Introduction to Global Navigation Satellite Systems
Introduction to Global Navigation Satellite Systems ASEN 5090
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This 72 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 Penina Axelrad in Fall. Since its upload, it has received 37 views. For similar materials see /class/232168/asen-5090-university-of-colorado-at-boulder in Aerospace Engineering at University of Colorado at Boulder.
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Tropospheric Effects ASEN 5090 Colorado aaaaaaaaaaaaaaaaaaaaaaaa g ASEN 5090 LECTURENOTESV LARSONAXELRAD Outline Characteristics of the troposphere Effect of troposphere on GNSS observations Zenith delay models amp mapping functions Measurement of tropospheric delay Occultation measurements Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEM 2 Index of refraction a measure for how much the speed of light or other waves such as sound waves is reduced inside the medium I The refractive index n of a medium is defined as the ratio of the phase velocity 0 of a m phenomenon such as Lgm or m in a reference medium to the phase velocity vp in the medium itself r1cvp The phase velocity is defined as the rate at which the crests of the waveform propagate The groug velocityis the rate that the envelope of the waveform is propagating Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEM a httpwwwmike wiiscomTutorialrefractionhtm httpenwikipediaorgwikiListofrefractiveindices Snell s Law sine1 n2 sine2 n1 For Air at STP n10002926 quot quot m gt n2 gtn3 gtn4 delay 1ds Refractivity N n110E6 Coloradn ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 4 Standard Atmosphere 20 7 7 mm m 7 7 aau1 7 77mm 7 001 an 7 m 5 Mn 1 6n a g swam use 7 E 7 pa 1 J lt E 40 7 Sm my m 20 7 100 7 I I 0 200 mm mm re Figure 21 Standard afmosphere Colorado ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a Tropospheric effects frequency up to 15GHz Wet component contributes 310 Total is about 25 m for zenith to 25 m for 5 deg Colorado Dry component contributes 9097 Lowest region ofthe atmosphere n10003 at sea level Neutral gases and water vapor causes a delay which is not a function of li y 7r hrlz401uu wet quot A ltIrml km I1 0 quot A R Uhsel39VH Lio n eartl s surface ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a Troposphere errors Equ rmrent Range Error 30 4o 50 50 Eremuon Angre degrees Colorado ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 7 Dry Troposphere Delay Saastamoinen model TM 2277 x104 1 00026005 27 000028hP P0 is the surface pressure millibars 4 is the latitude h is the receiver height m 25 m at sea level Hopfield model TM 776x104 hd is 43km U T0 is temperature K Mapping function md I 1100143 E satellite elevation SlnE m Colorado ASEN awn lacrqu NOTES 7 mason AXEUEM a Wet Troposphere Correction Less predictable than dry part modeled by T 2277x10393 1255 005 en Saastamomen model M T T 0373 Hop eld model a hW is 12km 60 is partial pressure of water vapor in mbar Ma in function39 m 4 pp 9 39 d 39 000035 smE tanE 0017 Colorado ASEN awn Lacrqu NOTES 7 wasom AXEUEAI a U N B MODELS University of New Brunswick Canada REFERENCES John Paul Collins Assessment and Development of a Tropospheric Delay Model for Aircraft Users of the Global Positioning System PhD Thesis and TR203 University of New Brunswick WM Paul Collins Richard Langley James LaMance Limiting Factors in Tropospheric Propagation Delay Error Modelling for GPS Airborne Navigation Institute of Navigation 52nd Annual Meeting Cambridge Massachusetts 19th 21st June 1996 httpgaussggeunbcapaperspdfion52amcollinspdf Colorado ASEN awn LECTUPE NOTES 7 mason AXEUEAI in Measurement amp Estimation of Tropospheric Delays WaterVapor Radimeter VWR forwet delay zenith or pointed Add tropo states to estimatorsolver El D D E Colorado Constant over given time period Linearpiecewise continuous Time varying stochastic zenith delay Time varying stochastic zenith delay time varying azimuthal parameters ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI u Variation in Wet Zenith Delay Zenith De ay Colorado ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 12 Simplified ASEN 5090 Tropospheric Model T241 23leih7unu 01 m Tm Tzw sinE T Colorado ASEN awn Lacwizg NOTES 7 wasom AXEUEAI 13 How are researchers using