Sensor Networks CMPE 259
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Date Created: 09/07/15
Exploring Data Aggregation Ignacio Solis isolissoeucscedu Data Aggregation Overview What is aggregation Data collection Taxonomy Some aggregation algorithms for collecting data from all nodes Escan TAG Cascading timeouts Isolines Data Collection Taxonomy 39 Aggregate data as it ows through the network When is data generated Sporadic Periodic Where is data generated all producing selected producing single producing Where is data collected fullsite selected site singlesite Data must meet certain criteria Not all data can be aggregated Lossy amp Lossl ess aggregation arr How is data packaged Lossy or Lossless Concatenation fusion addition reduction Allproducing aggregation schemes Characteristics All nodes produce periodically Data can be aggregated Via addition Tree construction is done by simple broadcast Not the focus 0 Types Noaggregation Periodic aggregation Perhop aggregation eScan Aggregation Topology An eScan Node constructs eScan with its information Only reports on signi cant change Gateways express INTERESTS INTERESTS construct trees eScans ow through trees Nodes receiving scans can aggregate them if they are near each other and of similar values Representation and aggregation of eScans Query Propagation SELECT COUNT 0 S CELEDQ lg 9 Epoc Com Slot TAG 39 Innetwork processing of aggregates Common data analysis operation 0 Aka gather operation or reduction in H programming Communication reducing Operator dependent bene t Across nodes during same epoch 39 Exploit semantics improve efficiency Aggregation timing Schemes packets WWI 39 E x w x I period end Slotted l l l I l Simple Cascading Timers Simulation Parameters O Q 0 NSZ 80211like MAC 39 100 nodes No movement j 39 Transmission range 100m 1 I 1 RI Kl Area 500x500 3 scenarios corner sink center sink random sink Random sink is presented here Data Freshness Weighted Freshness 1 T m 7 77 Name m 0 75 FHSimpi gt i 1 a m L a a 5 Pen N E w E 05 2 J E E m i U 3 m o 25 n m mm i m W um i m Wm n iiii N 0 i i i i t i t i i u u 1 u 2 u s u o B u 9 Number of packets collected Collection under Packet loss Can39t spend time recovering Loosing aggregated packages is a risk FEC DoubleSend MaxSend AdaptiveSend Readings collected per round Loss probability Packets sent per round a Number of packets sent 02 o 3 Loss probability Packets per reading Number of packets per reading collected m uz u d Lass probability Real Freshness Aggregating Data by Grouping When to aggregate is not enough for collecting all Algorithm ls Period 10s period None 0563 5003 the data on the network Tag 0413 4233 We need to exploit the correlation between the Cascading Timeouts 0283 0283 data being collected Periodic 2 04s 1 91 33 PerH0p 1543 15353 Can we group nodes How do we determine the grouping How do we represent them Average delay per packet from being sent to being considered at sink lsoclusters Grouping by value Isolines Group nodes into isoclusters where all the members have a sensed variable in the same range ie contour maps isotherms c When collecting data we can Focus on 911993 isopleths r Isolines Isoclustering Example 39 Isolines are lines which pass 0 NS27 400 X 400 meter 11D through our network and A have the same value Nodes 39 16 X 16 sensor nodes In gr1d patter 7 1 J detect them by comparing 40 the value they are sensing meter communlcauon range 7 Wlth the nelghbors We map reality no aggregation and isoclusters 9 g 39 When nodes detect a nearb isohne they send a report tg Isoclusters sends 13 of the readlngs no the data aggregatlon sends 39 Only nodes detecting lines 39 We map with GMT mapping tools report Isoclustering Example cont Isoclustering Example cont Reality All nodes reporting Reality Isoclusters g a f L a 5 f Ll Isoclustering Example cont Reality Isoclusters reporting nodes bf Front monitoring magfw v ltA Czgt r v 4 None Polygon 1 Continuous Monitoring