank van Diggelen, Figure 1: GPS signal propagation
2001), it was shown that GPS signals become very weak


This paper focused on signal strength fading due to
reflection and masking by surrounding objects such as SIGNAL CLASSIFICATION
trees and buildings.
With respect to fading effects, GPS signals can be
Huygens’ principle tells us that waves are propagated by divided into three categories:
wavelets on sequential wave fronts. When an object
blocks some wavelets, waves of other wavelets can still Clear line-of-sight (LOS) signal: This kind of signal
reach the shadowed region, but the signal strength is gets to the receiver antenna directly without any object in
decreased, as shown in Figure 2. the way of propagation. Fading is only due to free space
loss and atmosphere absorption.

Shadowed signal: For this kind of signal, the
propagation takes place over the first Fresnel zone
through a medium that just attenuates the signal, such as,
tree canopies.

Blocked signal: The propagation path within the first
Fresnel zone is completely obstructed so that signal
reception is accomplished through diffraction and
reflection (multipath).

URBAN THREE STATE FADE MODEL
Figure 2: Huygens’ Principle
This is a statistical model, and has been utilized in the
Normally, the concept of the Fresnel zone especially the study of land-mobile communication system (J.
first Fresnel zone is used to characterize the shadowing Goldhirsh and Wolfhard J. Vogel 1998). It is used here to
and blocking effects (Barry McLarmon), as shown in describe the GPS signal fading distribution. The idea of
Figure 3. the model is quite simple: The fading distribution of the
three types of signals discussed previously can be
expressed by specific probability density functions (pdf),
and the composite amplitude probability density function
of GPS signals is the combination of them.

Clear signals from a satellite correspond to clear LOS
and multipath signals. In this case, the fading distribution
can be expressed by a Ricean pdf

[ ]
f Ricean (v ) = 2 Kv exp − K (v 2 + 1) I 0 (2 Kv ) (1)

where v is the received voltage relative to the clear path
voltage, K is the ratio of the direct power received to the
Figure 3: Fresnel Zone multipath power, and I 0 ( ) is the 0th order modified
The Fresnel zone is the volume of space enclosed by an Bessel function.
ellipsoid, which has the two antennas A and B at the ends
of a radio link as its foci. The first Fresnel zone is an If signals from a satellite are blocked, the received
ellipsoid defined such that the distance summation of a signals consist of only multipath signals. In this case, the
point C on the ellipsoid to A and B is one wavelength fading distribution can be expressed by a Rayleigh pdf
longer than the direct distance between A and B, i.e. which is a special case of Ricean function without LOS
AC+CB = AB + λ. From experience, the fading effect is signal
negligible if there are no objects in the first Fresnel zone,
and the fading effect is thought serious if there are [
f Rayleigh (v ) = 2 Kv exp − Kv 2 ] (2)
objects in this region.


If signals from a satellite can be directly received but are In this paper, the fading histograms of real data were
attenuated by trees or other materials, these signals are fitted by adjusting the coefficients and parameters in the
called shadowed signals and the fading can be described model. The results indicate the composition of the
by Loo’s function (Chun Loo, 1985) received signals.

2 Kv
f Loo ' s (v ) = 8.686 EXPERIMENT DESCRIPTION
π σ (3)
∞
 (20 log(z ) − m )2 
− K (v 2 + z 2 ) I 0 (2 Kvz )dz
1 Some experiments had been done to study how well the
∫z 
0
exp −
 2σ 2 

statistic model can describe GPS signal fading. The data
were collected by the scheme shown in Figure 5.
In fact, shadowed signals consist of two parts: attenuated
LOS signals of which the fading is log normally
distributed and multipath signals of which the fading is Reference
Rayleigh distributed.