GPS to monitor the Weather one person s error is another person s signal What do weather forecasters need Researchers at NOAA39s Forecast Systems Lab FSL made the first GPS observations of upperair moisture within the eyewall of Hurricane Ivan September 16 2004 The maximum quantity of precipitable water vapor retrieved from the GPS signal delays by FSL was 804 mm As a rule of thumb the ratio of precipitable water vapor to zenith wet delay is 015 Its actual value can vary by as much as 20 since it is a function ome which varies with location altitude season and weather Tm is the weighted mean temperature ofthe atmosphere This means Hurricane Ivan caused 533 cm of zenith wet delay and much more along the path ofthe satellite signal Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI l4 NOAAIGSD GroundBased GPS Meteorology GPSMET D 3 W Hawall httpgpsmet noaagovjspindexjsp 5 wuzpsnetunaagm urnmin n927n5 mm my a may ASEN awn LECTUkE NOTES 7 wasth AXEUEAI 15 httpgpsmetnoaagovjspbackg roundbackg round jsp CONTROL sITEs ORBITS 45 EPH 4 UTFOLE sI39I39E POSITION i mum I TAB 39 I SON39DES SURFACE MET RREc I DATA 1 VAPOR amp EVALUATION TER DERIVED PRODUCTS lt FORECASTERS 47mm 0R CALVAL lt IMPROVED POSITIONING Colorado ASEN awn IENORE NOTES 7 LARSON AXELPAD Ia SuomiNet RealTime Water Vapor Sensing Overview htt91lwwwsuominetucaredul 24539 25039 39 28039 Di05091317212529333741454953576185 p 71019 WV in centimeters ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 17 GPS Occultations Researchers have studied the atmospheres of Mars Venus and Jupiter since the 197039s through radio occultation Planetaryprobe transmitters on a planet39s far side sent signals to earth that brushed by the planet being studied so closely that they were bent and slowed as they passed in and out of the planet s atmosphere The signal delay produced by the occultation is used to extract data on pressure and LEOS doing Occultations Limb Soundin t COSMIC chanl GRACE u CHAMP D D D Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI m COSMIC Universitan Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 19 Progression of Tangent Point for a Setting desending Occultation Tangent point ado mummy 042mm army GPS Radio Occultation R0 Data Climate u Characterize climate its variability and change a Evaluate global climate models and analyses u Monitor climate change and variability with unprecedented accuracyworld s most accurate thermometer Meteorology Improve global weather analyses particularly over data void regions such as the oceans and polar regions a Improve skill of global and regional weather prediction models a Improve understanding of tropical midlatitude and polar weather systems and their interactions lonos here haracterize global electronic density distribution Observe the interactions among the upper stratosphere mesosphere and iono r u Improve the analysis and prediction of space weather Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 21 Characteristics of GPS RO Data I 39 L 39 instruments Global 3D coverage 40 km to surface a 39 viewing 1 I 1 39 a I quot High vertical resolution 01 km surface 1km tropopause I I r r I All weatherminimally affected by aerosols clouds or prec Independent height and pressure Requires no rst guess sounding Independent of radiosonde calibration No instrument drift No satellitetosatellite bias Compact sensor low power low cost Colorado ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 22 Sunday May 6 2007 Global coverage in all weather 2111 soundings 5 0 pUruam deg North casm rcrtoccb atm 150 1 1 U 0 0 39I 00 3mg ngi mm mm cosmicmocd ufmpmlnnn deg East m mu ram Colorado ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 23 Occultation Locations for COSMIC 6 80 6 Planes 24 Hrs 60 I 30 a o t fquot 3933 o 0 0 quoto a 90009 9 ol 3900 0 m a o o 9 o o o A 9 o 9 O 9 9 3 v 0g 0 3 30 s 1 9 0 9 3 9 60 Colorado University of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 24 Comparison of SSMl retrieval with COSMIC GPS vs SSMI Wentz GPS vs SSMI Schluessel 7 ii QH Bi i l ibi i i li quot ii LHBii i g g 6E 6 RMS Difference 0317098 3 6 RMS Difference 0396601 Corr Coef 0968993 E Corr Coef 0973007 0 E 0 g I b 5 i 5 C E Q E D i 2 f g g 4 s 3 2 3 0 2 quot 2 g 2 1 021m 1 1111111 1111111 5 6 7 GPS vs SSMl Alishouse GPS vs SSMl