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 Changlin Ma is a graduate student of the department of Geomatics Engineering at the University of Calgary. He received his B.S.(1992) and M.S.(1995) in Electronics Engineering from Northwestern Polytechnical University (Xi’an, China), and his first Ph.D.(1998) also in Electronics Engineering from Tsinghua University (Beijing, China). His current research is focused on GPS receiver technology. Gyu-In Jee is a Professor in the Department of Electronics Engineering at Konkuk University in Seoul, Korea. He received his Ph.D. in Systems Engineering from Case Western Reserve University on 1989. He has worked on several GPS related research projects; GPS receiver software design, GPS/INS integration for land vehicle, DGPS system development, GPS engine design using the Mitel chip sets, wireless location in CDMA network, etc. His research interests include software GPS receiver, wireless positioning for E911, and GPS/INS integration for personal navigation. Mr. Glenn MacGougan is a MSc. student in the Department of Geomatics Engineering at the University of Calgary. In 2000 he completed a BSc. in Geomatics Engineering at the University of Calgary. He will complete his second degree in September 2002. Dr. Gerard Lachapelle is a Professor and Head of the Department of Geomatics Engineering where he is responsible for teaching and research related to positioning, navigation, and hydrography. He has been involved with GPS developments and applications since 1980. Scott Bloebaum received the B.S. and M.S. degrees in Electrical Engineering from Virginia Tech, and the Ph.D. degree in Electrical Engineering from North Carolina

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State University. He has been with Ericsson since 1990, where he has held a variety of roles in research and development for cellular phones and networks. Currently, he is a Technical Manager in Ericsson Mobile Platforms and Technologies in Research Triangle Park, NC where he is responsible for positioning technology development. He has been involved with GPS for four years and played a key role in setting GSM standards for network-assisted GPS. His technical interests are hybrid cellular-satellite positioning technology, speech enhancement and compression, and multicarrier modulation and transmission systems. He holds four U.S. patents. Geoffrey F. Cox received his B.A. degree in Geology/Chemistry and Mathematics at the University of Maine in 1992, M. Eng. in Geomatics Engineering from the University of Calgary in 1996. His area of study at that time was GPS Positioning and Navigation with emphasis on the Foliage Effects on GPS Signals. Since 1996, Mr. Cox has worked in many engineering and business capacities ranging from WADGPS development for Terrestrial and Aviation Precision Agricultural Systems, Commercial RTK Survey and Mapping Systems. In beginning of 2000, Mr. Cox consulted for various companies by providing GPS related engineering and marketing services. Mr. Cox joined SiRF Technology, Inc. in the fall of 2000 as Senior Applications Engineer. Lionel Garin is Lead Architect at SiRF Technology. Prior to joining SiRF he worked on Multipath Rejection techniques, survey quality GPS and Glonass receivers at Ashtech and Sagem. Mr. Garin holds a MSEE from EcoleNationale Supérieure des Télécommunications. John L. Shewfelt received a B.Sc. in Electrical Engineering from the University of California Santa Barbara in 1981. Since that time Mr. Shewfelt has been

involved in design, development, test and integration of complex avionics and guidance systems for various types of aircraft and naval platforms, including working with microwave radars and receivers, Jammers, UV and IR imaging systems, and GPS/INS guidance and control. In March of 2000, Mr. Shewfelt joined SiRF Technology Inc. as Applications Engineering Manager to facilitate the integration of GPS technology into embedded products and platforms. ABSTRACT This paper attempts to provide some insight into the fading properties of GPS signals. When a GPS signal gets to an antenna, it suffers from masking and blocking effects from surrounding objects. With respect to these effects, GPS signals can be divided into clear LOS signals, shadowed signals, and blocked signals. A statistic model, Urban Three-State Fade Model (UTSFM), is discussed in this paper. Experimental results show that this model can describe the fading distribution of GPS signals very well. After model fitting, the model parameters can indicate the composition of the incoming signals in terms of the relative magnitude of the three signal types. INTRODUCTION Although GPS was first designed as a military system to provide real time position, it is becoming a necessity in people’s daily life. GPS receivers are now being made smaller and smaller and can be integrated into many devices to provide both position and time with high accuracy. Its application has already extended to many areas, such as, earthquake detection, cellular phone positioning, so on and so forth. 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, 2001), it was shown that GPS signals become very weak