In the Urban Three-State Fade Model, the composite
amplitude probability density function is the combination
of the above three pdf (R. Akturan and W. Vogel, 1997). Rover
f v (α , v ) = C (α ) f Ricean (v ) + S (α ) f Loo (v ) + B(α ) f Rayleigh (v ) (4)
C (α ) + S (α ) + B (α ) = 1

Where α is the elevation, and C (α ) , S (α ) , and B (α ) are Figure 5: Data collect scheme
weight coefficients. These coefficients can be thought as
indicators of the relative magnitude of the three kinds of The reference station receiver was located on the roof of
signals at a certain elevation. a five story building with a very good view of the sky.
The rover receiver was mounted on a car. The fading data
The following figure is an example of Ricean pdf, of rover were obtained by comparing the carrier to noise
Rayleigh pdf, and Loo’s pdf. density ratio, C/N0, between the two receivers. An
assumption that there was not extra fading at reference
0.09
PDF of Ricean, Rayleigh, and Loo station was made. This means that the fading at reference
station was due only to free space loss and absorption
Ricean
0.08
Rayleigh from atmosphere. This fading was also shared by the
Loo
0.07 rover and could be removed by differencing. The fading
0.06 difference between the rover and the reference station
was thus due to masking effects of the surrounding
Probability(%)

0.05
objects near the rover. The receivers used at reference
0.04
station and rover were the same in order to guarantee that
0.03 the algorithms used to calculate the C/N0 were identical.
0.02
Several typical working environments were chosen, and
0.01
the masking effects varied from light to heavy. These
0
-40 -30 -20 -10 0 10 20 30 40 scenarios were as follows:
Fade (dB)

• Open sky (stationary test, data rate: 1Hz, time
Figure 4: pdf of Ricean, Rayleigh, and Loo’s length: 1.5 hour)
• Road-side tree shadowing (kinematic test, update
The blue line is a Ricean pdf and is centered at 0dB for rate: 1 Hz, velocity: up to 50km/h, distance: about 50
clear signals. The red line corresponds to Loo’s function km, time length: about 2.5 hours)
and is commonly centered less than 10 dB for shadowed • Moderate sub-urban with 2 or 3 floor buildings
signals. Finally, the green line corresponds to a Rayleigh (kinematic test, update rate: 1Hz, velocity: up to
pdf and is normally centered larger than 10 dB for 50km/h, distance: about 40 km, time length: about 2
blocked signal. hours)


• Urban canyons (Calgary, kinematic test, update Downtown San Francisco
rate: 1Hz, velocity: up to 50km/h, distance: about 40
km, time length: about 2.5 hours )

As discussed previously, the signal components were
determined by adjusting weight coefficients and
parameters in the model to fit the fading histograms of
collected data. The coefficients gave us the relative
magnitude of three categories of signals. To conduct the
model fitting, four elevation regions were chosen: 0-20°,
20-40°, 40-65°, and 65-90°. A separate model fitting was
done in each elevation region; Thus, the change of
signals with respect to the elevation could be studied.

The following steps are needed to complete a separate
model fitting:
1. Compute the signal fading histogram of collected
data.
2. Adjust coefficient and parameters of Ricean function
for clear signals
3. Adjust coefficient and parameters of Loo’s function
for shadowed signals Figure 6: Downtown San Francisco
4. Adjust coefficient and parameters of Rayleigh’s
function for blocked signals 0.03
San Francisco Urban Canyon : Elevation (0-20 Degs)

5. The resultant coefficients give relative magnitude for Field Data
3-State Model
each category of signals 0.025

0.02
Probability(%)

EXPERIMENTAL RESULTS 0.015

In this section, the model fitting results for each scenario 0.01

are presented.
0.005

Urban Canyon Tests
0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)
Two urban canyon tests were performed to test the signal
fading in a location with heavy masking and blocking (a) Elevation 0-20°
effects. One was in downtown San Francisco and the 0.045
Field Data
other in downtown Calgary. Experimental results showed 0.04
3-State Model
that the fading effects in these two areas were consistent
in major signal components and fading magnitude. 0.035

0.03

Figure 6 shows a typical view of the signal environment
Probability(%)

0.025
in downtown San Francisco. The plots in Figure 7 show
0.02
the theoretical pdf and the corresponding histogram of
the collected data. The blue lines in Figure 7 are the 0.015

histograms of the test data while the green lines 0.01

correspond to the model. 0.005

0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)

(b) Elevation 20-40°


San Francisco Urban Canyon : Elevation (40-65 Degs) collected data. The blue lines in Figure 9 are the
0.1
Field Data histograms of the test data while the green lines
0.09 3-State Model
correspond to the model.
0.08

