Positioning: A Computing Perspective Outline Motivation, Use-Cases Navigation Mapping Geo-localization: Determining ones position Geo-Referencing: Specifying a position Positional Accuracy Geo-Privacy Conclusions 2 Location Based Services Open Location Services Location: Where am I? (street address, ) Directory: Where is the nearest clinic (or doctor)? Routes: What is the shortest path to reach there? 3 Motivation, Use-Cases Consumers Hikers : Where am I in a mountain range? Tourists: Where am I in a new city? Asset Tracking: Where is my smartphone? Car? Key ring? Businesses Transportation: Taxi-sharing (e.g., Uber), Connected & Self-driving Cars Agriculture: Precision Agriculture Asset tracking: Where are the trucks in my fleet? Government Health: Where is an Alzheimer patient ? Public Safety: Find epi-center of an Earthquake, Geo-targeted alerts and warnings Military: Precision Targeting, Avoid friendly fire, Navigation 2 5 Outline Motivation, Use-Cases Geo-localization: Determining ones position Problem Definition & Taxonomy Localization Approaches: (Tri)angulation, (Tri)lateration, Fingerprint map, Proximity, Simultaneous localization and mapping Geo-Referencing: Specifying a position Positional Accuracy Geo-Privacy Conclusions 2 Geo-localization : Problem Definition Output: Object Os location Cases: (a) A point (b) A zone, (c) Sub-area of Earth Inputs A map = A set S of well-known objects & their properties Objects: (a) Natural: stars, landmarks, (b) Man-made: satellites, cell-towers, Properties: (a) Locations, (b) Signal frequency & coding Line of sight relationship(O, S), e.g., distance(O, S), angle(O, S), Objectives, Constraints Positional Accuracy, Fast response Large Coverage, Low cost and power cost 2 Geo-localization Approaches Vectors Use a distance and an angle Angulation Use only angles Lateration Use only distances Database Search Fingerprints, Map matching Simultaneous Localization & Mapping 2 A Vector to find unknown position Vector = (distance, angle) to a landmark L from the unknown point P Range finder: find |a| = distance (P, L) Compass: find v = angle(P, L) Geometric Method Draw a circle of radius d with L as center Draw a ray from L at angle a Algebraic Method Suppose L = (xL, yL), P = (xP,yP), v is angle from east Then xP = xL |a|*cos(v); yP = yL |a|*sin(v) Physical Measurement of Angles On Paper Map - Protractor Outdoors Compass Sextant Theodolite, 2 Physical Measurement of Distance Tape or chain measure Clocks Rangefinder (round-trip time / (signal_speed * 2) Delay in receiving a clock source Signal_travel_time/speed (clocks synchronized) Dead reckoning f(direction, speed, acceleration, elapsed time) Other Power decay Doppler shift in frequency of a source 2 Geo-localization Approaches Vectors Use a distance and an angle Angulation Use only angles Lateration Use only distances Database Search Fingerprints, Map matching Simultaneous Localization & Mapping 2 Find distance using angles from 2 known positions Triangulation: Measurement using triangles Locate 3rd vertex, measure angles two known vertices Find distance 2D: use 2 angles + 1 distance 3D: 2 angles + 1 distance + 1 azimuth Ex. Estimate Distance(ship, shore) measure angles from 2 well-known points l = d *( cotangent(alpha) + cotangent(beta) ) Does it also position the Ship? Find unknown position from angles to 2 landmarks Angulation: Measurement using angles (lines) Intersection of 2 straight lines locates a point Resection: Locate a unknown point Measure angles to 2 landmark to locate Measure angles to 3 landmarks to locate & verify Geometry: Use a compass & a topo map Algebra: Given: (a) angle a1 (from East vector) to point p1 = (x1, y1) (b) (counter-clock) angle a2 (from East) to pint p2 = (x2, y2) Find equations of two lines L1 and L2 L1 is y = tan(a1) *x + y1 x1*tan(a1) L2 is y = tan(a2)*x + y2 x2*tan(a2) Find intersection point (x,y) between L1 and L2 Triangulation: Other Meanings Q?: Which of following meanings are relevant to positioning? Surveying : Measurement using triangles Geometry: Divide (polygon or plane) into triangles Linear Algebra: find an upper triangular matrix similar to a matrix Computer Vision: Compute a 3D point given its projection on to two or more images Social Science: Use multiple cross-checked sources and methodology 2 Geo-localization Approaches Vectors Use a distance and an angle Angulation Use only angles (e.g., compass) Lateration Use only distances Database Search Fingerprints, Map matching Simultaneous Localization & Mapping 2 Lateration using 1 distance Lateration: Locate position using distance from reference points Mono-lateration: Use one distance Linear referencing system, e.g., highway mile-marker Dead Reckoning Proximity sensors, e.g., tile (blue-tooth), RFID, IR, Lateration in 2-dimensions Lateration: Infer P from its Distance from K locations Is K = 2 sufficient in 2-dimensions, where P = (x, y)? 