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in this case, thus requiring a GPS receiver to be able to acquire and track weak signals. Secondly, GPS signals in these serious situations can contain serious multipath signals, which can degrade positioning accuracy significantly. To understand and perhaps solve these problems knowledge about the GPS signal channel is obviously a prerequisite. Unfortunately, not much research has been done in this area. Thus, the motivation for this paper was to further such research. This paper examines the GPS signal channel near receiver antennas. Specifically, it focuses on the signal fading distribution due to masking and blocking effects of surrounding objects. To do so incoming GPS signals are first divided into three categories: Clear LOS signals, Shadowed signals, and Blocked signals. A statistic model, Urban Three-State Fade Model (UTSFM), is introduced to fit the fading histogram of real data. The fitting results describe the signal composition based on the data. The outline of this paper is a follows: the GPS signal channel is discussed, a signal classification is presented, the Urban Three State Model is explained, and finally experimental data and model fitting is discussed. Some conclusions and discussion of ensuing research conclude the paper. GPS SIGNAL CHANNEL When a GPS signal propagates from a satellite to a receiver antenna, it suffers from degradation effects, such as, free space loss, refraction and absorption from the atmosphere, reflection and masking from surrounding objects such as trees and buildings, jamming, and environmental noise.

Figure 1: GPS signal propagation

This paper focused on signal strength fading due to reflection and masking by surrounding objects such as trees and buildings. Huygens’ principle tells us that waves are propagated by wavelets on sequential wave fronts. When an object blocks some wavelets, waves of other wavelets can still reach the shadowed region, but the signal strength is decreased, as shown in Figure 2.
Figure 2: Huygens’ Principle Normally, the concept of the Fresnel zone especially the first Fresnel zone is used to characterize the shadowing and blocking effects (Barry McLarmon), as shown in Figure 3.

Figure 3: Fresnel Zone The Fresnel zone is the volume of space enclosed by an 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 ellipsoid defined such that the distance summation of a point C on the ellipsoid to A and B is one wavelength longer than the direct distance between A and B, i.e. AC+CB = AB + λ. From experience, the fading effect is negligible if there are no objects in the first Fresnel zone, and the fading effect is thought serious if there are objects in this region.

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SIGNAL CLASSIFICATION With respect to fading effects, GPS signals can be divided into three categories: Clear line-of-sight (LOS) signal: This kind of signal gets to the receiver antenna directly without any object in 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 This is a statistical model, and has been utilized in the study of land-mobile communication system (J. Goldhirsh and Wolfhard J. Vogel 1998). It is used here to describe the GPS signal fading distribution. The idea of 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

( ) ( )[ ] ( )KvIvKKvvf Ricean 21exp2 02 +−= (1)

where v is the received voltage relative to the clear path voltage, K is the ratio of the direct power received to the multipath power, and ( )0I is the 0th order modified Bessel function. If signals from a satellite are blocked, the received signals consist of only multipath signals. In this case, the fading distribution can be expressed by a Rayleigh pdf which is a special case of Ricean function without LOS signal

( ) [ ]2exp2 KvKvvf Rayleigh −= (2)

If signals from a satellite can be directly received but are attenuated by trees or other materials, these signals are called shadowed signals and the fading can be described by Loo’s function (Chun Loo, 1985)

( )

( )( ) ( ) ( )∫∞

+−−−

=

00

222

2

'

22

log20exp1

2686.8

dzKvzIzvKmzz

Kvvf sLoo

σ

σπ (3)

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 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).

( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) 1

,=++

++=

ααααααα

BSCvfBvfSvfCvf RayleighLooRiceanv (4)

Where α is the elevation, and ( )αC , ( )αS , and ( )αB are weight coefficients. These coefficients can be thought as indicators of the relative magnitude of the three kinds of signals at a certain elevation. The following figure is an example of Ricean pdf, Rayleigh pdf, and Loo’s pdf.