0.07
Probability(%)

0.06

0.05

0.04

0.03

0.02

0.01

0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)

(c) Elevation 40-65°
0.25
Field Data
3-State Model

0.2
Probability(%)

0.15

0.1 Figure 8: Downtown Calgary

Calgary Urban Canyon : Elevation (0-20 Degs)
0.05 0.045
Field Data
3-State Model
0.04
0
-40 -30 -20 -10 0 10 20 30 40 50 0.035
Fade (dB)
0.03
(d) Elevation 65-90°
Probability(%)

0.025

Figure 7: Model Fitting Results for Urban Canyons 0.02
in San Francisco 0.015

The following conclusions can be drawn from these 0.01

results: 0.005

0
• In urban canyons, most signals were clear LOS -40 -30 -20 -10 0 10
Fade (dB)
20 30 40 50

signals and blocked signals. This is because there (a) Elevation 0-20°
were mainly concrete buildings instead of trees in
downtown. Calgary Urban Canyon : Elevation (20-40 Degs)
• The fading of blocked signals were centered at 10- 0.06
Field Data
15dB. 3-State Model
0.05
• With the increase of elevation, the percentage of
clear signals increased, and the percentage of 0.04
blocked signals decreased. This is obvious because
Probability(%)

of more open sky at higher elevation. 0.03
• The UTSFM fits the fading of real data well
although there are large discrepancies at the peaks of 0.02
the histograms.
0.01

Downtown Calgary
0
-40 -30 -20 -10 0 10 20 30 40 50
Figure 8 shows a typical view of the signal environment Fade (dB)

in downtown Calgary. The plots in Figure 9 show the (b) Elevation 20-40°
theoretical pdf and the corresponding histogram of the


Calgary Urban Canyon : Elevation (40-65 Degs)
0.09
Field Data
3-State Model
0.08

0.07

0.06
Probability(%)

0.05

0.04

0.03

0.02

0.01

0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)

(c) Elevation 40-65° Figure 10: Campus Buildings

Calgary Urban Canyon : Elevation (65-90 Degs) Campus Urban : Elevation (0-20 Degs)
0.16 0.08
Field Data Field Data
3-State Model 3-State Model
0.14 0.07

0.12 0.06

0.1 0.05

Probability(%)
Probability(%)

0.08 0.04

0.06 0.03

0.04 0.02

0.02 0.01

0 0
-40 -30 -20 -10 0 10 20 30 40 50 -40 -30 -20 -10 0 10 20 30 40 50
Fade (dB) Fade (dB)

(d) Elevation 65-90° (a) Elevation 0-20°

Figure 9: Model Fitting Results for Urban Canyons 0.14
Campus Urban : Elevation (20-40 Degs)

in Calgary Field Data
3-State Model
0.12

The results in downtown Calgary were consistent with
0.1
those in downtown San Francisco:
• Most signals were clear LOS signals and blocked
Probability(%)

0.08
signals.
• The fading of blocked signals was centered at 10- 0.06

15dB 0.04
• With the increase of elevation, the percentage of
clear signals increased, and the percentage of 0.02

blocked signals decreased.
0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)
Sub-Urban Test
This test was done at the University of Calgary where
there are many 2-3 story buildings. Figure 10 shows a
few buildings in the testing area, and Figure 11 shows the
model fitting results.


0.18
Field Data
3-State Model
0.16

0.14

0.12
Probability(%)

0.1

0.08

0.06

0.04

0.02

0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)


0.35
Field Data
Figure 12: Roadside Trees near the University of
0.3
3-State Model
Calgary

0.25 Calgary Road Side Tree : Elevation (0-20 Degs)
0.07
Field Data
Probability(%)

0.2 3-State Model
0.06

0.15
0.05

0.1
Probability(%)

0.04

0.05
0.03

0
-40 -30 -20 -10 0 10 20 30 40 50 0.02
Fade (dB)

(d) Elevation 65-90° 0.01

0
Figure 11: Model Fitting Results for Suburban -40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)
in the University of Calgary
(a) Elevation 0-20°
The following conclusions can be drawn from these
results: 0.12
Calgary Road Side Tree : Elevation (20-40 Degs)

