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# Introduction to Global Navigation Satellite Systems ASEN 5090

GPA 3.96

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This 131 page Class Notes was uploaded by Laila Windler on Friday October 30, 2015. The Class Notes belongs to ASEN 5090 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 41 views. For similar materials see /class/232175/asen-5090-university-of-colorado-at-boulder in Aerospace Engineering at University of Colorado at Boulder.

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Date Created: 10/30/15

Observable Combos Colorado aaaaaaaaaaaaaaaaaaaaaaaa g ASEN 5090 LECTURENOTESV LARSONAXELRAD Outlines Observables Remove clocks Remove ionosphere Isolate pseudorange multipath Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 2 Observables pl Rc6tu 6fTIpl Mplspl pZ Rc6tu 6fTIpZ MpZ 5Z 11 12 Ipl IpZ Mpl MpZ pl p2 1A1Rc6tu 6fT Ipl M l 1le1 1 4M2 Rc6tu 6fT Ipz M Z NZAZ 5 1A1 z 7 IpZ Ipl Mm MM Nzi z 5m z Cglorado Unwer m mm mm ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Remove clocks Satellite clocks Receiver clocks Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 4 Ionosphere pl Rc6tu 6fTIpl Mplspl pZ Rc6tu 6fTIpZMpZ 5Z 11 12 Ipl IpZ Mpl MpZ pl pZ Seek observable with original dependence on range and clocks but does not have an ionosphere term in i 403TEC II P ff Colorado Unix25391an may i may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXELRAD e Pseudorange Multipath pl Rc6tu 6fTIpl Mpl 5l 1A1Rc6tu 6fT IPIM 1N1A1 1 4M2 Rc6tu 6fT Ipz M Z NZAZ 5 Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 7 Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXELRAD a Least Squares Least squares will produce a mathematical solution to the graphical solution we associate with GPS the intersection of three spheres where radii are defined by pseudoranges and receivertiming errors removed by 4th satellite We start with simple examples C01 rado ASEN 5090 LECTURE NOTESV LARSON AXELRAD WWW may it may Outline Model Linear Model Least Squares solution Residuals UncertaintyError Covariance Weighted Least Squares solution Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEM 2 Least Squares Requirements Mathematical model that describes the observations data Observations are linearly related to parameters in the model Observation errors are zero mean and randomly distributed Goal is to find the best estimate ofthe unknown parameters given the observations and knowledge of their error characteristics Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEM a Gaussian or Normal Distributio QWY e 202 1 am pdfx Fora normal distribution 68 ofthe points are within 10 95 of the points are within 20 997 of the points are within 30 2 where M IS the mean value and 0 IS the varlance ttt II II ll 9999 PPR 0 moon 5 4 3 2 4 0 l 2 3 4 5 From http iien Wikipedia orgWikiimage Normaidistributionpdf pngi fiie Univeisnyoi Coleman Bauider ASEN 5090 LECTURE NOTES LARSON AXELRAD 4 Linear Model ymtbs y is the observation m is slope b is offset 5 is model misfit m x E b 10 observauons 0fds1 mce y Ax s where At 1 and the misfit or eITOI S g is assumed to be zero mean with variance oz 1 dislmce km 5 8 4935 1995 1996 199 1993 1999 2 DO 7 time yws Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Least Squares Solution Accumulate all your measurements into a matrix equation ymtbs lt Iquot v E It 12 1 yz where A I3 1 y y3 IN 1 yN Colorado Unix25391an may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Least Squares continued How do you decide how to penalize misfit s y Ax De ne a cost function Jx 5 y Axf y Ax To nd 3c that gives minimum J set delivative of J wrt x to 0 0 2AT y AJE ATy ATAJE Note if A were a square matrix so The unweighted least squares solution is 2 ATA 71 AT y Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEM 7 How do you implement this in Matlab You can set up the A matrix and actually type invtra nsposeAAtra nsposeAy You can use a special matlab command Backslash Ay Colorado Umvus vat my may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Colorado help mldivide Backslash or left matrix divide AB is the matrix division ofA into B which is roughly the same as INVAB except it is computed in a different way lfA is an NbyN matrix and B is a column vectorwith N components or a matrix with several such columns then X AB is the solution to the equation A X B computed by Gaussian elimination A warning message is printed if A is badly scaled or nearly singular AEYESIZEA produces the inverse of A lfA is an MbyN matrix with M lt orgt N and B is a colum vectorwith M components or a matrix with several such columns then X AB is the solution in the least squares sense to the under or overdetermined system of equations A X B The effective rank K ofA is determined from the QR decomposition with pivoting Univus va may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a Hidden least squares Matlab polyfit Matlabdetrend Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI m Uncertainty of the solution H ATAy1 If you xvectorwas m b then the Hmatrix follows the same order 2 2 am Gmb 2 2 Gmb Ob am xQU 1 The offdiagonals give you the correlations between the parameters But notice that this used no input about the uncertainty in the measurements Colorado Univus yat may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI Data and Estimate Uncertainty ymtbs Reany y is the observation m is slope b is offset afarQ04 xaibi y Ax s where A I 1 and the misfit or error 3 is assumed to be zero mean gt with variance oz Your book calls 0 the URE user range error 0 Colorado Umvus va my may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 12 How do you check your least squares solution I Postfit residuals tell how well the LS solution amp model fit the data pfr y A I Residuals should be zero mean and normally