Front monitor l 2 a 0 Monitor an area for events mapping a continuous variable like monitoring temperature We want to exploit both spatialcorrelation and temporalcorrelation 0 Report only when data has changed significantly Be careful about dead nodes and packet drops None Optimized Isocluster iitr39oduction to GPS A Brief Introduction to the Global Positioning System GPS CMPE 259 Guest Lecture Prof Gabriel H Elkaim 9February2005 Satellite Navigation system Multilateration based on oneway ranging signals from 24 satellites in orbit Operated by the United States Air Force Nominal Accuracy 0 10 m Stand Alone 0 15 m Code Differential o 001 m Carrier Differential introduction to GPS Navigation Terminology 0 Navigation Answer the to the question Where am Iquot Implies the use of some agreed upon coordinate system 0 Related Terminology Guidance Deciding what to do with your navigation information Control Orienting yourselfvehicle to follow out the guidance decision 0 Area of Study GNC Guidance Navigation Control Latitude Parallels are formed by the intersection of the surface of the earth with a plane parallel to the equatorial plane Longitude Meridians are formed by the intersection of the surface of the earth with a plane containing the earths FIi raductmn EGPS Latitude Longitude and Altitude North Pole 0 One of many coordinate systems used to described a location on the surface of the earth 0 Latitude parallels measured from the Equator North is o Longitude meridians measured from Greenwich Observatory East is o Altitude measured above reference datum MSL Normally Up is Stability of Clocks U l 11 JLlL Lm l li l VAL Emlmiuri in Tin kquing Malnuw Inr r l H Lita inquot Sam Pcrfmunse has Promded LIME mm Meier Bene t to Society During his Millemium in vaeuiLiTElujv i Figure from HewlettPackard Application Note 1289 The Science of Timekeeping by D W Allan Neil Ashby and CliffHodge PunkErwin a Jrzv le 55m Hm 32d F uu I IJI39dLlumi qulis a Earmtrl tI3muquotulm m I l1 rlri 1quot III W umJt lempuin lllt LEW I39ll IJ I Car Ill1l39l quot5 1ZEIL Cllll lE Hm uni lr39 mmuri g E l1n39 if E 4Fl I I aEIELI le I31 t Eiluzlmsr Hpu udmliJlmllull Ilium l39l Hm balms Clock stability is directly related to Navigation because Earth rotates 15 hour Difference between local celestial time and reference yields Longitude Atomic clocks are too big and too expensive for general use 9039 I1 ur pg i 39 K Arrbiguow ix kdill In In use aquot39 D MU sta tiuns fa From Kyton and Fried Avionics Navigation Systems 2quotquot1 Ed pp 113 BTJ AD 1 or sry one Ii39a TIME of stalmzs provide a fill a b c d Bearing and range p e position fixing DMEVOR Dual bearing 0 9 position fixing VOR VOR Range p p position fixing DMEDME GPS Hyperbolic position fixing LORAN Omega 71w u uillcl i i Assuming you can make the range measurements piywhere i 123 then the following three equations can be formed pixX12yy12 pizixX22yy22 pizixstHyysiz Fundamentals of Position Fixing The figure on the previous page raises to important questions How do you estimate or measure the ranges How do you solve the equations for the unknown x and y The range based on measuring the timeofflight of a RF signal that leaves t e transmitter at t t1 and arrives at the user at t t2 IS given by pEct2t1 In the presence of a clock error St bc the range estimate or measurement becomes Ep bc12 tlc tctZ tlb GPS Pseudoranges 6 sv 1 As a user located at point X the true range measurements to the three GPS satellites are pfm 201 cbu 0 02ch 0 203 cbu Your GPS receiver however measures p1 pzand p3 These range measurement are called pseudoranges 3910 OF 62 Pseudorange Measurement Error Resulting Position Uncertainty Areas Geometry plays a role in the accuracy of the final solution pm Paeudorangas measurements x lkil W 24kb Satallita positicns known Fm xllkaer ykyfzilz9 b k12 K If Kl 4 r solve for user position x y z and receiver clock hlas b jtroduction ESPE Solving Navigation Equations 0 Solve the p p