Petty 73 ii QH Bi i 1335123 W WC 3quot ii LH Si i g 13395952 6 RMS Difference 0306797 39 g 6 RMS Difference 0314781 g E Corr Coef 0972703 E E Corr Coef 0971870 8 E E lt5 E 9 5 5 8 E i 4 4 2 E lt E 3 i E 3 2 m 2 2 D 2 2 i 2 6 7 Colorad U University of Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 25 GPS RO data 01 16 November 2006 o 1 2 3 4 5 6 COSMIC IWV Comrade Universityof Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 26 Using COSMIC for Hurricane Ernesto Prediction Results from Hui Liu NCAR Colorado Univershyof Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 27 Clocks quotA man with a wawh knows what time it is A man with two wawhes is never sure quot w Segal39s Law ASEN 5090 Even a broken wawh gives the correct time twice a dayquot Colorado Unmnm my ai may ASEN 5090 LECTURENOTESV LARSONAXELRAD Time amp Time Scale Colorado The second is fundamental measurement of time interval Selection of a reference epoch Solartime Based on rotation rate of the earth Apparent solar day interval between times pointed toward the sun Mean solartime based on average period Until 1960 1 sec was defined as 186400 of a mean solar day Time at the Greenwich meridian is GMT or Zulu time Time zones are approximately every 15 deg of longitude corresponding to 1 hour steps instead of continuously varying time Universal Time UT is a time scale based on the rotation rate of the earth so it is not uniform UTO mean solar time at the prime meridian as measured at an astronomical observatory UT1 UTO corrected for polar motion Ephemeris time is based on the revolution of the earth about the sun 1 sec defined fraction of a year EDD D Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI CLOCK HISTORY Hydrogen Masers Improved Cesium Clocks A 1o8 49 5 1o1 Early e Cesium Clocks 1Dquot a 105 1 O l 104 3 Quartz C t l W a 104 g C 2 39 Shortt 1 8 ree Pendulum 0 Harrison 10 E Ch I 39 rcnome er 1 Huygen Pendulum 10 l I l 1700 1000 1900 2000 Year Colorado Unwers yal Eoluradoak mug ASEN 5090 LECTURE NOTES 7 LARSON AXELRAD 3 ATOMIC CLOCKS GPS satellites use atomic clocks a precision clock that depends for its operation on an electrical oscillator regulated by the natural vibration frequencies of an atomic system as a beam of cesium atoms Types of atomic clocks on GPS satellites How things Work Cesium atomic clocks emplo a beam of cesium atoms The clock separates cesium atoms of different energy levels by magnetic eld Hydrogen atomic clocks maintain hydrogen atoms at the required energy level in a container with walls of a special material so that the atoms don39t lose their higher energy state too quickly o o Rubidium atomic clocks the simplest and most compact of all use a glass cell of rubidium gas that changes its absorption oflight at the optical rubidium 39equency when the surrounding microwave frequency is just right o I You do not need to use an atomic clock for your ground receiver but you can if you want to Useful info 1 millisec 300 km 1 microsec 300 meters o o o 1 nanosec 300 mm Colorado WWW my 1 may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 4 Why is Cs so frequently used in atomic clocks The SI unit of time defined as the duration of 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of cesium133 in a ground state at a temperature of absolute zero and at rest This was value was chosen to correspond to ephemeris time Continuous time scale based on SI second International Atomic Time TAI This drifts off from UT1 Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a Coordinated Universal Time UTC ICoordinated Universal Time UTC uses the SI second for interval but is adjusted by leap seconds to stay close to UT1 ISet UTC UT1 on Jan 1 1958 Leap seconds are introduced usually at the end of June or Decemberto keep UTC UT1 lt 9 sec httn39lhniers nhsnm 39 39 39 39 39 39 quot 39 rlat IUTC is determined based on cooperation between 65 labs and 250 clocks but dominated by the US contribution In the US we have UTCNST and UTCUSNO Why Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI a GPS Time Defined like UTC based on a group or ensemble of clocks These are all located at the M08 in Colorado Springs GPS Time done more quickly no leap seconds GPS Time steered to remain within 1 microsec of UTCUSNO modulo 1 sec but in reality it is much