distributed Distribution ot Residuals I Number of points in bin x N Ax earl2 5 Where N is total number of 3 m z E m E o E z points and Ax is bin size 72 n C d standard deviations WSW quot WW ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 13 Residual examples Posllll Reslduals lonosphere Free Pseudorange Colorado Huh SAW mm H mm ASEN 5090 LECTURE NOTESV LARSON AXELRAD 14 Posllll Reslduals lonosphere Free Pseudorange o Colorado Huh SAW mm H mm ASEN 5090 LECTURE NOTESV LARSON AXELRAD 15 Posllll Reslduals lonosphere Free Pseudorange uals I 50 led lemperalure 5 5 Colorado un vus yn Cnlondc a some ASEN 5090 LECTURE NOTESV LARSON AXELRAD m Same Residuals Posltll Reslduals Ionosphere Free Pseudorange Poslm Reslduals Ionosphere Free Pseudorange 40 60 80 elevallon anglerdegrees Colorado Huh SAM mm H mm ASEN 5090 LECTURE NOTESV LARSON AXELRAD 17 What is the hardest thing about least squares Colorado Univus yat may it way You need to keep track of your dimensions Make sure you re A matrix has the right number of columns and rows In GPS you will have the same number of parameters to estimate at each epoch but will have a different number of satellites at each epoch Recommendation you should clear your A matrix after each use While Matlab makes histograms easy to plot you should use it Intelligently Instead of histpfr normalize your pfr by 0 histpfro 5055 ASEN awn Lacrqu NOTES 7 wasoN AXEUEM m What About Weighted Least Squares If each measurement has its own uncenainty define weight matrix 1x 7 0 0 Instead of ATA1ATy W 51 12 0 55 ATWA1ATWY and Q ATWAY1 lt72 0 0 1 2 Dismnce Observations 7 4995 5 499 4935 quot 1995 1996 1997 1993 1999 2 00 time yws Colorado ummm mm mm ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 19 Other Examples of why data weights matters Lust Squares Lust Squm If 7 original t v ghled il 7 wei hted fu 4995 4995 499 E 499 4935 V 49115 1995 1996 1997 1993 1999 2 00 4 o 1995 1996 1997 1992 1999 2000 quotme 0 quot lime yws Colora 0 uman com1m Bvuwer ASEN 5090 LECTURE NOTESV LARSON AXELRAD 20 How do you propagate uncertainties For the linear example we can use m and b to predict the yvalue at any time Dismnce Observations m Y2002 2002 1 b 4995 E 2002 g 499 Q2002 2002 1Q 1 Do the matrix dimensions make sense quot 1995 1996 1993 1999 2 00 1997 time yws Colorado ummyoq Dnlnmdnn Boulder ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 21 Calculate uncertainty from 1992 thru 2002 Pmpagaled Uncemimy 2000 22 1993 time 7 yws T992 1994 Dislznce Observations 49957 1 K 7 499 4985 s quot 1995 1996 1997 1993 1999 20 time yams Does this make sense Colorado University Coioradoat Bouider ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 22 Combining the information Pmpagaled Mode 1mm 500 5 uncenmmy 500 4995 5 499 4935 493 4975 1992 1994 1996 1993 2000 2 2 time 7 yws Colorado mm mm My ASEN 5090 LECTURE NOTESV LARSON AXELPAD 23 Error Propagation from XYZ to ENV Transformation matrix sin cos 0 0 sinqcos sinqsin cosq 0 mv commas coquSinA sinq 0 1 7 AE Original estimate My What we would A AN 3 739 rather have rm AV AZ 1 RM RM T QW WQ W Colorado unim yni mm 3 swim ASEN 5090 LECTURE NOTESV LARSON AXELRAD GPS 101Introduction to GPS Jargon ASEN 5090 Lecture 3 Jargon review PRN pseudorandom noise tells you which code is being generated by a certain satellite The codes get reused so PRN15 in 2008 will be a different spacecraft than it was in 1989 SVN satellite vehicle number tells you exactly which spacecraft it is This number is never reused as you need it to know the design specifications of the satellite Constellation status is maintained by the Coast Guard website Notice Advisory to Navstat Users NANU I Why do they tell you whether a satellite is running a Rb or Cs clock Because the noise properties of these clocks are pretty well known so an advanced user could estimate the likely clock error for each satellite A normal user won t care Followup LORAN vs GPS LORAN is a 2D 250 meter positioning system x2 xgt2 lty2 ygt2 4m xgt2 lty1 ygt2 c121 x3 x2 Y3 3 2 Xx1x2 Y1Y2 d31 GPS is a 3D 5 meter positioning system better with WAAS x1 xgt2 lty1 ygt2 Z1 zgt2 d1 x2 xgt2 yz ygt2 zz zgt2 d2 x3 xgt2 yg ygt2 zg zgt2 d3 x4 xgt2 m ygt2 Z4 zgt2 d4 Outline Space Segment signals Control Segment takes care of the satellites orbits clocks User Segment us GPS Signals carriers codes Position solution ranging and geometry Augmentations WAAS Reading Assignment Ch 2 44 Space segment t 5 Uplink data 0 Satellite ephemeris position constants 0 C oc correction actors 0 Atmospheric clgto 0 Almanac Downlink data Coded ranging signals 0 Position intormotion 0 Atmospheric data I GPS Space Segment Black Elfo 24satellite nominal constellation Six orbital planes inclined at 55 deg four satellites per plane Not geosynchronous Semisynchronous nearly circular orbits 20200 km altitude Redundant cesium andor rubidium clocks on board each satellite Antenna array pointed at the earth GPS Constellation Status Currently 32 satellites onorbit Block lllllA Built by Boeing Aerospace Rockwell Launched 1989 1997 Block quotF Built by Boeing Launching 2009 L5 signal Block lllA Built by Lockheed Martin Contract announced 52008 Block 11 satellites one launch failure Built by Rockwell Launched 1978 1985 Block llRIllRM Built by Lockheed Martin Launched 1997 2007 llRM have CA on L2 Age Summary 1 All satellites have greatly exceeded original design lifetime Block Demonstration phase I With only 10 satellites could not be used to prove global 247 coverage Satellites were specifically placed in orbits that would allow good 4 satellite coverage for 4 hours over Yuma Arizona thus the name of the YUMA almanac The Block satellite inclination was a little higher than the current constellation 63 degrees There was no ability to degrade the GPS signal on Block Notes I If you wanted to work in the field precise orbit determination POD the