Radiolocation in Cellular Networks - Virginia Tech of A-GPS Cellular ... (for super-resolution) ......
Transcript of Radiolocation in Cellular Networks - Virginia Tech of A-GPS Cellular ... (for super-resolution) ......
Radiolocation in
Cellular Networks Document ID: PG-TR-090603-GDD
Date: 3 June 2009
Prof. Gregory D. Durgin
777 Atlantic Ave. Atlanta GA 30332-0250 Voice: (404)894-8169 Fax: (404)894-5935
http://www.propagation.gatech.edu
Abstract – This tutorial presents an overview of how cellular phones can be found within a cellular network for both E911 dispatching and location-based services. We show how real radio location systems work with examples of measurement campaigns in live systems. After reviewing all location techniques, significant attention is paid to emerging received signal strength “finger-printing” techniques that have been deployed across the US and beyond. The tutorial concludes with several case studies in applications and radio forensics – using cellular location to fight crime.
No portion of this document may be copied or reproduced without written (e-mail)
consent of the Georgia Institute of Technology.
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AcknowledgementsGeorgia Tech FoundationPolaris Wireless Inc.Cingular (now AT&T)Comarco WirelessNSF CAREER Grant ECS-0546955Aerospace Corp.
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Credits
Albert Lu:measurementsLab Engineer2006-2008
Greg Durgin:Professortenure 2009
Josh Griffin:measurementsPhD 2009
Anil Rohatgi:measurements & web demoMS 2006
Ryan Pirkl:measurementsPhD 2009
Jian “Jet” Zhu:models, analysis, measurementsPhD 2006
Chris Durkin:models, measurementsMS 2005
Special Thanks to the Polaris Wireless Team…Robert MartinMarty FeuersteinSteve SpainTarun BhattacharyaSoma PitchaiahManlio Allegra
Prof. Paul Steffes:cellular consultantcolleague
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Radiolocation in Cellular Networks
by Prof. Gregory D. Durgin
Section I: Basics of Cellular Location; Assisted GPS
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AcknowledgementsGeorgia Tech FoundationPolaris Wireless Inc.Cingular (now AT&T)Comarco WirelessNSF CAREER Grant ECS-0546955Aerospace Corp.
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Credits
Albert Lu:measurementsLab Engineer2006-2008
Greg Durgin:Professortenure 2009
Josh Griffin:measurementsPhD 2009
Anil Rohatgi:measurements & web demoMS 2006
Ryan Pirkl:measurementsPhD 2009
Jian “Jet” Zhu:models, analysis, measurementsPhD 2006
Chris Durkin:models, measurementsMS 2005
Special Thanks to the Polaris Wireless Team…Robert MartinMarty FeuersteinSteve SpainTarun BhattacharyaSoma PitchaiahManlio Allegra
Prof. Paul Steffes:cellular consultantcolleague
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This Tutorial is Geared Towards…Engineers interested in how location works on a cellular networkResearchers who are looking for interested research topics in new location areasTechnologists interested in the possibilities of real-time location systems and their applicationsPeople who want to have a good time
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Outline of Section IRecommended ReadingHistory of Cellular LocationTaxonomy of Location TechniquesTrade-offs for Different TechniquesReview of GPS PrinciplesAssisted Global Positioning System
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E911 Position Location Mandate1996 FCC mandate for all US carriers
Original Target: <50m 67%, <100m 95% (3D)Handset Target: <100m 67%, <300m 95% (2D)Network Target: <50m 67%, <150m 95% (2D)
Numerous delays, failuresToday’s systems use a conglomerate of
Time-difference-of-arrivalAssisted GPSReceived Signal Strength Matching
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Cell Global Identity (CGI)CGI uses serving cell identificationIn most areas, CGI error is > 1 kmEasy and cheap to implement
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Cellular Global Identity (CGI)
Serving cell provides location estimate for the cell phone
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MS
NeighborCell
ServingCell
Antenna Array
Location Calculation & Control
Antenna Array
AOA: Angle of Arrival– Location solution based on apparent signal arrival angle
ProsOnly 2 base stations neededLegacy handsets covered
ConsLOS condition essentialLow location accuracy Additional equipment costLong deployment period
FactsModerate open area accuracyAtlanta area deployment cost : Several million dollars
Angle-of-Arrival
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Time-Difference Of Arrival (TDOA)
Time-of-Arrival triangulationRequires at least 3 audible base stations for 2D location
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MSNeighborCell
ServingCell
Location Calculation & Control