equations Easy and give you insight into the linearization process GPS navigation equations o The p p position fixing system of equations where three independent range measurements are available was given as pixx12yy12 pdxxdzdyydz pi Xxs2yy32 L J Y Exact Equations you would solve in an ideal world ipi6pi 5cx5x iy5y Equations the you can or will solve Linearization by Expansion 2 For the range measurements piZpl 5pl2 pf2 pi5p5p2pi22 pi p dropped higher order terms For the position coordinate x 3c xi2x5x xi2x xi22x xi5x For the position coordinate y 9 yi2y5y yZ2y yi22y yi5y Where i12n Linearization by Expansion 3 Taking the difference between the true and estimated values pfpA2p pf2pi5p2pi5p2xxi5x2jyyi5y Normally you have more equations than unknowns Thus you can do a least squares solution That is 601 6p2 60quot 6x 5y 16 OF 62 Introduction to GPS quotMilk Linearization by Expansion 4 239 Because we don t have true ranges but pseudoranges we augment the G matrix With a column of ones for the time bias We need at least 3 measurements for the 2D solution xx1 JV 3 1 1 6p 01 01 xx2 JV 3 2 53 6p2 1 5y 02 02 39 Z 3 g 61 5pm x XJ y yJ 1 pn pn 5 G 5 RJ 39 lLntroduc ticm 5135 Least Squares Solution For the moment without proof we state that the least squares solution is given by gt 1 gt 5xlGTG Glap Algorithm for solving the navigation equation 1 Pick an initial guess for x and y 2 Compute pl for as many measurements as you have 3 Form 51 for all measurements and then form G 4 Solve for 5X 5 Update your initial guesses for x and y as follows xx5x yllzyll5y 6 Repeat until convergence 3918 OF 62 tarnfnrl Cnluh39nn Numerical Example Initial and Final Range l39snimains I quotquot ltiquotl39rue Ueur Hti ill39i ll IX ea i lulllle II Iquot Solution is donein MATLAB Assumes an initial position of 000 Walks solution in to the final position Red raws the range circles at each iteration tion to GPS GPS Signal Structure GPS broadcasts a modulated carrier on L1 157542 MHz Pseudo Random Noise PRN sequence of 1023 chips used to spread the signal PRN is carefully chosen to have unique auto and cross correlation properties All signal components generated from the same 1023 MHz satellite clock GPS L1 Signal Generation J2 cosh I mm L Carrier GI A cud L 1 E Transmitted W5 a Multiply Muhiply I I1 hit 20 m5 F u IS Fe m I 39 39 50 I395 39 I 1 bit 20 m5 I J 11 m F f f f rrT r mme 4 03912345575113192u Wmmfinds part3 4 1IhlmEIQFFSI13 ql I Unapmiud ms I H H H II I r 1 mm Hi U U U I J l w 1m3cf tina39perlnd hhhh L1 Garner 1 rquot l 1 53512 MHz ijif v k quot 154D cyclesfdIip quot I i tion to GPS GPS Signal DeSpreading o In order to use the PRN code correlation properties to de spread the GPS signal need to recover code down to baseband no carrier 0 Use trigonometric identities to mix down and remove the carrier cos0i6cos0icos6 sin0isin6 cos0i Bcos0icos6sin0isin6 2000icos6cosa cosa B 4 Hymnle V mzumIr Ham snagg 1Escumi VLWWHEWI I WWI 39 ammu raw Finn I l I 39 0 2G0 139 Bill HUD 10M 921m 140G 15130 13M 39L1mus 39 39 quot mJIAMH Lag 55553 I m UGISPSAHM I I I Wyn 39 39 PM aquot r 39 r I mquot D roductinn to GPS PRN Auto and CrossCorrelation i MWV MWH INl H WWWMWMM W In troductian to GPS PRN Correlation Example HDNTIE RESEWEQ DETERMIPIES HE PEEJDCIFIAHGE gt1 CODEAS HEGEIVED PRON rm I k I ll 1 i II III 39I II I I II III 39 VI Iquot II III I III III D I II Iquot I I YII II III 39139 I 39III I I Jl II I II II r 39III a 39 4 1 I I 1 II I 39I I II II II If I I 39I I39 394 39 I 39 39 II It I I II I39 Il 39I I 1I l I II ll IV 1 I II quot I39 Iquot I39 I l I39 l quotI 39I I II llquot I39 l II I IJI II I A IquotI ii II Il39 I I IIII I 39 I I l l l 5 W 15 EC 25 30 35 In 2 39 I l I I I B CDTIE GEHEHHTED N HEGE VEH TO DETERMINE FHI39OSE I quot II II f II Cquot l I VI fquot l I I 39 I39 39I I III I II I 39I 3 1 I 1 I l 391 l 39I I II39 I Iquot I II I l ny v Iquot I 7 I I l I y H II I V I Y Yll II I x 4 I7 I l I I 5 TI 15 EC H5 SI 35 1 A f a in jail VI l