fact that each type of GPS satellite is different would be very important I Mass area volume are important parameters for POD I Vector between the transmitter phase center is not in the same place as the satellite center of mass differences between Blocks are important I Navigation capabilities are the primary payload for GPS satellites This doesn t mean they are the only payload Control Segment Broadcasts the SIS PRN codes Lband carriers and 50 Hz navigation message stored in memory SPACETOUSER INTERFACE a 1 1 I I MASTER CONTROL STATION Checks for anomalies MONITOR STATION Computes SIS portion of URE GROUND ANTENNA I Sends raW Generates new orbit and clock observations to MCS predictions Builds new upload and sends to GA CONTROLSPACE INTERFACE Sends new upload to SV MCS Schriever previously Falcon AFB in Colorado Springs Critical Role of the Control Segment I Takes GPS ranging data Assuming positions of tracking stations are known computes orbital parameters ln same process estimates the bias and drift of each satellite s clock relative to GPS time Uploads new orbits and clocks so that they can be broadcast on the GPS signal I GPS orbits can be computed very simply There are two forms used in this class a The GPS almanac 1 km is NOT for positioning It is primarily used by the receiverto aid tracking e tells it which satellites should be visible 1 The GPS broadcast ephemeris 1 meter is for lowaccuracy realtime positioning The GPS precise ephemeris 2 cm is not broadcast by the DoD It is generated by geodesists and will not be used in this class Orbits Almanac Almanac YUMA format 099 radians 5672 deg Contrast with Week 419 almanac for PRN01 ID 01 Health 000 Eccentricity 0683927536OE002 Time of Applicabilitys 4055040000 Orbital lnclinationrad 09909240253 Rate of Right Ascenrs 07794610391E008 SQRTA m 12 5153359863 Right Ascen at Weekrad 04613413514E000 Argument of Perigeerad 1806921136 Mean Anomrad 01432259810E001 Af0s 01506805420E003 Af1ss 03637978807E01 1 week 419 Week 419 almanac for PRN32 ID 32 Health 063 Orbits Almanac Almanac YUMA format Week 419 almanac for PRNO1 ID 01 Health 000 Eccentricity 0683927536OE002 Time of Applicabilitys 4055040000 Orbital lnclinationrad 09909240253 Rate of Right Ascenrs 07794610391EOO8 SQRTA m 12 5153359863 Right Ascen at Weekrad 04613413514E000 Argument of Perigeerad 1806921136 Mean Anomrad39 O 143225981OEOO1 AfOs 0150680542OEOO3 Af1ss 03637978807EO11 week 419 Approximate value 015E3 s 3OE8 ms 45 km Note c is not equal to 3OE8 ms in this clas We are 8 years into second go round with 1023 weeks Orbits Broadcast ephemeris The YUMA Almanac is written in English I The broadcast ephemeris as provided in RINEX is written to be read by a computer 1 7 9 7 0 0 00 150940846652D 03 250111042988D ll 000000000000D00 106000000000D03 808750000000D02 373944147703D 08 243283535665D01 412575900555D 05 683927175123D 02 392831861973D 05 515340405273D04 432000000000D06 372529029846D 07 461125894282D00 596046447754D 07 990918556284D00 317687500000D03 18067557l467D01 781853995929D 08 227152318949D 09 100000000000D01 000000000000D00 100000000000D01 000000000000D00 372529029846D 08 106000000000D03 424800000000D06 Time of ephemeris 432000000000D06 GPS week 144300000000D04 Almanac 0683927536OE002 1443 1024 419 Broadcast 683927175123D 02 Control Segment Monitor Stations Monimrstations o NlMA Site All a NlMA Site NunrAll 5 k F Site 5 l Original US Air Force GPS Monitor Stations u Hawaii Ascension Island Diego Garcia Kwajalein and Colorado Springs I New monitoring stations incorporated 2005 a Cape Canaveral USAF a Washington DC UK Argentina Ecuador Bahrain and Australia NGA GPS Signals Codes a CIA Code 1023 MHz Clear Acquisition code repeats 1 ms 1 PY Code 1023 MHz Encrypted a M Code New Military Split spectrum not relevant to this class a L2C L5C New Civil codes Carriers 1 L1 157542 MHz CA and PY u L212276 MHz PY only Block I II A HR 1 L5 117645 MHz none currently Effect of encryption policy a Civilians only have single frequency L1 1 Military has both frequencies L1 and L2 1 The ionosphere is dispersive and failure to correct for its effect can producing ranging errors up to 100 meters and thus equivalent posmonlng errors Degradation mostly of interest for historical reasons 1 SA selective availability 1 AS antispoofing Navigation Data 1 50 bps Satellite ephemeredes and almanacs Satellite clock parameters lonospheric model for single frequency users Health and status DUDE GPS User Segment GPS receivers are specialized radiosquotthat track GPS M39ma y Spuemm signals and produce position and velocity solutions N31 000 000 u Wde range ofcostsophistication depending on the application Signals from 4 or more GPS satellites are required but 310 are typically available at any time Many civil SP8 receivers track only the L1 CIA signal Pricision civil users track both L1 and L2 without the PY co es PPS receivers have special ke s that allow tracking ofthe 39 military PY code over both L and L2 amusyGemm Dvmmtcs Consumer Recreation N10 SurveyingScience 10000 cmxtesyTnmble cautesy G mm GPS NAVIGATION GPS Augmentations WAAS a WAAS provides augmentation information to GPS receivers to enhance the accuracy and reliability of position estimates a Space Based Augmentation System SBAS covering nearly all of the National Airspace System NAS u Commissioned July 2003 LAAS u Augmentation to GPS that focuses its service on the airport area approximately a 2030 mile radius a Broadcasts correction message via a very high frequency VHF radio data link from a groundbased transmitter NASA Global Differential GPS DGPS a NASA provides realtime corrections to the broadcast GPS satellite ephemeris and clock data a Reduces ephemeris and clock errors from a few meters to a few cm Fundamentals of Satellite Navigation Satellite based navigation is fundamentally based on u The precise measurement of