TOA: Time of Arrival– Location solution based on apparent signal arrival time
NeighborCell
ProsLegacy handsets covered
ConsPrecisely synchronized clocksLOS condition essentialPoor in rural areaAdditional equipment for GSM,TDMA
FactsModerate open area accuracyAtlanta area deployment cost : Several million dollars
Brother technologiesTDOAE-OTD
Time-of-Arrival
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Global Positioning System (GPS)Requires separate RF chain in every handsetRequires LOS to at least 3 satellitesMust be adapted to the cellular network
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MSServing
Cell
GPS Assist Location Calc
& Control
A-GPS: Assisted Global Positioning System– Location solution based on apparent TOA from GPS space vehicles
GPS SV ProsHigh outdoor accuracy
ConsLOS condition essentialLegacy handset not covered
FactsAtlanta area deployment cost : Several million dollars to be absorbed by consumer
Assisted Global Positioning System
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MSServing
Cell
Location Calc & Control
RSS: Received Signal Strength Fingerprint– Minimum of 1 site measurements attributes of received signal
ProsIndoor accuracyLow deployment costFast deployment speedLegacy handsets covered
ConsPoor coverage in rural area (Better than TOA and AOA solution though)
FactsModerate indoor and outdoor accuracyAtlanta area deployment cost : several thousand dollars
Received Signal Strength
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RSS Position Location for E911
Received Signal Strength (RSS)Measurements by a cellular handset…
…are matched against a Database of RF Maps
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PoorGreatPoorPoorRural Accuracy
LowLowHighHighOperation Cost
CoveredNot CoveredCoveredCoveredLegacy Handset
FastSlowModerateModerateDeployment Speed
RSSA-GPSAOATOA
LowModerateVery HighVery HighDeployment Cost
ModerateHighModerateModerateOutdoor AccuracyModeratePoorPoorPoorIndoor Accuracy
Comparison of Techniques
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Basics of A-GPSCellular implementation of a GPS receiverOften implemented as a single chip solution in a handsetOperates similarly to a portable GPS unit, with some important simplifications
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GPS Satellites24 satellites
6 constellations with 4 satellites each“spares” in orbit, too
Each orbit inclined 55 degrees, at 60 degree longitudinal orientationAll-earth coverage
Minimum 4 satellitesMaximum 9+ satellites
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Pseudo-Noise Generator
R. Pirkl, “A Sliding Correlator Channel Sounder for Ultra-Wideband Measurements”. Georgia Tech MS Thesis. PG-TR-070510-RJP.August 2007, http://www.propagation.gatech.edu/Archive/PG_TR_070510_RJP/PG_TR_070510_RJP.pdf
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Pseudo-Noise Sequence
R. Pirkl, “A Sliding Correlator Channel Sounder for Ultra-Wideband Measurements”. Georgia Tech MS Thesis. PG-TR-070510-RJP.August 2007, http://www.propagation.gatech.edu/Archive/PG_TR_070510_RJP/PG_TR_070510_RJP.pdf
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GPS Satellites TransmissionUses a Gold Sequence
Two 10-bit shift registers XORed togetherEasy to generate and correlate in early hardwareDoes not require an extensive table in memory
Different delays between two sequences result in different codes
Uniquely identifies each satelliteAbout 64 “useful” delay offsets (other delay offsets result in partial correlation in some Gold codes)Correlation with a PN provides relative time-of-arrival estimate
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GPS TransmissionThe GPS satellites also spread a low-rate (50 bps) data waveform that helps…
Correct for satellite orbit variations (ephemeris)Synchronize the clockProvide satellite “health and history” (almanac)
Spread spectrum allows reception in the presence of some interference
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Example Calculation
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Example Calculation
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How Easy is it to Jam GPS?Sample Problem:
A typical, open-sky GPS receiver picks up 8 approximately equal-powered satellite signals when operated near Hartsfeld-Jackson International Airport. These signals (the GPS C/A codes) are 50 bit/sec identifcation and timing data that are spread at 1.023 Mcps to an RF bandwidth of 2 MHz. You are hired by the department of homeland security to evaluate the ability to jam GPS receivers near the airport. If a malevolent agent has a 7 dBi-gain Yagi antenna connected to a jammer/transmitter and aims this device at a plane beginning a landing approach from 5 kilometers away, how much jamming power is required to make the C/A code have a C/I < 6 dB after despreading?