2 equations and 2 unknowns (x, y) 3 circles determine a point in 2-dimensions Trilateration: Use distance from 3 locations Listen to sources (e.g., satellites, wi-fi, cell towers) If Os clock is synchronized with source clocks Distance = Signal_travel_time / speed 2 Mathematics of Lateration Given: Distances r1, r2 and r3 to 3 known positions (x1, y1), (x2, y2), (x3, y3) Find: unknown location = (xu, yu) Equations: sqr(x1 xu) + sqr(y1 yu) = sqr (r1) Sqr(x2 xu) + sqr(y2 yu) = sqr(r2) Sqr(x3 xu) + sqr(y3 yu) = sqr (r3) Subtract 3 rd equation from first two and reorder 2(x3 x1) xu + 2(y3 y1) yu = (sqr(r1)-sqr(r3)) (sqr(x1)-sqr(x3)) (sqr(y1)-sqr(y3)) 2(x3 x2) xu + 2(y3 y2) yu = (sqr(r2)-sqr(r3)) (sqr(x2)-sqr(x3)) (sqr(y2)-sqr(y3)) Two linear equations in two unknowns (xu, yu) Provides unique solutions if equations are independent Lateration (With Error) Given: Distances r1, r2, , rk to K known positions (x1, y1), (x2, y2), , (xk, yk) Find: unknown location = X = (xu, yu) (K 1) Equations : A X = b 2(xk x1) xu + 2(yk y1) yu = (sqr(r1)-sqr(rk)) (sqr(x1)-sqr(xk)) (sqr(y1)-sqr(yk)) 2(xk x2) xu + 2(yk y2) yu = (sqr(r2)-sqr(rk)) (sqr(x2)-sqr(xk)) (sqr(y2)-sqr(yk)) ... 2(xk x(k-1)) xu + 2(yk y(k-1)) yu = (sqr(r(k-1))-sqr(rk)) (sqr(x(k-1))-sqr(xk)) (sqr(y(k-1)-sqr(yk)) Estimate X = (xu, yu) given matrix A and vector b to minimize mean square error of fit Multi-Lateration If Os clock not synchronized with source clocks Multi-lateration : use distance from K (> 3) locations Estimate clock bias (b) and location (x, y, z) 2 Global Positioning System A GPS receiver computes its position(x, y, z) on earth by measuring its distances from four of the satellites. position in space of the i th satellite position of the receiver time delay for signal from satellite i Speed of light The error of receivers clock Satellite-based Positioning Pioneers: NASA GRARR, Army SECOR, Navy Transit, NOAA ARGOS, Global Navigation Satellite System (GNSS) US NAVSTAR GPS NAVigation Satelite Time And Ranging Global Positioning System A few dozen satellites + 6 control station + many differential GPS transmitters NIST F-2 Caesium clock (accuracy of 1 second in 1211 Million Years) Receivers use 3 satellites to estimate location & time Receiver accuracy: (cm to m, 14ns to 100 ns) GLONASS (Russia), Galileo (EU), Beidou (China), IRNNS (India), DORIS (France), QZSS (Japan), 2 GPS Pros and Cons Strengths of GPS Unified coordinate system worldwide Low device cost, High accuracy & Broad coverage outdoor Weaknesses & New Approaches Power hungry, Long time-to-first-fix Assisted GPS : A server computes position and shares with clients However, it reduces positional accuracy for clients Drifts Map matching for vehicles Coverage Gaps, jamming & spooofing Indoors: augment with wi-fi, cell towers Outdoors: GPS III stronger signal and encryption Outdoors: Fingerprinting: Earths gravitational and magnetic fields 2 Geo-localization Approaches Vectors Use a distance and an angle Angulation Use only angles Lateration Use only distances Database Search Fingerprints, Map matching Simultaneous Localization & Mapping 2 Fingerprinting: A big data approach General Idea : No two places on Earth are exactly alike! Signals of FM stations, cell towers, wi-fi, Gravitation anomaly maps (US GRACE satellite) Magnetic anomaly field (EU CHAMP satellite) Plant and animal species, Ecological variables, Method Create a database of fingerprints of many locations Fingerprint (location) = value of N signals To localize an unknown location L Search database for closest matches Output map of locations matching fingerprint(L) Applications Localization in GPS-denied environment Find location of an image or video from content 2 US Public