time you have to agree on what you mean by time u The constancy of the speed of light GPS and other systems use the concept of trilateration a Satellite transmitter positions are known a Receiver position is unknown 1 Satelliteto receiver range measurements are used to estimate position Position Solution The position solution involves an equation with four unknowns u Receiver position x y z in what reference frame a Receiver clock correction correction to what gt Position accuracy of 1 m implies knowledge of the receiver clock to within 3 ns 1 GPS accuracy is based almost entirely on knowing satellite orbits and satellite clocks I Requires simultaneous measurements from at least four satellites u The receiver makes a range measurement to the satellite by measuring the signal propagation delay a A data message modulated on the ranging signal provides the precise location of the satellite and corrections for the satellite clock GPS accuracy is based almost entirely on knowing these two things How Do You Degrade the Position Solution Since GPS accuracy is based almost entirely on knowing satellite orbits and satellite clocks you have two choices Provide inaccurate information about where the satellites are Provide inaccurate information about the behavior of the clock In GPS speak this is called selective availability SA Selective Availability Turned on in 1990 Turned off during first Gulf War Turned back on after war Turned off for good May 1 2000 Block III is not supposed to have SA capability Emp Hewgm Scaner m What did SA look like to a user AMMN w Empsumax Hewgm Kom w Empsumax Hewgm t i 5M g ran W g H 2 i H Hg at it 3 45 4 Ann 72m 45D 7 u mum nnun anunu mum 5mm EDDDD mum EDDDD annun H mm 2mm 3mm 4mm mm mm mm mm Tune Pasmh GPS ZrMayVZEIEIEI 5 Courtesy Richard Snay Tune Past Uh GPS ZrMayVZEIEIEI s annnn 24 Why did many people not care about SA Longllude 39 30 40 time 7 minutes Longitude time series when SA was on Most of this was clock dither Longllude melers 10 2 0 30 40 Ilme r mlnules Longitude records for two receivers fairly close together Which means the longitude difference is much better known PN17PN2 Longllude melers 20 30 40 Number 0 Vlslble Salelllles 44 69 10 2 0 30 40 lime r minules You can get position for your site if you KNOW the position of the Other sites This is the general principle used in differential positioning or using a base station Selective AvailabilityAntispoofing Selective availability severely impacted standalone users But with the ability to broadcast base station corrections it became a non issue even the Coast Guard was broadcasting corrections Antispoofing is an encryption issue It directly impacted receiver manufacturers and indirectly impacted users I Remember the Codes a CIA Code 1023 MHz Clear Acquisition code repeats 1 ms 1 PY Code 1023 MHz Encrypted The military made the Pcode available during the Block testing era Starting with Block II 1990 satellites 1 DoD had the ability to encrypt the P code which they called the Y code a Thisautomatically made P code receivers into single frequencyl receivers Including satellites wnth GPS receivers launched by ASA 1 DoD turn on antispoofing in 1994 It is still on Observables a P code on the L1 frequency is often called P1 Ditto for P2 a CIA code on the L1 frequency is often called C1 Short Summary of Civilian Response to AntiSpoofing Reverse engineering noted that the encrypted Y code is really the original P code plus the W code Making some assumptions engineers were able to extract P code pseudoranges on both L1 and L2 I Other engineers noted that P2 is reallyjust CA on L1 the ionospheric delay They used VLBlprinciples to estimate the ionospheric delay and added it to CA thus producing a P2 observable Other engineers did the following a If you think of a code being all 1 s and 1 s 1 Multiply your unknown code by itself Now the code is gone and you can extract the carrier signal I In response 1 DoD has added CA code to L2 No further receiver tricks will be needed on Block llRM Block F Block lll Measurement Equation GPS receiver measures Pseudorange by measuring the transit time of the Signal pg C tr is i i time of signal reception time of transmission based on receiver clock encoded in signai by can be significantly in error GPS satellite Clock better known Again you need to agree about what you mean by time Measurement Equation cont Measured pseudorange to a satellite is comprised of R UUUUU S S Pr 6395 63951 Ptrop Plano Pmultz Prel 5 true range receiver clock error satellite clock error known ionosphere and troposphere delays estimated or measured other errors satellite ephemeris and clock mismodeling measurement errors multipath receiver noise pier ism Km Solution Accuracy Two primary factors affect the fundamental position and time accuracy possible from the system a Ranging error a function of the quality of the broadcast signal and data a Geometry the distribution of satellites in the sky I The actual positioning accuracy achieved depends on many other factors a The design of the receiver receiverantenna noise levels modeling errors etc an Environmental effects such as ionosphere and troposphere signal delays field of view obstructions multipath signals and jamminginterference How does this relate to homework I First we ll work on finding out where satellites are I You need to be able to go from LatLongHeight to XYZ and vice versa What is an ellipsoid What is the geoid Predict XYZ coordinates of satellite compare with XYZ for GPS receiver Calculate Elevation and Azimuth angle We will work on ourjargon Azimuth and Elevation angles East Visibility 5 is a unit vector in the direction from the user location to the satellite at time of transmission How do you decide if a satellite is visible 0 i iii 4i p is the direction opposite the radius vector approximately r in ECEF k eLos o cosmosifi