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Jamming GPS
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Accuracy in GPS SystemsNsat – number of satellites used in estimateTb – bit duration (20 ms)Tc – chip duration (1 μs)Tint – integration period (for super-resolution)(C/N)despread – carrier-to-interference ratio after despreading (linear)
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Dilution of Precision (DOP)Previous formula assumes near-ideal arrangement of GPS satellites receivedIf decoded satellites are clustered in one area of the sky, significant DOP resultsDifferent types of DOP
GDOP – geometrical dilution of precisionPDOP – position dilution of precisionHDOP – horizontal dilution of precisionVDOP – vertical dilution of precision
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Sources of Error in GPS 2.4m – Receiver noise4.3m – Ephemeris error (orbit discrepancies)3.5m – Clock errors 6.4m – Ionospheric delay2.0m – Tropospheric delay3.0m – Multipath (optimistic)32.0m – Selective Availability (discontinued)Total error of 9.5m without selective availability
T. Pratt, C. Bostian, J. Allnutt, Satellite Communications, 2th edition, Pratt, Bostian, and Allnutt. Wiley, 2003.
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Augmented GPS Concepts Which errors are avoidable?
2.4m – Receiver noise4.3m – Ephemeris error (orbit discrepancies)3.5m – Satellite clock errors6.2m – Ionospheric delay2.0m –Tropospheric delay3.0m – Multipath
Make a fixed location measurement in a local area to check for these errorsBroadcast this corrective information
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The “A” in Assisted GPS for CellularHandset receives synchronization cuesBase station has information about local atmospheric delayHandset only calculates pseudo-ranges, sends to base station for the final calculationsPrinciple issue is yield, not accuracy
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Applications for Cellular NetworksE911 Emergency LocationFind a friendSite-specific advertising and vendor locationReal-time traffic modelingSite-specific driving directionsSmart network optimization (by carrier)
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For Further Reading…S. Ahonen and H. Laitinen, “Database correlation method for umts location,” Jeju, South Korea, 2003, vol. vol.4 of 57th IEEE Semiannual Vehicular Technology Conference. VTC 2003 (Cat. No.03CH37431), p. 2696, IEEE.
M. Aso, M. Kawabata, and T. Hattori, “A New Location Estimation Method Based on Maximum Likelihood Function in Cellular Systems,” in Vehicular Technology Conference 2001 Fall. IEEE VTS 54th, 2001, vol. 1, pp. 106 – 110. Y. Chen and H. Kobayashi, “Signal Strength Based Indoor Geolocation,” in Communications, 2002. ICC 2002. IEEE International Conference on, May 2002, vol. 1, pp. 436 – 439.
G.D. Durgin, “Location Estimation of Wireless Terminals Using Indoor Radio Frequency Models.,”Patent filed on, December 2003.Federal Communication Commission, “Enhanced 911 - Wireless Services,” Online at http://www.fcc.gov/911/enhanced/, 1999.I. Y. Kelly, Deng Hai, and Ling Hao, “On the feasibility of the multipath fingerprint method for location finding in urban environments,” Applied Computational Electromagnetics Society Journal, vol. 15, no. 3, pp. 232, 2000.H. Koshima and J. Hoshen, “Personal Locator Services Emerge,” Spectrum, IEEE, vol. 37, pp. 41 –48, Feb 2000.Pratt, Bostian, and Allnutt, Satellite Communications, 2nd edition, Wiley, 2003. J. Warrior, E. McHenry, and K. McGee, “They Know Where You Are [location detection],” IEEE Spectrum, vol. 40, no. 7, pp. 20, 2003.