I f I I quotIII 39I Iquot If I I Y I I I I Initial Acquisition Search In roduct n to GPS sume As 1 channel amp 1 ms dwell period Exhaustive search if real time requires39 32 x 2046 x 20 x lms 1309 seconds 12 channel assumption requires 1309 12 109 seconds n rroductinn to GPS m moume mm mm tion to GPS Things to remember about GPS 0 Navigation is a hard problem and only recently has GPS made this easy 0 GPS is a p p system that has precise clocks on board that give you position and your time bias 0 PRN signal has correlation properties that allow you to find the signal in the noise even without any knowledge of position 728 OF 62 Questions 529 OF 62 The Sky Above Palo Alto on Jan 6 2002 P Ularis I I TU Emu ZEmh Fij t anon 315 quotquot Em Fl quot x I gI aitude it 3 l I quot3 x 39 1 I 39u 1 i F r11 mirrr l tutL3 t Actual location of Polaris is 89 05 oduc ion to GPS Instruments of Navigation Iu lint I vuuwn MIIAaTIJIIhT a quotmu Shanit IEHIWH 5 MfrIran Illml I39ll NICE Innu MI E An Astrolabe A Sextant Sun39s Image in Horizon Mirror in troductian to GPS Easier to align Sun s or other celestial body s limb with the horizon fIn roductl n to P5 A9007 Sun39s Altitude Sun39s Declination 5 m SLI 39Il39lEI39iquot 0 o Celestial map changes because of Earth s 15 0hr approximately rotation rate39 w Longitude Determination o Longitude Determination Methods Methods based on time 0 Compare the time between a clocks at the current location and some other reference point 0 Requires Stable Clocks Celestial Methods 0 Eclipses of Jupiter s Moons o Lunar Distance Method 39 Introduction to GPS Fundamentals of Radionavigation Lineolsight propagation Figure 14 Propagation of radio waves Radio Frequency RF signals emanating from a source or sources The generators of the RF signal are at known locations RF signals are used to determine range or bearing to the known location 738 OF 62 gyiitrpduction w i n 3 Classification of Radio Frequencies Name of Band Frequency Range Wavelength Very Low Frequency VLF lt 30 kHz gt 10 km Low Frequency LF 30 300 kHz 1 10 km Medium Frequency MF 300 kHz 3 MHz 100 m 1 km High Frequency HF 3 30 MHz 10 100 m Very High Frequency VHF 30 300 MHz 1 10 m Ultra High Frequency UHF 300 MHz 3 GHz 10 cm 1 m Super High Frequency SHF 3 30 GHz 1 10 cm Propagation characteristic of RF signals is a function of their frequency R LEW3111 1th R in nautical miles in in feet 0 VHF VOR ILS Localizer and UHF ILS Glide Slope TACANDME are line of sight systems Limited Coverage area 0 LORAN and OMEGA are over the horizon systems Large coverage area In the case of Omega coverage was global 0 Frequency band in which GPS operates makes it a line of sight system However because of the location of the satellites it is able to cover a large geographic area 140 OF 62 gaggmnrrmmmm to 5P3 INS and Radionavigation Systems 55 4 39 39 A Iication NaVIgatlon System IOIO I Land Sea Air NDB Non Directional Beacon X LORAN Long RAnge Navigation X VOR VHF Omnidirectional Range DME Distance Measuring Equipment ILS Instrument Landing System Lhtrprluction to GPS Phases of Flight I ElkeDH Climb I En Route Approach 3 The required navigation accuracy and reliability ie integrity continuity and availability depend on the phase of flight Currently as well as in the past this meant that an aircraft had to be equipped with various navigation systems Provides Bearing 1 Information Operates 112 118 MHz Accuracy 10 to 2 0 Principles of Operation Enge et aI Terrestrial Radionavigation pp 81 Transmits 2 Signals 0 1st Signal has azimuth dependent phase 0 2nd Signal is a reference 0 A between the phases of signal 1st and 2nd signal is 1 VHF Omnidirectional Range VCR J VOR T North n troduction to 6P5 7 Distance Measuring Equipment DME 0 Measures Slant Range p o Operates between 962 and 1213 MHz 0 Based on Radar Principle Airborne unit sends a pair of pulses Ground Station receives pulses After short delay 50 us ground station resends the pulses back Airborne