whm cos sinx1 sin 7 Elevation is A A e1 acosem ems 7 Azimuth is 32 a tauLOSE mos How we plot them AZE I I39I i v 33rl quotI x t 5g 242 39 4 3 r ilii x 4241 I f v39 V gt ultra But at any given time the constellation looks very different uson UTC M mm 4 54 50 D 7 7 r as J 39y 47 Geometry Dilution of Precision Geometric Dilution of Precision GDOP is a quantitative measure of the quality of the receivertoGPS satellite range geometry a Related DOPs exist for position horizontal vertical and time dilutions of precision Used in conjunction with the URE user ranging error to forecast navigation and timing performance weight measurements I For GPS DOP can range from 1 to infinity with values in the 23 range being typical Good GDOP Poor GDOP The DOPS We ll skip the math for now I HDOP horizontal Ge On GDOP geometric XYZ VDOP just vertical Dilution of Precision Examples Some results from a Matlab code 7 Four satellites similar directions GDOP 181 39 HDOP 2131 39 VDOP 145 7 Four satellites spread out in azimuth O Imu minring mom in er u LAM u Dilution of Precision Examples Some results from a Matlab code 1 Six satellites low elevations GDOP 33 HDDP z 09 VDUP28J Six satellites two at gt 45 deg el GDOP 22 39 39 HDOP 1 39VDOPE2E Aerospace Engineering Sciences quot 39 University of Colorado 39i Combining GPS and Galileo to increase satellites improve DOPs GPS GALILEO Combined 24 55mm awngm vDoi I 1 Mtquot nil J n nil J z i in F T i i i i a 1n 2 30 10 50 w 7n um iMAILpMiL Rum AM Agih mi i i i i i i a 12 1a 30 w n MinL nl 1imam umimoill pun Mumiii i A a Courtesy ni Logan 5mm Ranging Error User Range Error URE u A measure of the accuracy of the pseudorange along the line ofsight direction from a particular satellite to the user a Indication of signal quality Composite of several factors a stability of particular satellite s clock a predictability of the satellite s orbit GPS Measurements ASEN 5090 Lecture 12 Colorado Unmnm my a may ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD Outline Measurements The Code also known as pseudorange Carrier phase Doppler will not be used in this class Reading Assignment Ch 51 Colorado ASEN awn LECTUPE NOTES 7 mksoN AXEUEAI 2 GPS receiver output latitude longitude height Receiver positions strongly dependent on satellite geometry The effect of satellite geometry can be quantified but uses skills we don t have quite yet Satellite geometry directly influences solution uncertainties least squares Beyond geometry the GPS signal is influenced by GEOMETRIO RANGE IONOSPHERE FREE ELECTRONS TROPOSPHERE NEUTRAL ATMOSPHERE MULTIPATH RELATIVITY NOT SHOWN N EQUATIONS CLOCKS MEASUREMENT NOISE Colorado I D D D D D D D ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a WHICH ONES ARE IMPORTANT Colorado They are all important at some level In some cases you can t even evaluate one error source without removing the effects of the others Think in terms of the magnitude of the error source can an atmospheric delay cause a 5000 km error and its timevarying behavior le would the atmosphere change like that Does a clock behave that way My first goal is to give you a feel for the different error sources and their behavior My second goal is to show you how to extract these different error sources from the observable equations ASEN awn Lacrqu NOTES 7 wasoN AXELEAD 4 ATMOSPHERIC DELAY SUBTLETIES G PS a ntenna Colorado ASEN awn LECTUPE NOTES 7 LARSON AXEUEAI a OBSERVABLES MEASUREMENT TYPES L1 Phase L2 Phase L1 pseudorange CA or PY L2 pseudorange CA or PY CA only on Block llRM satellites Doppler not used in this class Signal to noise ratio SNR not used in this class Colorado ASEN awn LECTUle NOTES 7 wasoN AXEUEAI a BASIC GPS MEASUREMENT PSEUDORANGE Receiver measures difference between time of transmission and time of reception based on correlation of received signal with a local replica pctu f I time of reception as observed by the receiver f time of transmission as generated by the satellite The measured pseudorange is not the true range between the satellite and receiver That is what we clarify with the observable equation Colorado ASEN awn Lacrqu NOTES 7 wasoN AXELEAD 7 CARRIER PHASE MEASUREMENT Receiver accumulates changes in the carrier frequency ofthe received signal This accumulation provides a measure ofthe change in range to the satellite ADR or accumulated delta range This means that carrier phase data have an unknown bias that must be estimated for the data to be used Carrier phase data are used extensively by scientists and surveyors It was not considered a primary tool by the DoD when GPS was designed Think of it as a freebie Colorado ASEN awn Lacrqu NOTES 7 wasoN AXELEAD a PSEUDORANGE OBSERVABLE MODEL pl Rc6tu 6fTIplMplspl pZ Rc6tu 6fTIpZMpZspz pl pseudorange measured on L1 frequency based on code pZ pseudorange measured on L2 frequency based on code R geometrical range from satellite S to user u 61 userreceiver clock error 6f satellite clock error T tropospheric delay I ionospheric delay in code measurement on Ll2 plZ M m n multipath delay in code measurement on Ll2 5 m n other delayerrors in code measurement on Ll2 Colorado ASEN awn Lamar NOTES 7 LARSON AXEUEAI a GEOMETRIC RANGE Distance between position of satellite at time of transmission and position of receiver at time of reception R x x zyx yuzzx39zuZ Colorado ASEN awn LECTUPE NOTES 7 LARSONAXELRAD m EXAMPLE OF PSEUDORANGE 1 anogadee PRNZS 25000 200007 E 150007 I a 10000 plRc6tu 6fTIplMplspl 5000 l I I I I I 4000 8000 12000 16000 Colorado seconds since midn wgh c Unmnm my a may ASEN awn LECTUPE NOTESV wasoN AXEUEAI u EXAMPLE OF PSEUDORANGE 2 Yorqgodee PRNZS 2550 25000 24500 24000 P1 km 25500 23000 22500 I I I I l 4000 8000 12000 16000 Colorado Seconds since midni ht Ag 9 NammmNomsymsomxam 2 l PSEUDORANGE minus GEOMETRIC RANGE pl Rc6tu 6fTIplMplspl Difference is typically dominated by receiver clock