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Radiolocation in Cellular Networks
by Prof. Gregory D. Durgin
Section I: RSS System Trials
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Outline of Section IITrials on Georgia Tech Campus
Indoor/outdoor data collectionUrban campus performance
Trials in Greenville, SCWide area urban/suburban performanceMulti-story buildingsEnhanced Algorithms
Trials in Manhattan, NYUrban environmentIndoor penetration modeling
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Why RSS Signature Location?Moderate indoor and outdoor accuracyLow deployment costFast deployment speedLegacy handsets coveredCovers multiple cellular technologiesAdditional capability: indoor/outdoor discriminationFits in different sizes of networkExpandable to other communication technologies such as WLAN2
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How an RSS Signature Engine Works
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How an RSS Signature Engine Works
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Corresponding toCell ID
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RSS
ChannelNumber
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NMR: Network Measurement Report
MSServing
CellLocation Calc
& Control
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Cramer-Rao Lower Bound
The CRLB provides a lower bound on the covariance matrix of the unbiased estimator
( ) )(CovˆCov cr zz ≥
⎥⎦
⎤⎢⎣
⎡=
yx
z where
Path loss exponent
Geometry of base station
Measurement correlation
Number of NMRs used
Number of audible base station
Measurement Error
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CRLB- Simulation Environment
−3 −2 −1 0 1 2 3 4
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Uni
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irect
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Baseline:Path loss exponent: 3.3
Average base station separating distance: 500(m)
Measurement correlation from same base station: 0.5
Number of NMRs: 30
Standard deviation of measurement error: 3.5
Number of audible base station: 4
Output: 82.0 m
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Numerical Result: Path Loss-Related
2 2.5 3 3.5 4 4.5 520
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larger path loss exponent because higher path loss increases the uniqueness of the RSS signature.
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Performance: Base Station Separation Distance
the location error increaseslinearly with the base station separation distance.
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Numerical Result: Measurement Error-related
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of measurement error leads to a more inaccurate location estimation.
The standard deviationof the measurement error has to be lower than 6.5 dB so that the standard deviation of the locationerror is lower than 100 m when six base station signals are reported in an NMR.
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Numerical Result: NMRs Used
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Using more NMRs increase location accuracy.
The location accuracy improves dramatically when the number ofNMRs used increases from 1 to 10.
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Phase I: Georgia Tech Campus Study
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Three Keys to Accurate RSS LocationAccuracy of Predicted Signal Database
Most difficult aspect of the problemRequires propagation modeling
Repeatability of Measurement at Handset Location Algorithm
Many different variations possibleAttempt to achieve CRLB limit
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Information used in preparing RF maps:
• Base station longitude
• Base station latitude
• Sector antenna orientation
• Sector antenna height
• Frequency channel
• Transmit power
Preparing a Predicted Signal Database
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Level 0 Predicted Signal Database
0 50 100 150 200 250
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Modified Hata Model:
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Level 1 Predicted Signal Database
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Level 1 Predicted Signal Database
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Measurement Route Record at Architecture Building
Building Measurement Sample
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Measurement Photos
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Indoor Location
Stat: 67% of all European cell-phone calls are indoors.
RSSI-based system perhaps the only way to discriminate indoor/outdoor users.