Radio Stations Atlantic, 11/22/2013 (Road) Map matching Idea : Urban vehicles are seldom off-road Estimate best-matched position on a road network Method Closest position on road center-lines Constrained by velocity and history Applications Address GPS inaccuracy, drift, low sampling, temporary loss 2 Simultaneous Localization and Mapping (SLAM) Use-case: If GPS signal is weak, use wi-fi to improve positioning Challenge: private owner may not share location & movement Method: Iterative refinement with a set of (moving) cars/phones Localize self via GPS, known wi-fi, cell towers, FM, map-matching, dead-reckoning, Map: Location of unknown wi-fi transmitter = f (observation from 3 or more locations) Correlate wi-fi locations with wi-fi hotspot MAC addresses Repeat synchronously or asynchronously Example2 Outline Motivation, Use-Cases Geo-localization: Determining ones position Geo-Referencing: Specifying a position Symbolic place names Reference Systems Linear, Spheroid, Ellipsoidal, Translating across specifications Positional Accuracy Geo-Privacy Conclusions 2 Geo-Referencing Why should we care? To compare maps To register GPS coordinates to a Map To compute distance, direction, Alternative Georeferencing Symbolic Geo-Referencing Place names (e.g., Dinkytown, Eyjafjallajkull, ) Street address (200 Union St. SE, MN 55455) Internet URLs, MAC address Numeric Geo-Referencing (Latitude, longitude), GPS reading, map projections, Geo-code: Translate symbolic to numerical geo-reference Ex.: street address to latitude-longitude on map Reverse Geo-code: translate numeric geo-reference to symbolic Ex. GPS coordinate to a street address Numeric Geo-Referencing Coordinate system A method for assigning unique codes to locations Goal: locations can be found using its code Relative location Using units of maps paper sheet East-ing, e.g., x-direction value North-ing, e.g., y-direction Absolute locations Projected: e.g., Universal Transverse Mercator System Relative to Earths center: e.g., latitude, longitude, elevation On surface of the Earth: Q? What is shape of Earth? WGS-84 Earth is modeled as an spheroid (bi-axial ellipsoid) a = km, b = km (WGS-84) Measure by GPS ground stations, periodically aligned with ITRF 2 Gravity field Outline Motivation, Use-Cases Geo-localization: Determining ones position Geo-Referencing: Specifying a position Positional Accuracy Motivation Factors affecting accuracy Typical Accuracy Geo-Privacy Conclusions 2 Accuracy GPS Accuracy depends on Number of visible satellites Occlusion by tall trees, building, hills, Accuracy of clocks at receiver and satellites Multi-path reflections, Atmospheric conditions Availability of additional signals, e.g., wi-fi, cell tower, differential GPS, Other methods accuracy issues F(accuracy for distance, directions) 2 Accuracy of other methods Triangulation accuracy depends on Reference point positional accuracy Angle measurement resolution Distance to reference points 2 Outline Motivation, Use-Cases Geo-localization: Determining ones position Geo-Referencing: Specifying a position Positional Accuracy Geo-Privacy Stakeholders & their interests Common Grounds Privacy Enhancement Techniques Conclusions 2 38 Check-in Risks: Stalking, GeoSlavery, Ex: Girls Around me App (3/2012), Lacy Peterson [2008] Others know that you are not home! The Girls of Girls Around Me. It's doubtful any of these girls even know they are being tracked. Their names and locations have been obscured for privacy reasons. (Source: Cult of Mac, March 30, 2012)Cult of Mac, March 30, 2012 Challenge: Privacy vs. Utility Trade-off Geo-privacy Emerging personal geo-data Trajectories of smart phones, gps-devices, life-trajectories and migrations, Reveals home, work, frequented places, Privacy: Who gets my data? Who do they give it to? What promises does a citizen get? Socio-technical problem Need policy support Challenges in fitting location privacy into existing privacy constructs (i.e HIPPA, Gramm-Leach-Bliley, Children's Online Privacy Protection Act) Geo-privacy conversation starters Gr oups interested in Geo-Privacy Civil Society Economic Entities Public Safety Policy Makers Outline Motivation, Use-Cases Geo-localization: Determining ones position Geo-Referencing: Specifying a position Positional Accuracy Geo-Privacy Conclusions 2