or satellite clock How can you tell which Colorado melers Hobart PRst 02an01 r100 7150 7200 3 4 5 6 hours since mldnlie ASEN awn LECTUPE NOTES 7 LAESONAXELkAb 13 l L1 PSEUDORANGE L2 PSEUDORANGE pl Rc6tu 6fTIp1Mp1 pl pZ Rc6tu 6fTIpZ Mpz pZ 1 pz Ipl IpZ Mpl MpZ pl p2 Differencing pseudoranges on two frequencies Yomqodee PPNZE removes geometrical 53 i M E effects clocks N x a troposphere and some i 4 R ionosphere K 6 I s f x L i i i x i i i 4000 8000 i WOOD domain Seconds since midnighi ASEN awn Lgcruug NOTES 7 LAESONAXELEAD l4 CARRIER PHASE MODEL Colorado 1A1Rc6tu 6fT Ipl M 1 Nl1 s 1 ple Rc6tu 6fT IpZ M Z NZAZ s Z 1 canier phase measured on L1 frequency CA or PY parts 2 canier phase measured on L2 frequency R geometrical range from satellite S to user u 61 userreceiver clock error 6f satellite clock error T tropospheric delay I m I M ionospheric delay in code measurement on Ll2 M 1 M Z multipath delay in carrier phase measurement on L1 2 M NZ carrier phase bias or ambiguity A1 AZ carrier wavelength 5 5M other delayerrors in carrier phase measurement on L1 2 ASEN awn LECTUPE NOTES 7 LAESONAXEL2A 15 COMPARE PSEUDORANGE and CARRIER PHASE pl Rc6tu 6fTIpl Mplspl 1A1RC6Iu 6fT Ipl M 1 MA1 s 1 bias term N does not appear in pseudorange ionospheric delay is equal magnitude but opposite sign troposphere geometric range clock and troposphere errors are the same in both multipath errors are different phase multipath error much smaller than pseudorange noise terms are different factor of 100 smaller in phase data Colorado ASEN awn LECTUPE NOTES 7 tAizsoNAxEtizAigt m l PSEUDORANGE CARRIER PHASE pl Rc6tu 6fTIplMplspl 1A1Rc6tu 6fT Ipl M 1 Nl1 s 1 p1 1 1 21m Mpl M l pl 1MA1 Colorado p141 memrs Yaruqadee PRNZS 2 hours since midnight ASEN awn LECTUPE NOTES 7 LAQSONAXEUEAI 17 l L1 CARRIER PHASE L2 CARRIER PHASE Compare with AA R c6tu 6f T I1 M 1 N1A1 s pseudorange difference M2 Rc6tu 6f T I 2 sz N2A2 st 11 1 722 2 172 Ip1M 1 Mb2 N1 1 N2A2 15 2 anuqadee PRNZS Yaruqadee PRNZS 307 VA 307 I 257 quot 257 v E 207 gt g 207 a v E E I 15 r39 E 157 3quot 5 f 7 I 7 Q 10 I 10 57 57 O x xN M o J 7 o w 5 o w 5 2 3 4 2 3 hours since midnight hours since midnight l L1 PSEUDORANGE L2 PSEUDORANGE pl Rc6tu 6fTIp1Mp1 pl pZ Rc6tu 6fTIpZ Mpz pZ 1 pz Ipl IpZ Mpl MpZ pl p2 Differencing pseudoranges on two frequencies Yomqodee PPNZE removes geometrical 53 i M E effects and clocks N x a troposphere and some i 4 R ionosphere K 6 I s f x L i i i x i i i 4000 8000 i WOOD domain Seconds since midnighi ASEN awn Lgcruug NOTES 7 LAESONAXELEAD w ASEN 5090 39 39 quot to GNSS Fall 2008 GNSS VISIBILITY Assigned 29 August 2008 Due 12 September 2008 Individual Assignment OBJ ECTIVES Predict satellite visibility using the broadcast almanac Explore the visibility limits at different locations on the earth OVERVIEW This software project provides you with some basic codes for determining satellite position from the broadcast almanac data note the broadcast almanac is not the same as the broadcast ephemeris You will use and expand on these codes to generate visibility plow and explore satellite coverage at different locations on the earth We ll also add a PDOP calculation to characterize the geometry ASSIGNMENT 1 You ve been provided with code that computes satellite and user positions in ECEF coordinates See runivis m Familiarize yourself with the code working out the file formats input and output This code requires YUMA almanac formats Note these codes were written by PC people and thus do not necessarily work properly in unix or on a Mac N V 10 pm Write a function that takes as input a satellite and a user position in ECEF coordinates and returns the elevation and azimuth getAzEliASEN5190 m Write a separate function that determines if the satellite is visible based on the elevation and the mask angle Check to make sure that both work correctly L V 10 pm Find the satellites visible at 2007 97 1200 in Boulder Latitude 400 Longitude 1050 and Altitude 1631 meters Turn in satellite names azimuth and elevation angle in degrees to 3 decimal points 4 V 20 pm Create an AZEL plot of the satellites visible throughout the day on Sept 7 2007 at the following locations on the earth a 0 N 0 E b 90 N 0 E c Boulder d Somewhere in Australia Describe the differences in visibility U V 10 pm Using your previous resulm for Boulder CO calculate and plot the number of satellites that are visible as a function of time On the same plot show the number of satellites above 10 degrees 0 V 10 pm For Boulder CO compute the time shift for any three satellites to reappear in the same place in the sky on Sept 6 and 7 Describe your approach and your resulm using figures or tables as needed ASEN5090Visibility Projectdoc 1 ASEN 5090 39 39 quot to GNSS Fall 2008 REPORT OUTLINE AND GRADING Title Page 5 Executive Summary Summarize brie y what was done results and conclusions Provide an overview of the rest of your report 60 Answers to questions 5 Conclusions and Recommendations describe what you learned about satellite visibility and recommend changes to the project the codes or potential for future investigations References Appendix Well commented code for any new or modified routines 10 Style and Clarity clarity spelling grammar organization neatness 80 TOTAL ASEN5090Visibility Projectdoc 2 ASEN 5090 39 39 quot to GNSS Fall 2008 MATLAB SOFTWARE A demo of the software will be given in class on the date the project is assigned Brief descriptions of all files included in the software download are provided below Readmebrt 7 information on the provided codes runivis m 7 top level calling routine useriinputm 7 sew up the input for the visibility calculations getAzE175090 m 7 function to compute azel given receiver and satellite positions To be written by strident loadSimulationParametersm 7 reads input from user loads the almanacs fills up structures getSatelliteStatem 