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Predicted Signal Database Modeling
Octant model of orientation loss
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Level 2 Predicted Signal Database
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Level 2: Calibration with outdoor measurements and indoor modeling
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Level 3 Predicted Signal Database
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Comparison of Different PSDs
Level 3Level 2Level 1Level 0
HighModerateModerateLowGenerating Cost
Very SlowModerateModerateFastGenerating Speed
BestHighModerateLowAccuracy
Level 0: Pure Prediction
Level 1: Calibration with outdoor measurement
Level 2: Calibration with outdoor measurement and indoor modeling
Level 3: Calibration with exhaustive outdoor and indoor measurements
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Collecting Handset Test DataManually log indoor data
Connect cellular scanners to palmtop computerRecord data on indoor mapsActive call data
Separate acquisitionsScanner data for predicted signal databaseActive call data to build a test database
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Three Keys to Accurate RSS LocationAccuracy of Predicted Signal Database
Most difficult aspect of the problemRequires propagation modeling
Repeatability of Measurement at Handset Location Algorithm
Many different variations possibleAttempt to achieve CRLB limit
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Repeatability MeasurementsHead-handset shadowing
Measure tracks of data in the same area, but with different orientationsAverage variation has σ = 2 dB
Small-scale fading within a “bin”Measure tracks of data through a binNote: pure Rayleigh fading predicts σ = 5 dBAverage variation of σ = 2 dBHandsets perform some temporal averaging in their measurements
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Three Keys to Accurate RSS LocationAccuracy of Predicted Signal Database
Most difficult aspect of the problemRequires propagation modeling
Repeatability of Measurement at Handset Location Algorithm
Many different variations possibleAttempt to achieve CRLB limit
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Assumption in Absolute RSS Location: – Assume prefect knowledge of the antenna/RF chain bias between the user
handset and the scanner used to calibrated the PSD
Algorithm: Absolute RSS Location
LocationError
Statistics
67%45%20%<100m
86%78%32%Indoor/OutdoorDiscrimination Rate
95%90%60%<300m
Level 3Indoor/Outdoor Meas.
Level 2Indoor Model
Level 1Outdoor Meas. PSD level
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Relative RSS Location: – Mean is removed from Both NMR and each roaster point in PSD
Algorithm: Relative RSS Location
LocationError
Statistics
60%54%54%<100m
51%43%43%Indoor/OutdoorDiscrimination Rate
95%94%94%<300m
Level 3Indoor/Outdoor
Meas.
Level 2Indoor Model
Level 1Outdoor Meas. PSD level
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Assumption for Hybrid RSS Location: – All commercial hand sets have roughly similar attenuation in
RF chain.
Fact: – Indoor/Outdoor discrimination information is embedded in
absolute RSS– Fingerprint method is more accurate by using relative RSS
information
RSSA: Received Signal Strength Aggregate, The average of the strongest several channels, could be used to discriminate indoor/outdoor caller.
Algorithm: Hybrid RSS Location
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RSS Indoor/Outdoor Discrimination
-97.8dB -85.5dB
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Algorithm: Hybrid RSS Location
LocationError
Statistics
65%56%56%<100m
90%90%90%Indoor/OutdoorDiscrimination Rate
96%96%96%<300m
Level 3Indoor/Outdoor
Meas.
Level 2Indoor Model
Level 1Outdoor Meas. PSD level
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10 NMRs were linearly averaged to form an averaged NMR to increase the Repeatability of Measurement at Handset
Algorithm: Location With Averaging
LocationError
Statistics
78%64%61%<100m
91%92%92%Indoor/OutdoorDiscrimination Rate
98%98%97%<300m
Level 3Indoor/Outdoor
Meas.
Level 2Indoor Model
Level 1Outdoor Meas. PSD level
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Comparison of Different Algorithms
SatisfiedCloseNot goodNot goodE911 Mandate
Hybrid with Averaging
HybridRelativeAbs
SlowFastFastFastLocation Fix Generation Time
BestLowModerateHighLocation Error Statistics
BestHighLowLowDiscrimination Rate
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RSS location techniques meet the FCC's requirements for E911 accuracy.
The techniques remain accurate for indoor handsets.
