GPS Signal Degradation Modeling
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GPS Signal Degradation Modeling Document Transcript

  • 1. 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, CABIOGRAPHY State University. He has been with Ericsson since 1990, where he has held a variety of roles in research andChanglin 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 Mobilereceived 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 fourElectronics 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 hybridreceiver technology. cellular-satellite positioning technology, speech enhancement and compression, and multicarrierGyu-In Jee is a Professor in the Department of modulation and transmission systems. He holds fourElectronics Engineering at Konkuk University in Seoul, U.S. patents.Korea. He received his Ph.D. in Systems Engineeringfrom Case Western Reserve University on 1989. He has Geoffrey F. Cox received his B.A. degree inworked on several GPS related research projects; GPS Geology/Chemistry and Mathematics at the University ofreceiver software design, GPS/INS integration for land Maine in 1992, M. Eng. in Geomatics Engineering fromvehicle, DGPS system development, GPS engine design the University of Calgary in 1996. His area of study atusing the Mitel chip sets, wireless location in CDMA that time was GPS Positioning and Navigation withnetwork, etc. His research interests include software GPS emphasis on the Foliage Effects on GPS Signals. Sincereceiver, wireless positioning for E911, and GPS/INS 1996, Mr. Cox has worked in many engineering andintegration for personal navigation. business capacities ranging from WADGPS development for Terrestrial and Aviation Precision AgriculturalMr. Glenn MacGougan is a MSc. student in the Systems, Commercial RTK Survey and MappingDepartment of Geomatics Engineering at the University Systems. In beginning of 2000, Mr. Cox consulted forof Calgary. In 2000 he completed a BSc. in Geomatics various companies by providing GPS related engineeringEngineering at the University of Calgary. He will and marketing services. Mr. Cox joined SiRFcomplete 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 theDepartment of Geomatics Engineering where he is Lionel Garin is Lead Architect at SiRF Technology. Priorresponsible for teaching and research related to to joining SiRF he worked on Multipath Rejectionpositioning, navigation, and hydrography. He has been techniques, survey quality GPS and Glonass receivers atinvolved with GPS developments and applications since Ashtech and Sagem. Mr. Garin holds a MSEE from1980. EcoleNationale Supérieure des Télécommunications.Scott Bloebaum received the B.S. and M.S. degrees in John L. Shewfelt received a B.Sc. in ElectricalElectrical Engineering from Virginia Tech, and the Ph.D. Engineering from the University of California Santadegree in Electrical Engineering from North Carolina Barbara in 1981. Since that time Mr. Shewfelt has beenION GPS 2001, 11-14 September 2001, Salt Lake City, UT 882
  • 2. involved in design, development, test and integration of in this case, thus requiring a GPS receiver to be able tocomplex avionics and guidance systems for various types acquire and track weak signals. Secondly, GPS signals inof aircraft and naval platforms, including working with these serious situations can contain serious multipathmicrowave radars and receivers, Jammers, UV and IR signals, which can degrade positioning accuracyimaging systems, and GPS/INS guidance and control. In significantly.March of 2000, Mr. Shewfelt joined SiRF TechnologyInc. as Applications Engineering Manager to facilitate To understand and perhaps solve these problemsthe integration of GPS technology into embedded knowledge about the GPS signal channel is obviously aproducts 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 nearThis paper attempts to provide some insight into the receiver antennas. Specifically, it focuses on the signalfading properties of GPS signals. When a GPS signal fading distribution due to masking and blocking effectsgets to an antenna, it suffers from masking and blocking of surrounding objects. To do so incoming GPS signalseffects 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 statisticsignals, shadowed signals, and blocked signals. A model, Urban Three-State Fade Model (UTSFM), isstatistic 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 onresults 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 signalincoming 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. SomeINTRODUCTION conclusions and discussion of ensuing research conclude the paper.Although GPS was first designed as a military system toprovide real time position, it is becoming a necessity in GPS SIGNAL CHANNELpeople’s daily life. GPS receivers are now being madesmaller and smaller and can be integrated into many When a GPS signal propagates from a satellite to adevices to provide both position and time with high receiver antenna, it suffers from degradation effects, suchaccuracy. Its application has already extended to many as, free space loss, refraction and absorption from theareas, such as, earthquake detection, cellular phone atmosphere, reflection