much much better As of January 2006 GPSTUTCUSNO 14s Correction from GPST to UTCUSNO given in the navigation message 7 Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 7 NISTF1 Cesium Fountain Atomic Clock The Primary Time and Frequency Standard for the United States Right here in Boulder Colorado Univers vat may it may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a httptfnistgovtimefreqcesiumfountainhtm Frequency Uncenalnly gt I E m 5 239 5 a 3 a u 2 U I 980 I 970 1980 1 590 as of thesummer of 2005 the uncertainty has been reduced to about 5 x 1016 which mans it would neither gain nor lose a second in more than 60 million ymts Colorado Unmnm may i may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI a But I thought you said the US Naval Observatory was responsible fortime NISTF1 does not operate 247 An operational timescale must be available at all times USNO defines UTC for the US But more importantly who defines time for GPS Colorado WWW may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI m GPS MASTER CLOCK AT USNO UTC is an international paper clock Univers Colorado itynf Coluradoat Euul u httptychousnonavymimctohtml The atomic clock timescale ofthe USNO is based on an ensemble of 50 cesiumbeam frequency standards and a dozen hydrogen masers Frequency data from this ensemble are used to steer the frequency of another such maser designated Master Clock 2 MC 2 until its time equals the average of the ensemble The reference ofthe actual Master Clock is called UTC USNO UTC USNO is usually kept within 39 39 quot quot 10 nanoseconds of UTC ASEN 5090 LECTUkE NOTES LAkSON AXELkAD 11 The Alternate Master Clock lives at the GPS Master Control Station in Colorado Springs Schriever AFB Colorado Umvars va may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 12 GPS SATE LLITE CLOCKS GPS has flown both rubidium Rb and cesium Cs oscillators onboard which are very stable New launches have only used Rb I believe Clocks are constantly monitored by the control segment Part of the navigation or data message includes clock correction information Precise vs Broadcast Satellite Clocks Precise vs Broadcast Satellite ClocksResidual Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 13 BROADCAST CLOCK CORRECTION Example January1 in 1995 at hour 4 PRN 1 Here is the navigation le ent 155 1 1 a n nnrn651767o77wanrmrn216mw 1671nr11nnnmnmnmnmonn n minnnnnnnnnoonarn 26375nnnnnnnDom n amaMmaBnnDrnB n znznzonaee mom 7n maemwaanm n azaaaumaanDrnz n balaeeanmneun n 515357786653Dom n a oman zanzoonn n 28353125nnnn0onarn12M351526880omrn Blazoaaeamauna n mmmaaaum n lunnnnnnnnnnoom n minnnnnnnnnoona n nunnnnnnnnnnoonn n aznnnnnnnnnnoonz n nunnnnnnnnnnDonn n laaeaaaamazorna n Mannnnnnnnnoona n Banannnnnnnnoom n nunnnnnnnnnnoonn n nunnnnnnnnnnoonn n nunnnnnnnnnnoonn The values you need are I clock bias a0 of0651767477393D04 sec clock drilt a1 of0216004991671D 11 sedsec If you want the satellite clock correction at ttoe a clock correction 0 0651767477393D04 1953949740921 km At t14400 3600 1800 Le 1 hour later a clock correction c 0651767477393D04 0216004991671D113600 19541828649 km Colorado Umvars vat my 1 may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 14 Clock Model in Broadcast Message value of a2 other than zer Colorado Three parameters am am and an in the navigation message for satellite clock corrections At af0 a ttoe af2ttoe2 where toe is time of ephemeris af0 can be up to 1 ms aM 10M I have never seen a PRN 25 Sulellile Cluck 10 4 km 227 JPL 5 DoD ln39mldc m Unix25391an may it may l U 20 hours Other Examples Satellite Clocks mean removed 0 Mean 2 0 km 5 a u E O Mean 143 mquot N Mean 223 km h lu 0 5 15 20 0 hou rs Colorado Unmnm my may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI m Colorado CLOCK The frequency of an oscillator is not exactly constant over time so the frequency you measure depends on when it is measured A constant or systematic frequency offset y0 can be calibrated The remaining random part of the frequency error must be characterized Normalized or fractional frequency error yt is characterized in terms of Allan Variance a 1 Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI l7 FREQUENCY ERROR TYPES a T I oc M 1 for ZsMsZ 12 10 8 W222 W WWW TM 1 1 Flicker PM WWWWVUWW JMWW MW 1 m g e 1 3 FlickerFM