RSS location engine has ability to discriminate between indoor and outdoor handsets
Research provide performance up-limit for Indoor modeling
Phase I: Conclusions
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Different commercial network trials in varied environmentsUrban, suburban, rural environments in Triton’s GSM network at
Greenville, SCLarger testing area allow the existing of egregious location errorThe effect of high-rise building
Accurate propagation modelingBased on more knowledge: building structure, building materials,
surrounding environment, multi-path effects, base station location and elevation. Reduce the time and cost of extensive drive-testing
More complicated RSS fingerprint location algorithmDSP filtering technology: matching vs. trackingIterative calculation
Phase II: Large Area GSM Experiments
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The 7000 m by 9000 m test area in Greenville, SC
Extended Experiment in Greenville, SC
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Longitude/Latitude map of base stations (* and O) in Greenville, SCusing DCCH 786 on Dec 14, 2004. The thick path s a single drive-test route throughthe test area.
Base stations in Greenville
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RSS Indoor/Outdoor Discrimination
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RSS Indoor/Outdoor Discrimination
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GPS effectiveness
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RSS in a High-rise Building
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RSS Location Performance in Greenville
Location error statistics for the relative RSS-method with limited search area and distance matrix aggregate. (10 NMRs, 6 sectors)
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Phase III: Manhattan, NYThe “ultimate urban environment”Indoor modeling is criticalA-GPS struggles in this kind of environment
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Indoor Propagation Model
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Example Indoor Prediction Mask
Indoor Pattering Block
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Location Results in Manhattan (Fall 2005)
100%99.1%92.5%83.5%67.4%Level 1 PSD
Outdoor Test PointsIndoor Test Points
100%100%95.4%77.0%36.8%Level 2 PSD
100%100%<500m100%98.9%<300m95.3%92.0%<150m85.1%75.9%<100m68.0%25.3%<50mError
Statistics
Level 2 PSDLevel 1 PSDPSD Level
Level 1 PSD: RF database calibrated with outdoor measurement
Level 2 PSD: Calibration with outdoor measurement and indoor modeling
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Radiolocation in Cellular Networks
by Prof. Gregory D. Durgin
Section III: Propagation/CSI
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AcknowledgementsGeorgia Tech FoundationPolaris Wireless Inc.Cingular (now AT&T)Comarco WirelessNSF CAREER Grant ECS-0546955Aerospace Corp.
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Outline of Section IIIPath Loss ModelsData Mining Propagation Elements
Antenna PatternsRoadsTerrain DiffractionClutter Effects
Crime-Fighting with CellularCase Study: 2000 Dekalb Co. Murder Investigation
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Path Loss Exponent Model
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Dynamic Range Limits
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Path Loss Exponent Model
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Exhaustive Propagation Prediction
Virginia Tech Campus
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Example RF Measurement (5.8 GHz)
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Basics of a Seidel-Rappaport Model
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Tuning a Seidel-Rappaport Model
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Tuning a Seidel-Rappaport Model
This linear system is over-constrainedMay be solved using MMSE Normal Equations:
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Generalized Seidel-Rappaport ModelModel distance-related loss as free spaceAdd attenuation factors for each object blocking the line-of-sightBenefits
IntuitiveFast computationLinear optimization
Pit fallsNot deterministicRequires some measurements for tuning
5
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For Cellular Location Systems, We HaveDistance between base station and handsetBearing angle with respect to BS antennaBase station antenna height & downtiltGeographical Information Services
Terrain mapsClutter mapsRoad vectorsBuilding footprints (urban areas)
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Distance-Related LossesUse a path-loss exponent model for lossKey differences
Other losses presentTypically lower than exponent-only models
( )d10log17.2
3.0010
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧− 2.60
Example from 900 MHzMacrocells
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Distance and Antennas Only2 x 2.5 km Received Signal Strength Map
6
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Antenna PatternsMMSE fit to a 4th-order harmonic expansionMost important is the first harmonic cos θθ is angle between center sector and handset bearing angleThis model consistently outperforms the range-measure base station antenna patterns
Table 1: Basic analysis of all data, sorted by frequency and base station type.