and masking from surroundingpositioning, so on and so forth. objects such as trees and buildings, jamming, and environmental noise.These new applications impose more seriousrequirements on GPS itself. Traditionally, a GPS receiverwas required to function in an open area with a clearview of the sky, but in new applications it is required towork in degraded signal environments.One typical example is the use of GPS in cellular phonesthat are required to be “location Aware” for the E911mandate in the near future ( FCC 2001). GPS is apromising solution to this requirement since it canprovide position autonomously. However, when lookingat this problem in detail, there are many issues to address.First, cellular phones are used in many places, not only inopen areas. This means the GPS receiver built in acellular phone must work well in places where there isnot much open sky, such as, urban canyons or inside abuilding. From previous a study (Frank van Diggelen, Figure 1: GPS signal propagation2001), it was shown that GPS signals become very weakION GPS 2001, 11-14 September 2001, Salt Lake City, UT 883
  • 3. This paper focused on signal strength fading due toreflection and masking by surrounding objects such as SIGNAL CLASSIFICATIONtrees and buildings. With respect to fading effects, GPS signals can beHuygens’ principle tells us that waves are propagated by divided into three categories:wavelets on sequential wave fronts. When an objectblocks some wavelets, waves of other wavelets can still Clear line-of-sight (LOS) signal: This kind of signalreach the shadowed region, but the signal strength is gets to the receiver antenna directly without any object indecreased, 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 theNormally, 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 toand blocking effects (Barry McLarmon), as shown in describe the GPS signal fading distribution. The idea ofFigure 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 modifiedThe Fresnel zone is the volume of space enclosed by an Bessel function.ellipsoid, which has the two antennas A and B at the endsof a radio link as its foci. The first Fresnel zone is an If signals from a satellite are blocked, the receivedellipsoid defined such that the distance summation of a signals consist of only multipath signals. In this case, thepoint C on the ellipsoid to A and B is one wavelength fading distribution can be expressed by a Rayleigh pdflonger than the direct distance between A and B, i.e. which is a special case of Ricean function without LOSAC+CB = AB + λ. From experience, the fading effect is signalnegligible 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.ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 884
  • 4. If signals from a satellite can be directly received but are In this paper, the fading histograms of real data wereattenuated by trees or other materials, these signals are fitted by adjusting the coefficients and parameters in thecalled shadowed signals and the fading can be described model. The results indicate the composition of theby 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: attenuatedLOS signals of which the fading is log normallydistributed and multipath signals of which the fading is ReferenceRayleigh distributed.In the Urban Three-State Fade Model, the compositeamplitude probability density function is the combinationof 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 ) = 1Where α is the elevation, and C (α ) , S (α ) , and B (α ) are Figure 5: Data collect schemeweight coefficients. These coefficients can be thought asindicators of the relative magnitude of the three kinds of The reference station receiver was located on the roof ofsignals 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 dataThe following figure is an example of Ricean pdf, of rover were obtained by comparing the carrier to noiseRayleigh 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, updateThe blue line is a Ricean pdf and is centered at 0dB for rate: 1 Hz, velocity: up to 50km/h, distance: about 50clear 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 buildingssignals. Finally, the green line corresponds to a Rayleigh (kinematic test, update rate: 1Hz, velocity: up topdf and is normally centered larger than 10 dB for 50km/h, distance: about 40 km, time length: about 2blocked signal. hours)ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 885