Field Data
3-State Model

• The blocked signals appeared only at low elevation 0.1

because of the low height of surrounding buildings.
• Shadowed signals made considerable contribution to 0.08
Probability(%)

the overall signal, and appeared at low or middle
elevation regions. 0.06

• With the increase of elevation, clear LOS signals
0.04
increased a lot and shadowed signals decreased
quickly.
0.02
• The UTSFM fits the real data very well.
0
Road Side Test -40 -30 -20 -10 0 10
Fade (dB)
20 30 40 50

This test aimed to study the fading due to tree canopies,
and was done in a park close to the University of
Calgary. A picture of the park is shown in Figure 12 and
the model fitting results are shown in Figure 13.


0.14
Field Data
3-State Model
0.12

0.1
Probability(%)

0.08

0.06

0.04

0.02

0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)

Figure 14: Parking Lot in the University of Calgary
0.25
Field Data
3-State Model Open Sky : Elevation (0-20 Degs)
0.1
0.2 Field Data
0.09 3-State Model

0.08
Probability(%)

0.15
0.07

Probability(%)
0.06
0.1
0.05

0.04
0.05
0.03

0.02
0
-40 -30 -20 -10 0 10 20 30 40 50 0.01
Fade (dB)
0
(a) Elevation 65-90° -40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)

Figure 13: Model Fitting Results for Roadside Trees (a) Elevation 0-20°
near the University of Calgary
Open Sky : Elevation (20-40 Degs)
0.2
Field Data
0.18 3-State Model
The following conclusions can be drawn from these 0.16
results:
0.14
• Most signals were clear LOS signals and shadowed
signals.
Probability(%)

0.12

• Blocked signals appeared only at very low elevation 0.1

because there were some low buildings nearby. 0.08

• Shadowed signals consistently contributed to the 0.06

overall signal at all elevation.. 0.04

• The fading due to the shadowing effects of tree 0.02
canopies was about 2-5dB. 0
• UTSFM fits the real data very well. -40 -30 -20 -10 0 10
Fade (dB)
20 30 40 50


Open Sky Test

This test was a static test and performed at a large
parking lot in the University of Calgary. The picture of
the parking lot and the results of the test are shown in
Figure 14 and Figure 15.


Open Sky : Elevation (40-65 Degs) canopies was several dB. In this case, the satellites could
0.25
Field Data still be tracked. With the increase of elevation, the
3-State Model
percentage of clear signals increased and the percentage
0.2
of shadowed and blocked signals decreased because there
was more open sky when the elevation was higher.
Probability(%)

0.15

In the future, more experiments will be done in different
0.1
environments, and more analysis will be conducted to
determine the empirical values for model parameters.
Indoor GPS experiments and signal analysis will also be
0.05
addressed since GPS receiver may be required in such
serious conditions.
0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB)
REFERENCES

Open Sky : Elevation (65-90 Degs)
Barry McLarmon, VHF/UHF/Microwave Radio
0.35
Field Data
Propagation: A Primer for Digital Experimenters,
3-State Model http://www.tapr.org/tapr/html/ve3jf.dcc97/ve3jf.dcc97.ht
0.3
ml
0.25

Chun Loo (1985) A statistical model for a land mobile
Probability(%)

0.2
satellite link, IEEE Transactions on Vehicular
0.15 Technology, Vol. VT-34, No.3, Aug., 122-127.

0.1 FCC (2001), FCC wireless 911 requirements,
http://www.fcc.gov/e911/factsheet_requirements_012001
0.05
.pdf
0
-40 -30 -20 -10 0 10 20 30 40 50
Fade (dB) Frank van Diggelen (2001), Indoor GPS: Wireless
(d) Elevation 65-90° Aiding and Low SNR Detection, Navtech 218,
http://www.navtechgps.com/seminars/sem218.asp
Figure 15: Model Fitting Results for Open Ske Test
in the University of Calgary Julius Goldhirsh and Wolfhard J. Vogel (1998)
Handbook of propagation effects for vehicular and
Most signals here were clear LOS signals. Only at low personal mobile satellite system,
elevation were there some shadowed signals because http://www.utexas.edu/research/mopro/index.html
there were trees at the edges of the parking lot. In this
experiment, the model fitted the real data very well. R. Akturan and W. Vogel (1997), Path Diversity for LEO
Satellite-PCS in the Urban Environmenet, IEEE
In the appendix, the fitting results also appear in five Antennas and Propagation Vol. 45, No. 7, 1107-1116.
tables. The values of the model parameters show the
same results as discussed above.