W a 2 4 RandomWalk FM m 4 600 I 1 400 200 0 200 400 600 ASEN 5090 LECTURE NOTES LARSON AXELRAD 18 SHORT TERM STABILITY AND DRIFT 1 W Af of um Under Test Rb EXBME E 1 T Beat against RefFreq mo samples each taken Isec for 1 sec periuds um I m 5m Stop mu have a spread P me E vlt m1xm39 yr derL Statistically by L A plm V SEC AHan Variance method mm mm mo H or x 1 Q 15 data pint iv takes about we g H sec to obtain Q m ma39 f u E Rb Examgha 2 E 100 sampWas each taken Q g For39l 0 sec periods wiH g2 3 have a spread man Variance movlz a For t a 100 sec 15 12 data paint takes me 1o UsuaHy defined 1x 100 sec or ms rs as W term arm WHITE Nolsi Long term stamth Usua39Hy defined FLOOR K has drift inducted term 13 1 day 1 week 1 year mn39 lL 01 sec 1 sec m sec 100 52 m3 104 m5 705 m7 105 TIME IN SECONDSr Co ora do umvemyov Ealnradoat mum ASEN 5090 LECTUkE NOTES LARSON AXELIIAD 19 CLOCK STABILITY Why doesn t GPS use hydrogen masers STABHLL TY 01F FREQUENCY STANDARDS lolu WWWK l 0 1 WKIKMIIIIIIIMIIIIIIINH H39IIII E 12 D 10 1013 A14 10 c I quotE E a 3 E 10 I I I I I I II I I I 10quot 1039 102 103 10 105 10 1I TDVJE s URIEESEJIDEJIIEIE ASEN awn LECTURE NOTES 7 wasom AXEUEAI 2n BIIR Rb High Freq Noise Problem GPS Clock Instabilities 15 June 7 5 July 2007 Highr equency novse m BIIR m results m fmquant tter resets for these clocks Modmea Allan Devia an Seamus 8 1 02 1 03 5 Averagan Inlervm mantis rado O 0 mm mm My ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI Advances in satellite clock technology Colorado Univus yat may it may The Passive Hydrogen Maser with its excellent frequency stability performance has been chosen as the Master clock in the Galileo Navigation Payload The Passive Maser can guarantee stability performances within the Galileo requirements for more than eight hours without an correctionupload from ground ASEN awn Lacrqu NOTES imwsoN AXEUEAI 22 RECEIVER CLOCKS Receiver clocks are ofthree classes a Clocks which are allowed to drift in Clocks that are steered to keep synchronization with GPS Time a Clocks that are allowed to drift with respect to GPS Time within some tolerance and then reset internally As a general rule no geodetic quality receivers are allowed to drift very much because there is a lot to be gained by synchronizing observations Steering and resetting class receivers are more common Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI STEERING amp RESETTING CLOCKS Hymnquot Maw a war 507 n g an n n d Eryn an S Dung ma a a on u ED a u 39a a vague one 11 u as a 439 can u a w E 5 u 32 a 2 w 5 aw quoth Fa 4 azg emu W 40 D n n a a Iquot a H mm mm 39 20000 40000 50000 80000 mm mm m 200 44 gm mu 5 0 20005 40000 souro 500m Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 24 Clock and Timing Review SI second is defined via Cs atoms GPS satellites use Cs and Rb atomic clocks Galileo is launching H masers GPS time does not have leap seconds so differs from UTC by an integer number of seconds currently 14 Timing between satellites is coordinated bythe Master Control Station whose time is coordinated with UTC USNO Master Control Station broadcasts linear corrections for satellite clocks every 2 hours This doesn t mean atomic clock behavior is linear Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 25 Clock and Timing Review Colorado Univus ya may it may Receivers are usually built with an inexpensive oscillator the receiver steers the oscillator to stay within 1 millisec of GPS time 1 millisec 300 km You can typically tell how tight the steering is by examining the scatter on the receiver clock solutions V th the appropriate receiver you can use an external oscillator ie Rb Cs H This could be helpful for position solutions This external timing piece might not agree very well with GPS time Cables How do clocks affect the pseudorange and carrier phase observables ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 2a 3 VJ 2 gt gt a IfJ J v h m 1 A a u A 1 f a 3 1 quot n M mq nv f 4 3 Jw k v 39v if y 4 x x AJH E L 4 if 2 l l quot 5A a x a v m M m J 39 f mww 5mm 5W5 51020 51025 51030 moss MAD days Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 27 RELATIVITY Qolorado quotmm my a may ASEN 5090 LECTURENOTESV LARSONAXELRAD SOURCES Neil Ashby quotRelativity in the Global Positioning Systemquot Living Rev