  • 5. • 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 weredetermined by adjusting weight coefficients andparameters in the model to fit the fading histograms ofcollected data. The coefficients gave us the relativemagnitude of three categories of signals. To conduct themodel fitting, four elevation regions were chosen: 0-20°,20-40°, 40-65°, and 65-90°. A separate model fitting wasdone in each elevation region; Thus, the change ofsignals with respect to the elevation could be studied.The following steps are needed to complete a separatemodel fitting:1. Compute the signal fading histogram of collected data.2. Adjust coefficient and parameters of Ricean function for clear signals3. Adjust coefficient and parameters of Loo’s function for shadowed signals Figure 6: Downtown San Francisco4. 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 0.015In this section, the model fitting results for each scenario 0.01are presented. 0.005Urban Canyon Tests 0 -40 -30 -20 -10 0 10 20 30 40 50 Fade (dB)Two urban canyon tests were performed to test the signalfading in a location with heavy masking and blocking (a) Elevation 0-20° San Francisco Urban Canyon : Elevation (20-40 Degs)effects. One was in downtown San Francisco and the 0.045 Field Dataother in downtown Calgary. Experimental results showed 0.04 3-State Modelthat the fading effects in these two areas were consistentin major signal components and fading magnitude. 0.035 0.03Figure 6 shows a typical view of the signal environment Probability(%) 0.025in downtown San Francisco. The plots in Figure 7 show 0.02the theoretical pdf and the corresponding histogram ofthe collected data. The blue lines in Figure 7 are the 0.015histograms of the test data while the green lines 0.01correspond to the model. 0.005 0 -40 -30 -20 -10 0 10 20 30 40 50 Fade (dB) (b) Elevation 20-40°ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 886
  • 6. 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° San Francisco Urban Canyon : Elevation (65-90 Degs) 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 0.015The following conclusions can be drawn from these 0.01results: 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. 0.01Downtown Calgary 0 -40 -30 -20 -10 0 10 20 30 40 50Figure 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 theION GPS 2001, 11-14 September 2001, Salt Lake City, UT 887
  • 7. 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 0.12The results in downtown Calgary were consistent with 0.1those 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 (b) Elevation 20-40°This test was done at the University of Calgary wherethere are many 2-3 story buildings. Figure 10 shows afew buildings in the testing area, and Figure 11 shows themodel fitting results.ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 888
  • 8. Campus Urban : Elevation (40-65 Degs) 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) (c) Elevation 40-65° Campus Urban : Elevation (65-90 Degs) 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 theseresults: 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. 0Road Side Test -40 -30 -20 -10 0 10 Fade (dB) 20 30 40 50 (b) Elevation 20-40°This test aimed to study the fading due to tree canopies,and was done in a park close to the University ofCalgary. A picture of the park is shown in Figure 12 andthe model fitting results are shown in Figure 13.ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 889
  • 9. Calgary Road Side Tree : Elevation (40-65 Degs) 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) (c) Elevation 40-65° Figure 14: Parking Lot in the University of Calgary Calgary Road Side Tree : Elevation (65-90 Degs) 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 ModelThe following conclusions can be drawn from these 0.16results: 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 (b) Elevation 20-40°Open Sky TestThis test was a static test and performed at a largeparking lot in the University of Calgary. The picture ofthe parking lot and the results of the test are shown inFigure 14 and Figure 15.ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 890
  • 10. 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 (c) Elevation 40-65° 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 andMost 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.htmlthere were trees at the edges of the parking lot. In thisexperiment, the model fitted the real data very well. R. Akturan and W. Vogel (1997), Path Diversity for LEO Satellite-PCS in the Urban Environmenet, IEEEIn 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 thesame results as discussed above.CONCLUSIONS AND FUTURE WORKThe Urban Three-State Fade Model (UTSFM) is a usefulstatistical model for describing the fading distribution ofGPS signals due to masking and blocking effects ofsurrounding objects. The following conclusions resultfrom the experiments performed in this study. In urbancanyons, most received GPS signals were clear LOSsignals and blocked signals. The fading due to blockingeffects was larger than 10dB. In the case of roadside treesshadowing due mostly to trees, most signals were clearsignals and shadowed signals. The fading due to treeION GPS 2001, 11-14 September 2001, Salt Lake City, UT 891
  • 11. 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 Elevation C PDF S PDF B PDF (Degree) (Ricean) (Loo’s) (Rayleigh) 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) Elevation C PDF S PDF B PDF (Degree) (Ricean) (Loo’s) (Rayleigh) 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 = 120ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 892
  • 12. Table 4. Model Fitting Results for Road Side Trees Elevation C PDF S PDF B PDF (Degree) (Ricean) (Loo’s) (Rayleigh) 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 Elevation C PDF S PDF B PDF (Degree) (Ricean) (Loo’s) (Rayleigh) 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 = 1.5ION GPS 2001, 11-14 September 2001, Salt Lake City, UT 893