CONCLUSIONS AND FUTURE WORK

The Urban Three-State Fade Model (UTSFM) is a useful
statistical model for describing the fading distribution of
GPS signals due to masking and blocking effects of
surrounding objects. The following conclusions result
from the experiments performed in this study. In urban
canyons, most received GPS signals were clear LOS
signals and blocked signals. The fading due to blocking
effects was larger than 10dB. In the case of roadside trees
shadowing due mostly to trees, most signals were clear
signals and shadowed signals. The fading due to tree


APPENDIX: MODEL FITTING RESULTS

Table 1. Model Fitting Results for San Francisco Urban Canyons

Elevation C PDF S PDF B PDF
(Degree) (Ricean) (Loo’s) (Rayleigh)
0~20 0.27 K=2 0.13 K = 20 m = -4 σ = 3 0.60 K = 16

20~40 0.35 K = 14 0.10 K = 20 m = -4 σ = 0.5 0.55 K = 20

40~65 0.37 K = 70 0.18 K = 20 m = -4 σ = 2 0.45 K = 16

65~90 0.66 K = 100 0.19 K = 20 m = -2.5 σ = 2 0.15 K = 16

0~90 0.37 K = 30 0.18 K = 20 m = -4 σ = 2.5 0.45 K = 18

Table 2. Model Fitting Results for Calgary Urban Canyons

0~20 0.22 K =9.8 0.0 K = 20 m = -4 σ = 3 0.78 K = 15

20~40 0.38 K = 22 0.07 K = 100 m = -6 σ = 4 0.55 K = 20

40~65 0.49 K = 22 0.18 K = 100 m = -3.5 σ = 3 0.35 K = 25

65~90 0.74 K = 25 0.19 K = 120 m = -2 σ = 4 0.08 K = 50

0~90 0.52 K = 20 0.13 K = 100 m = -2 σ = 3 0.35 K = 18

Table 3. Model Fitting Results for Sub-Urban Area ( University Campus)

0~20 0.3 K =10 0.65 K = 20 m = -3 σ = 1.5 0.05 K = 100

20~40 0.58 K = 20 0.41 K = 20 m = -1.6 σ = 2.3 0.01 K = 120

40~65 0.68 K = 55 0.32 K = 20 m = -3.5 σ = 2 0.001 K = 120

65~90 0.90 K = 120 0.10 K = 150 m = -4.5 σ = 4.5 0.001 K = 120

0~90 0.70 K = 35 0.30 K = 20 m = -3.5 σ = 2.5 0.01 K = 120


Table 4. Model Fitting Results for Road Side Trees

0~20 0.38 K =15 0.55 K = 15 m = -4 σ = 0.5 0.07 K = 100

20~40 0.4 K = 35 0.58 K = 15 m = -2.5 σ = 2 0.02 K = 120

40~65 0.45 K = 60 0.54 K = 15 m = -3 σ = 4 0.01 K = 120

65~90 0.63 K = 150 0.46 K = 150 m = -4.5 σ = 4.5 0.01 K = 120

0~90 0.57 K = 35 0.41 K = 20 m = -4.2 σ = 3 0.02 K = 120

Table 5. Model Fitting Results for Open Sky

0~20 0.65 K =13 0.35 K = 30 m = -2.2 0.005 K = 120
σ = 1.5

20~40 0.955 K = 35 0.04 K = 70 m = -3.3 0.005 K = 120
σ = 0.5

40~65 0.975 K = 67 0.025 K = 15 m = -1.8 0.001 K = 120
σ = 0.3

65~90 1.0 K = 150 0 0

0~90 0.87 K = 38 0.13 K = 30 m = -2 0.003 120
σ = 1.5


GPS Signal Degradation Modeling

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