Relativity 6 2003 1 URL cited on October12 2007 httpwww ivingreviewsorgIrr20031 Colorado Unix25391an may i may ASEN awn LECTUEE NOTES 7 wasoN AXEUEAI an RELATIVISTIC EFFECTS ON GPS CLOCKS Sagnac Effect rotation of receiver during transit time of signal being careful about coordinate frame According to special relativity a clock aboard a satellite traveling at constant speed appears to lose time relative to a clock on the Earth According to general relativity a clock on a satellite would run faster than one on the Earth due to the difference in gravitational potential Average net effect for GPS is that the clock gains 384 secday Recall a usec is 300 meters To compensate the fundamental frequency which we define as 1023 MHz is set 000455 Hz lower Colorado Univus ya Ealarada at Eaulder ASEN awn Lacrqu NOTES 7 mason AXEUEAI 31 Net fractional frequency shift of a clock in a circular orbit Fractional Frequency Shift x 10quot12 Radial distance in kilometers quot quotmquot 1 Figure2 Colorado Umvus vat may at may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 32 RELATIVISTIC CORRECTION FOR ELLIPTICAL ORBIT GPS orbits are nearly but not exactly circular An additional relativity correction that compensates for the eccentricity ofthe orbit is Arm 4442810quot e asinE e eccenmclty a s uare root of semima39or axis MMn AnAt J q J E eccentric anomaly M mean anomaly M 0 mean anomaly at epoch J 3986004415kmys2 An mean motion correction AI time elapsed since epoch Colorado Unix25391an may it may ASEN awn Lacrqu NOTES 7 mason AXEUEAI 33 ORBIT CODE Once you are sure your broadcast ephemeris code is working you should change it to return the relativistic correction as well Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 34 mymm Rammed G lACE 396aACE u Co or Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 35 r aGMesinE c Predicted oncerev GRACE velahwslvc clock EHECI amphtude May 24 La Apm 1 a an no we no mo so so me C 1 1 days shoe 2004414701 Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 3a Relativistic corrections 2 L39 2aGM esmE c ZF39V r 2 C I 2 TSfdt1 r2q0 lV 2 C 26 ASEN 5090 LECTURE NOTES LARSON AXELRAD 37 Color Unmnm my a may GRACE Rn almsllc Clock sheds n5 s 6 4 0 r II393939 w v 1 1III39 ua 4 II39 VV 3 anl 1 2Hdm ldc Nu m msglalun m q 1 II r r A a IIr a x n ICI 15 20 m May 24 W xWW M r a an 39II I I r I 1 II I IUI ado 4 VHVUUVV VaUHHUVa1VUUVx 5 20 m 15 hams ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 38 dose up In May 24 Mama 4 Num Inlugval on Colorado Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 39 Faly39mlma Rewveu and Ru um Cavecuon Appquoted Co or Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 4n Colorado Unmnm my a may ns GRACE awed ns GRACE uumd o a G o o Pcwev m c Oak 211 oncerev 20 40 80 MD 1 SD 180 Almr 39ulalMly mud on 39 7 v and on cam Wmn ow 0 20 4D 1 20 MD 1 SD 130 D 80 100 days smca zomOCY m ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 4 1 Sources of timing errors Temperature lt 1 part in 103912degree C a Antenna temperature a USO receiver temperature South Atlantic Anomaly 3 parts in 103912pass Voltage variations lt 1 part in 103912volt Colorado Universityof Colorado at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 42 Toltage variations 32 iiiiiiiiiiiiiii as I I I l I I I I I I 3259 326 3261 3262 3263 3264 3265 3266 3267 3268 3269 327II BattVMTHPCBB38 0 Batt39v RTHF39CBGE9 Voltage effect 7 x 103912 x 15 hours x 3600 sechr38 ns Temp effect 01 x 103912 x 15 hours x 3600 sechr05 ns Colorado University of Colorad 0 at Boulder ASEN 5090 LECTURE NOTES LARSON AXELRAD 43 2104 December I3 7 GRACE A Vc mgu mum mack 401 War Doynorwm ms mus Co or Unmnm my a may ASEN awn LECTUPE NOTES 7 wasoN AXEUEAI 44 HISTORICAL TIMING ISSUE SELECTIVE AVAILABILITY From 1990 1991 thru May 1 2000 the DoD intentionally dithered the GPS signals This is known as selective availability SA Instead of f01023 MHz there was an unknown frequency added to this V th special quotkeysquot the effects of SA could be removed in realtime Since time ltgt position the impact of SA was degraded positions in realtime In September 2007 announced that future satellites would not have SA capability Colorado Univus ya may it may ASEN awn Lacrqu NOTES 7 wasoN AXEUEAI 4a
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