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PDF of Ricean, Rayleigh, and Loo

Ricean RayleighLoo

Figure 4: pdf of Ricean, Rayleigh, and Loo’s The blue line is a Ricean pdf and is centered at 0dB for clear signals. The red line corresponds to Loo’s function and is commonly centered less than 10 dB for shadowed signals. Finally, the green line corresponds to a Rayleigh pdf and is normally centered larger than 10 dB for blocked signal.

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In this paper, the fading histograms of real data were fitted by adjusting the coefficients and parameters in the model. The results indicate the composition of the received signals. EXPERIMENT DESCRIPTION Some experiments had been done to study how well the statistic model can describe GPS signal fading. The data were collected by the scheme shown in Figure 5.

Reference

Rover

Figure 5: Data collect scheme The reference station receiver was located on the roof of a five story building with a very good view of the sky. The rover receiver was mounted on a car. The fading data of rover were obtained by comparing the carrier to noise density ratio, C/N0, between the two receivers. An assumption that there was not extra fading at reference station was made. This means that the fading at reference station was due only to free space loss and absorption from atmosphere. This fading was also shared by the rover and could be removed by differencing. The fading difference between the rover and the reference station was thus due to masking effects of the surrounding objects near the rover. The receivers used at reference station and rover were the same in order to guarantee that the algorithms used to calculate the C/N0 were identical. Several typical working environments were chosen, and the masking effects varied from light to heavy. These scenarios were as follows: • Open sky (stationary test, data rate: 1Hz, time

length: 1.5 hour) • Road-side tree shadowing (kinematic test, update

rate: 1 Hz, velocity: up to 50km/h, distance: about 50 km, time length: about 2.5 hours)

• Moderate sub-urban with 2 or 3 floor buildings (kinematic test, update rate: 1Hz, velocity: up to 50km/h, distance: about 40 km, time length: about 2 hours)

• Urban canyons (Calgary, kinematic test, update 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 4. Adjust coefficient and parameters of Rayleigh’s

function for blocked signals 5. The resultant coefficients give relative magnitude for

each category of signals EXPERIMENTAL RESULTS In this section, the model fitting results for each scenario are presented. Urban Canyon Tests Two urban canyon tests were performed to test the signal fading in a location with heavy masking and blocking effects. One was in downtown San Francisco and the other in downtown Calgary. Experimental results showed that the fading effects in these two areas were consistent in major signal components and fading magnitude. Figure 6 shows a typical view of the signal environment in downtown San Francisco. The plots in Figure 7 show the theoretical pdf and the corresponding histogram of the collected data. The blue lines in Figure 7 are the histograms of the test data while the green lines correspond to the model.

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Downtown San Francisco

Figure 6: Downtown San Francisco

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San Francisco Urban Canyon : Elevation (0-20 Degs)

Field Data 3-State Model

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(d) Elevation 65-90°

Figure 7: Model Fitting Results for Urban Canyons

in San Francisco

The following conclusions can be drawn from these results: • In urban canyons, most signals were clear LOS

signals and blocked signals. This is because there were mainly concrete buildings instead of trees in downtown.

• The fading of blocked signals were centered at 10-15dB.

• With the increase of elevation, the percentage of clear signals increased, and the percentage of blocked signals decreased. This is obvious because of more open sky at higher elevation.

• The UTSFM fits the fading of real data well although there are large discrepancies at the peaks of the histograms.

Downtown Calgary Figure 8 shows a typical view of the signal environment in downtown Calgary. The plots in Figure 9 show the theoretical pdf and the corresponding histogram of the

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collected data. The blue lines in Figure 9 are thhistograms of the test data while the green linecorrespond to the model.

Figure 8: Downtown Calgary

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Figure 9: Model Fitting Results for Urban Canyons

in Calgary The results in downtown Calgary were consistent with those in downtown San Francisco: • Most signals were clear LOS signals and blocked

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

15dB • With the increase of elevation, the percentage of

clear signals increased, and the percentage of blocked signals decreased.

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.

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Figure 10: Campus Buildings

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Figure 11: Model Fitting Results for Suburban

in the University of Calgary The following conclusions can be drawn from these results: • The blocked signals appeared only at low elevation

because of the low height of surrounding buildings. • Shadowed signals made considerable contribution to

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

• With the increase of elevation, clear LOS signals increased a lot and shadowed signals decreased quickly.