Cell Type # Sites n Offset (dB) cos θ cos 2θ cos 3θ cos 4θ
Macro 900 558 2.56 24.3 -6.5 -0.5 0.0 -0.4 Macro 1900 2275 2.79 9.3 -9.7 0.0 0.4 -0.3 Micro 900 222 2.94 20.8 -4.7 -0.7 -0.8 -0.4 Micro 1900 71 1.73 55.6 -4.3 -1.6 -0.2 0.0
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Spatial Measurement Distribution
Copyright 2006-200918
Road Orientation LossesRoads cut “channels”through environmentPeak gain whenever BS bearing angle aligns with roadRoad orientation data is ubiquitously availableOften requires conversion to raster format
0
20
40
60
80
100
120
140
160
180
Road Orientation Map,(San Jose, CA area)
9
Copyright 2006-200925
Geometry of the Diffracting Half-Plane
y
zx
PEC ScreenShadow Boundary
Reflect
ion Bou
ndary
Point of Observation( , )
i
IncidentPlane Wave
i
i
π−
π−
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Exact Solution for Diffracting PEC Edge
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Geometrical Optics – Conducting Edge
Phase of the Geometrical Optics Field,
0
50
100
150
200
250
300
360Geometrical Optics Field, ( = 60o)
<-50
-40
-30
-20
-10
0 dB
−4λ 4λ−4λ 4λ−4λ
4λ
−4λ
4λ
10
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Sommerfeld Solution (Perp Pol)
Total ⊥ -Field, Phase of the Total ⊥ -Field, ( = 60o)
<-50
-40
-30
-20
-10
0 dB
0
50
100
150
200
250
300
360
−4λ 4λ−4λ
4λ
−4λ
4λ
−4λ 4λ
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Sommerfeld Minus GO (Perp Pol)
Phase of the Diffracted Field,
0
50
100
150
200
250
300
360Diffracted Field, ( = 60o)
<-50
-40
-30
-20
-10
0 dB
−4λ 4λ −4λ 4λ−4λ
4λ
−4λ
4λ
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Sommerfeld Solution (Par Pol)
<-40
-35
-30
-25
-20
-15
-10
-5
0 dB
5
( = 60 )
0
50
100
150
200
250
300
360
o
−4λ 4λ−4λ
4λ
−4λ
4λ
−4λ 4λ
Total ||-Field, Phase of the Total ||-Field,
11
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Sommerfeld Minus GO (Par Pol)
<-40
-35
-30
-25
-20
-15
-10
-5
0 dB
5
Phase of the Diffracted Field,
0
50
100
150
200
250
300
360Diffracted Field, ( = 60o)
−4λ 4λ −4λ 4λ−4λ
4λ
−4λ
4λ
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Comparison of Diffraction (Normal Inc.)
0 50 100 150 200 250 300 350
-30
-20
-10
0
10
20
30
Diffracted Power for ⊥- and ||-Polarizations
Azimuth Angle
P||
/P⊥
( dB
)
90o 270o180o
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Knife Edge Diffraction Formula
Total Field, Phase of the Total Field, ( = 60o)
0
50
100
150
200
250
300
360
−4λ 4λ−4λ
4λ
−4λ
4λ
−4λ 4λ
0 dB
<-40
-30
-20
-10
12
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Knife Edge Formula Minus GO
Phase of the Diffracted Field,
0
50
100
150
200
250
300
360Diffracted Field, ( = 60o)
−4λ 4λ −4λ 4λ−4λ
4λ
−4λ
4λ
0 dB
<-40
-30
-20
-10
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Terrain Diffraction Example
r2=500mφ2=225o
φ3=45or
3=500mr 1=500m
TX RXφ1=27.5o
φ4=242.5o
150m 150m
r2=500mφ2=270o
φ3=90o r3=500mr 1=500m
TX RXφ1=72.5
o
φ4=287.5o
150m 150m
Wedge Geometry
Equivalent Screen Geometry
Copyright 2006-200936
Example: FM Propagation Over TerrainWREK transmits a 91.1 MHz FM
radio signal with effective isotropic radiated power of EIRP = 54.0 dBW (about 250 kW). To reach one coverage area, the station must rely on double diffraction over the top of two terrain peaks of equal altitude that can be modeled as 90-degree wedges. How much received power would each GTD coefficient predict?