7 computes the satellite position and velocity from the almanac date and time GreenwichSidereal m 7 needed by getSatelliteState getYUMAFileNamem 7 figures out the right yuma file for the requested date getYumaAlmanac m 7 reads in the yuma file and fills the almanac structure for each satellite trimAlmanac m 7 gem rid of empty satellite slots loadFileVariableslntoWSm 7 reads the input file loadlnputm 7 fills up the structures with info from useriinput and additional conversions GPSweekm 7 converts time from YMDHMS to GPS Week and TOW julianDate m 7 needed for date conversion ecef2ned m wgslla2xyzm wgsxyzleam plotiazelm 7 plot satellite az and el slashTypem 7 deals with and issues ASEN5090Visibility Projectdoc 3 Signal Structure Qolorado quotmm my a may ASEN 5090 LECTURENOTESV LARSONAXELRAD Position Solution The position solution involves an equation with four unknowns Receiver position x y z in what reference frame Receiver clock correction correction to what Position accuracy of 1 m implies knowledge of the receiver clock to within 3 ns 1 GPS accuracy is based almost entirely on knowing satellite orbits and satellite clocks Requires simultaneous measurements from at least four satellites i The receiver makes a range measurement to the satellite by measuring the signal propagation delay i A data message modulated on the ranging signal provides the precise location of the satellite and corrections for the satellite clock GPS accuracy is based almost entirely on knowing these two things Colorado Univus vat may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEM How does the satellite measure the signal propagation delay At pseudorange p It uses the codes either CA or P The GPS receiver has the codes for all 32 PRN signals It can generate them internally and timetag them Then the GPS receiver compares the signals it receives with the codes it generates When it finds a match that tells them which satellite generated it The amount the codes had to be shifted in time to make that match tells them At The fact that CIA and P codes have different frequencies does intrinsically impact how well At can be determined and thus p GLONASS uses the Doppler shift not the PRN to determine which satellite sent the signal Colorado Univus yat mm it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a Outline L1 and L2 carriers PRN Codes CDMA BPSK Navigation Message Correlation properties Spectrum Signal power Reading Assignment in Ch 2 Questions to think about i What features of GPS are enabled by the codes a Whnyrequencies u Would there be an advantage to substantially increasing the GPS signal power Any downsides Colorado Univers ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEM 4 SIGNAL COMPONENTS Base frequency is f0 1023 MHz 10230000 Hz cyclessec L1 154 f0 157542 MHz L2 120 f0 12276 MHz L5 115 f0 117645 MHz future CA code chip rate f0 10 1023 Mcps MHz 1 ms long P code chip rate f0 1023 Mcps MHz 37 weeks long each satellite gets a 1 week segment Navigation Data rate 50 bps 20ms per bit 6 s per frame 30 s for individual satellite data 125 min for all Colorado Unix25391an may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a PROPERTIES OF CODES Protect against interference Reduce noise effects Permit many signals to be transmitted at the same frequency without interfering known as code division multiple access CDMA Permit high resolution ranging Enable communications security known as low probability of detection LPD Key characteristics of codes are their type length chip rate Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a PRN CODES pseudo random noise codes In GPS a pseudo random noise code used to modulate a carrier tone Types of modulation amplitude ADM flredunencv PM phase PM I 1 time ASK im 175K Lime IHHHH lllllllm li39i39ii39i39i39i mm ll llllllllllll Leick GPS principles Colorado Hallmarkn6 Cnlonav 3 Emler ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 7 PRN CODES pseudo random noise codes Colorado Univers va may it may GPS uses BPSK Biphase phaseshift keying sequence of quot139squot and 039squot that specify when phase of carrier should be reversed 1 or left alone 0 Can consider as a sequence of 039s and 139s or 1 and 139s in In terms of phaseshift keying 0 corresponds to quotdon39t shiftquot and 1 corresponds to quotshiftquot a In terms of digital amplitude modulation multiplying by a quot1quot leaves the carrier alone ie don39t shift and multiplying by a quot1quot inverts it ie shifts it by 180 deg These codes enable a GPS receiver to measure the transit time of a signal from a GPS satellite to the receiver antenna Reference Spread Spectrum Systems Robert C Dixon Wiley 1984 ASEN awn Lacrqu NOTES 7 wasoN AXEUEM a CORRELATION FUNCTION Correspondence between a code and a phase shifted replica of another code cross correlation correspondence between different codes autocorrelation correspondence of code wphase shifted version of itself Number of bits which agree minus the number of bits which disagree forthe original version of the code compared to the shifted version Forvalues of codes not 1 0 Rj39kn13xjixkin0j k Rn13xj ixj in0n 0 Colorado WWW may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a CORRELATION FUNCTION EXAMPLES 100111101110100010011011111111101 000010001010011100001110010010001 Every time the numbers agree add 1 Every time the numbers disagree subtract 1 UColorado quotwastian may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI m This example codes for 2 different satellites 100111101110100010011011111111111 000010001010011100001110010010001 14 agree 11 disagree Total score 3 Perfect agreement would be 35 UColorado quotmuslian my al may ASEN awn LECTUPE NOTES 7 LARSON AXEUEAI u This example same satellite codes but shifted Not so good score of 3 OllOOOlOlOlOllOOlOOOlOOlOOOOOllOOOOOllllOOOO llOOO1010101100lOOOlOOlOOOOOllOOOOOllllOOOOl