unit receives the signal and calculates range by using the following equann pcAT 50us 39 quot quotF u h gl uuq s f39 M quotL V 144 OF 62 ed Clr e F lerrm I am mu humor KP 39 IEllceEme Side View toe ilm 5 me lo View 0 Used extensively during approach and landing to Erovides vertical and lateral guidance 0 Principle of Operation Lateral guidance provided by a signal called the Localizer 108112 MHz Vertical guidance provided by another signal called the Glide Slope 329335 MHz 0 Distance along the approach path provided by marker beacons 75 MHz 445 OF 62 Sidereal Time Based on the time required by Earth to complete one revolution about its axis relative to distant stars Apparent Solar Day Time required for Earth to complete one revolution with respect to the sun Mean Solar Time Same as apparent solar day except it is based on Hypothetical earth Rotating in a circular orbit around the sun Axis of rotation perpendicular to the orbital plane Sameas Greenwich Mean Time M Universal amp Atomic Time 0 Universal Time UT Time based on astronomical observations UTO Mean Solar Time measured at the prime meridian UT1 UTO Corrected for Earth s irregular spin rate and polar motion 0 International Atomic Time TAI Based on Ce133 Atom 0 Coordinated Universal Time UTC Set to agree with UT1 on January 1 1958 Leap seconds introduced to keep it within 09 seconds of UT1 7 Introduction to GPS GPS Time 0 GPS Time GPST A continuous time scale no leap seconds Based on Cesium and Rubidium standards Steered to be within fractions of a microsecond modulo one second from UTC 0 Thus GPST UTC whole number of seconds a fraction of a microsecond 0 GPS time information transmitted by the satellites include GPS second of the week 604800 seconds per week GPS week number 1024 weeks per epoch 58 OF 62 yininduction to GPS GPS Time 2 GPS satellites carry atomic clocks Rubidium andor Cesium frequency standards Satellite clocks monitored by MCS 0 Clock bias is modeled as a quadratic 5taf0a t t00af2t toc2zltr 0 Parameters of the Quadratic are uploaded to Satellites which in turn broadcasts them as the navigation message Subframe 1 of the navigation message Clock correction term Arr takes into account relativistic effects Account for speed and location in the gravitation potential of the clocks Net effect results in satellite clocks gaining 384 usec per day Compensated for by setting the satellite fundamental frequency of 1023 MHz 000455 Hz lower 49 or 62 GPS Coordinate Frames Inertial Frame of Reference Defined to be a non accelerating or rotating coordinate frame of reference eg Earth Centered Inertial ECI Required for analysis of satellite motion inertial navigation etc Not convenient for terrestrial navigation Coordinate systems you will mostly encounter in GPS are Earth Centered Earth Fixed ECEF EastNorthUp ENU Geodetic Coordinates Other coordinate systems used in navigation NorthEastDown NED used widely in aircraft navigation guidance and control applications WanderAzimuth x 39 FlEfB l Cl39IGE meddle i roductian to FPS Coordinate Frame Relationships 0 Geodetic coordinates g2 A h to ECEF a6378137m e 008181919 N2 ill lesinli iizl xlNhlcospcosl ylNhlcospusinl zN1 e2h sinp Meridian ellipse gure 3J11 Carleeia39 and gaudmic cocr dinalaa o ECEF to Geodetic Iterative algorithm See Wgsxyzleam in toolbox Geometry of Earth 1 Crude Approximation A sphere R0 6378137 km A spherical model is only good for back of the envelope type of calculations Need a more precise model for navigation applications especially inertial navigation A more accurate model is an ellipsoid Parameters of the mathematical ellipsoid are defined in WGS84 HT pgmp hi5 Surface Reference Elllp mid EARTH Emirate r Geometry of Earth 2 Topographic Surface Shape assumed by Earth s crust Very complicated shape not amenable to mathematical modeling Geoid An equipotential surface of Earth s gravity field which best fits in a least squares sense global Mean Sea Level MSL Reference Ellipsoid