• The UTSFM fits the real data very well. Road Side Test 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.

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Figure 12: Roadside Trees near the University of Calgary

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Calgary Road Side Tree : Elevation (0-20 Degs)



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Figure 13: Model Fitting Results for Roadside Trees

near the University of Calgary

The following conclusions can be drawn from these results: • Most signals were clear LOS signals and shadowed

signals. • Blocked signals appeared only at very low elevation

because there were some low buildings nearby. • Shadowed signals consistently contributed to the

overall signal at all elevation.. • The fading due to the shadowing effects of tree

canopies was about 2-5dB. • UTSFM fits the real data very well. 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.

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Figure 14: Parking Lot in the University of Calgary

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Figure 15: Model Fitting Results for Open Ske Test

in the University of Calgary Most signals here were clear LOS signals. Only at low elevation were there some shadowed signals because there were trees at the edges of the parking lot. In this experiment, the model fitted the real data very well. In the appendix, the fitting results also appear in five 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

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canopies was several dB. In this case, the satellites could still be tracked. With the increase of elevation, the percentage of clear signals increased and the percentage of shadowed and blocked signals decreased because there was more open sky when the elevation was higher. In the future, more experiments will be done in different environments, and more analysis will be conducted to determine the empirical values for model parameters. Indoor GPS experiments and signal analysis will also be addressed since GPS receiver may be required in such serious conditions. REFERENCES Barry McLarmon, VHF/UHF/Microwave Radio Propagation: A Primer for Digital Experimenters, http://www.tapr.org/tapr/html/ve3jf.dcc97/ve3jf.dcc97.html Chun Loo (1985) A statistical model for a land mobile satellite link, IEEE Transactions on Vehicular Technology, Vol. VT-34, No.3, Aug., 122-127. FCC (2001), FCC wireless 911 requirements, http://www.fcc.gov/e911/factsheet_requirements_012001.pdf Frank van Diggelen (2001), Indoor GPS: Wireless Aiding and Low SNR Detection, Navtech 218, http://www.navtechgps.com/seminars/sem218.asp Julius Goldhirsh and Wolfhard J. Vogel (1998) Handbook of propagation effects for vehicular and personal mobile satellite system, http://www.utexas.edu/research/mopro/index.html R. Akturan and W. Vogel (1997), Path Diversity for LEO Satellite-PCS in the Urban Environmenet, IEEE Antennas and Propagation Vol. 45, No. 7, 1107-1116.

APPENDIX: MODEL FITTING RESULTS

Table 1. Model Fitting Results for San Francisco Urban Canyons

Table 2. Model Fitting Results for Calgary Urban Canyons

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

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

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

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

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

K = 16 0.60 K = 20 m = -4 σ = 3 0.13 K = 2 0.27 0~20

PDF (Rayleigh)

B PDF (Loo’s)

S PDF (Ricean)

C Elevation (Degree)

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

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

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

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

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

PDF (Rayleigh)

B PDF (Loo’s)

S PDF (Ricean)


K = 120 0.001 K = 150 m = -4.5 σ = 4.50.10 K = 120 0.90 65~90

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

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

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

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

PDF(Rayleigh)

B PDF (Loo’s)

S PDF (Ricean)


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Table 4. Model Fitting Results for Road Side Trees

Table 5. Model Fitting Results for Open Sky

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

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

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

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

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

PDF (Rayleigh)

B PDF (Loo’s)

S PDF (Ricean)


0 0 K = 150 1.0 65~90

K = 120 0.001 K = 15 m = -1.8 σ = 0.3

0.025 K = 67 0.975 40~65

120 0.003 K = 30 m = -2 σ = 1.5

0.13 K = 38 0.87 0~90

K = 120 0.005 K = 70 m = -3.3 σ = 0.5

0.04 K = 35 0.955 20~40

K = 120 0.005 K = 30 m = -2.2 σ = 1.5

0.35 K =13 0.65 0~20

PDF (Rayleigh)

B PDF(Loo’s)

S PDF (Ricean)


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