But if you recognize they are shifted by 1 OllOOOlOlO1011001000lOOlOOOOOllOOOOOllllOOOO llOOOlOlO1011001000lOOlOOOOOllOOOOOllllOOOOl Agreement is perfect Colorado WWW may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 12 Use Matlab xcorr Satellite 9 compared to Satellite 10 code Satellite 9 compared with Satellite 10 1 000 800 600 summation 400 200 O 1000 500 0 500 1000 shifts Colorado Unmisny cl Colurad n at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 13 Satellite 10 compared to Satellite 10 code Satellite 10 compared with Satellite 10 1 000 800 600 summation 400 200 1000 500 0 500 1000 shifts Cotoraao Univaisny cl Colurad n at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 14 Satellite 10 compared to Satellite 10 code that has been shifted by 200 Satellite 10 compared with Shifted Satellite 1O 1 000 800 g 600 a E E a 400 200 0 C01 1000 500 o 500 1000 39 Ila Urile y I Iwill not ask you to code up the GPS PRN sequences Instead I will provide you with Matlab code I found on the web that does it for you Colorado function gcacodesvfs function GCACODESVFS Generates 1023 length CA Codes for GPS PRNs 137 g nx1023 matrix with each PRN in each row with symbols 1 and 0 sv a row or column vector of the SV39s to be generated valid entries are 1 to 37 fs optional number of samples per chip defaults to 1 fractional samples allowed must be 1 or greater For multiple samples per chip function is a zero order hold WWW may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI m GENERATING PRN CODES Tapped feedback shift register Epoch state input bit output bit An n stage shift register PRN generator tapped at 3n 1 I Colorado Unix25391an may i may ASEN awn Lacrqu NOTES 7 wasom AXEUEAI l7 MAXIMAL LENGTH CODES Maximal length codes are the longest codes that can be generated by a given number of shift register stages For an nstage shift register the longest code is 2n 1 chips ie 139s or 039s Maximal length codes have many interesting properties especiallytheir autocorrelation function For a maximal length code the autocorrelation function for a phase shift other than 0 or 2n 1 is 1 For any code the autocorrelation for a 0 shift is equal to the number of chips in the code Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI m How do you create codes You use binary addition rules 000 I 101 011 1110 but only use the last bit 0 GPS uses shift registers The more shift registers you have the more complicated you can make your code Colorado Univus yat may it may ASEN awn Lacrqu NOTES 7 wasom AXEUEM w Here is an example with 3 shift registers I Register1 Register2 Register3 Code I 1 i 1 i 1 i Start with all 1 s in your shift registers Add Register1 and Register3 Forthis example 11 10 gt 0 The answer 0 goes into Register 1 and everything shifts to the right UColorado 1111111111 11111111 111111111 ASEN awn Lacrqu NOTES 1 wasoN AXEUEAI 2n Resulting in Register1 Register2 Register3 Code 1 1 1 0 1 1 1 Colorado Hun25391an my 1 may ASEN awn 151qu NOTES 7 wasoN AXEUEAI 2 1 Next 011 Register1 Register2 Register3 Code 1 1 1 0 1 1 1 1 0 1 A 1 Colorado Hun25391an my 1 may ASEN awn 151qu NOTES 7 wasoN AXEUEAI 22 A er 2N 1 steps N is the number of registers the code repeats Register1 Register2 Register3 Code gt 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 For 3 shift registers the code repeats after 7 steps Colorado WWW my 1 may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 23 Real GPS Uses 10 shift registers They add different registers to produce the codes for different satellites Satellite 1 uses registers 2 and 6 Satellite 2 uses registers 3 and 7 and so on A 10shift register code repeats after TM or 1023 Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasom AXEUEAI 24 IMPACT OF CORRELATION PROPERTIES What makes a useful code i For ranging in For CDMA in For acquisition UColorado quotmm may i may ASEN awn LECTUEE NOTES 7 wasoN AXEUEAI 25 NAVIGATION MESSAGE TIIUI unw p 1 n om 05 um N I A A A oquot m I 6 TLM HOW Clock corrections and SV healthaccuracy E 12 TLM HOW Ephemeris parameters E 18 TLM HOW Ephemeris parameters E 24 TLM HOW Almanac ionospheric model dUTC 30 TLM HOW Almanac thfrnmoc Misra amp Enge Fig 413 Colorado University of Colored at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 26 PRN CODE SPECTRUM PRN codes have a sinc2 spectrum Main lobe is 2x chipping rate Side lobes are 1x chipping rate Power density is very low L2 L1 QED QED QED QED Jill 24E r 25o a l l 7 ll 25o WW E r 1553 155 158 i l V 1215 122 1239 PSD dBWlMHzi Colorado University of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 27 LEGACY GPS SPECTRUM A Colorado Universllyol Comrades Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 28 C uris L 8 ll W a m Modernization Block IIAIIIR Block IIRM IIF Block III RM IIAIIIR capabilities amp M F capabilities amp CIA civil signal L1 CIA 2nd civil signal LZC Improved clvil signal L1G 39 Std SafViCB 1624 SEP New military code Increased accuracy 4812m Precise Service 16m SEP Flex AIJ power 7dB Navigation sure L1 K L2 Pm nav I Increased NJ power 20 15 E llRM capability plus CIA 3rd cIVII slgnal L5 c nquot In em u Pm PM I u SIGNAL POWER GPS Satellites transmit 27W toward the earth GPS Signal level on the ground in L1 CA 1585 dBW 10 l6Watts in L1 PY 1615 dBW in L2 PY 1645 dBW Spread spectrum signal is subthermal or below the noise floor After correlation in the receiverthe recovered or despread carrier is above the noise typical SNR s 615 dB Processing gain for spread spectrum is signal BW data BW Colorado Unix25391an may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI an GPS SIGNAL GENERATION L1 CARRIER 157542 MHz CIA CODE 1023 Mops 39i NAVIGATION DATA 50 bps WJ PY CODE 1023 Mops WVV L2 CARRIER 12276 MHz C010 139 0 mm mm My ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 31

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