Mathematical fit to the geoid that happens to be an ellipsoid of revolution and minimizes the meansquare deviation of local gravity and the normal to the ellipsoid 7 1i1trt3duction to GPS WGS84 Reference Ellipsoid Some geometric facts about the WGS 84 A Reference Ellipsoid Semimajor axis a 6378137 m Semiminor axis b 6356752 m Flattening f 1ba 129825722 Eccentricity e fa19 0081819191 Given the WGS 84 Ellipsoid parameters the following are derived quantities Lace Tang ant Heterence Eilap 5013137 R a1f3sin2 2t NS gt Equator REW ai1fsin2 I i i Geodetic Latitude if Geocentric Latitude whereltigtltigt tango391 f2tango w Peter H Dana 1 USES 7 1l1troduction to GPS quotE quoth H Nquot ga ao Ellipsoid 5 39 quotGaol1quot h Ellipooid Height Distance along ellipsoid normal D to P N Geoid Height Distance along ellipsoid normal Q to PD H Drmometrio Height Distance along Plumb liner FI to P Littmduction to GPS i Orbital Mechanics Kepler s Law Based on observations made by Tycho Brahe 15461601 0 First Law Each planet revolves around the Sun in an elliptical path with the Sun occupying one of the foci of the ellipse 0 Second Law The straight line joining the Sun and a planet sweeps out equal areas in equal intervals of time 0 Third Law The squares of the planets39 orbital periods are proportional to the cubes of the semi major axes of their orbits Explanation came later Isaac Newton 16421727 Universal Law of Gravitation where GMchnqiSbi ned With his law leads to F 2 7 Iquot s A439n1 9 ill 9 Vi i Srmri 3Er0 r r r second FEFS FE Introducth to GPS Recast the tworbodv equat on of motwon Characte ze orbwta empse e SermrmajorAth A e Eccenmcwty a Charactenze Orb t39s ortentatwon m space 7 Inchnauon I e nghtAscenswon ofthe 1 Ascendmg Node0 mm xx Characte ze em Se39s Vuma 3 ortentatwon m or ta p ane mum e Argumen Pengee w POStUOn otthe SateHwte m the orbwt 7 True anomaw v Sometwmes t S convement to Sum v and a to form a new v r b e caHed argument of latitude Perturb e emen a 9 av uona rorce gravmauona e ds orme sun and moon 7 so ar pressure Addmona 9 param t 5 Three to account for the rate of Change n htAscEnsmn cf the Ascendmu Nude 492 rdnt Mean mmmn nrd t 7 Three Pan39s s parameter tom to correc x hnaunn a u GPS Orbital Parameters ed Orbth r quaerepwerran 15 t Set i N gmtmsmmu m M m Mme 144 mm m 0V O Pertubative Torque caused by Earth s Equatorial Bulge GPS Constellation and Orbits Nominal Constellation 24 Satellites orbit Semimajor axis 26560 km Eccentricity less than 001 Period approximately 11 h 58 min Six orbital planes Planes designated A through F Inclination of 550 relative to the equatorial plane RAAN Q for the six orbital planes separated by 60 Four Satellites per orbital plane At present more than 24 satellites on PL39Inn A Eh Cl D E F m p quot 5 2 I39 VI 1 I m far I l a 1 I 15quot g i ii 39 pa L J L3quot 75 if 3 1 xquot 1 P3 2H o3 39 52 J a J Iquot I ll If VI39Iv f F akaquoti aquot 2 Elliil 5 a a39 i f3 Iquot is f2 a 4quot i1 x if rquot f a 0 39 5quot j 391 l quot 45 quot rquot 39 rm Iquot I I 1 I I II I j Satalllha d aplcgmm in an arbil Safelli te39SE in a given orbital plane are distributed unevenly to minimize the impamsef a si 39gl Satiellitbiia urfe 50 OF 62 introduction to 6P3 l GPS Ephemeris Calculation 0 Compute the satellites position in the orbital coordinate frame Solve Kepler39s equation E M e sinE for eccentric anomaly at epoch k E 0 Solution requires iteration if orbit is noncircular Compute the true anomaly v Compute the argument of latitude q k Use 15 to compute the corrections for argument of latitude radius and inclination then apply the computed corrections Compute the x and y coordinates xk and yk of the satellite in it s orbit o Covert the computed x and y position into ECEF coordinates Compute the correction for the longitude of the ascending node Apply the correction to the longitude of the ascending node Compute the ECEF coordinates
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