衛(wèi)星定位理論與方法-第13次課-偽隨機(jī)碼測(cè)距原理

1、 測(cè)量與導(dǎo)航工程系導(dǎo)航與定位教研室陳明劍第第1212次課次課 偽隨機(jī)碼測(cè)距原理偽隨機(jī)碼測(cè)距原理 GPS PositioningSatelliteSatelliteSatelliteSatellite1. Known position of satellites2. Range measurements from satellitesC Ca al lc cu ul la at te e p po os si it ti io on n& &t ti im me e你的位置是你的位置是:37o 23.323 N122o 02.162 WHow Does GPS Work?5 St

2、eps to GPSTrilateration from satellites is basis of system.1 GPS measures distance using speed of light.2 Once GPS knows distance, it needs to know satellites position4 5Then correct for ionospheric and trospheric delays.3To measure thedistance GPS needsgood clocks anda fourth SVfrom the satellitesT

3、rilateration from satelliteslBy measuring distance from several satellites you can calculate your position1TrilaterationOne measurement narrows down our position to the surface of a sphere 11,000 milesWere somewhere on the surface of this sphere.TrilaterationSecond measurement narrows it down to int

4、ersection of two spheres Intersection of twospheres is a circle 11,000 Miles12,000 MilesTrilaterationThird measurement narrows to just two points Intersection of threespheres is only twopoints. TrilaterationFourth measurement will decide between two points. Fourth measurementwill only go throughone

5、of the two points.4 Ranges to resolve for Latitude, Longitude, Height & TimeTrilaterationIn practice 3 measurements are enough lWe can discard one pointlOne point will be a ridiculous answerl We still need the 4th measurement because there We still need the 4th measurement because there are four

6、 dimensions to solve for (X,Y,Z and Time)are four dimensions to solve for (X,Y,Z and Time)How Does GPS Work?5 Steps to GPSTrilateration from satellites is basis of system.1 GPS measures distance using speed of light.2 Once GPS knows distance, it needs to know satellites position4 5Then correct for i

7、onospheric and trospheric delays.3To measure thedistance GPS needsgood clocks anda fourth SVfrom the satellitesSatellite RangingMeasuring the distance to a satellitelDone by measuring travel time of radio signals2Speed-of-Light Measurement Measure how long it takes the GPS signal to get to usl Multi

8、ply that time by 186,000 miles/sec Time (sec) x 186,000 = mileslIf youve got good clocks, all you need to know is exactly when signal left satelliteHow do we know when the signal left the satellite?One of the Clever Ideas of GPS: lUse same code at receiver and satellitel Synchronize satellites and r

9、eceivers so theyre generating same code at same timelThen we look at the incoming code from the satellite and see how long ago our receiver generated the same code difference betweenfrom satellitefrom ground receivermeasure timesame part of codeWhy a code?lCode lets many satellites operate on same f

10、requency lCode gives us a way to increase signal-to-noise ratio How Does GPS Work?5 Steps to GPSTrilateration from satellites is basis of system.1 GPS measures distance using speed of light.2 Once GPS knows distance, it needs to know satellites position4 5Then correct for ionospheric and trospheric

11、delays.3To measure thedistance GPS needsgood clocks anda fourth SVfrom the satellites Accurate clocks necessary to measure travel timeMaking sure both receiver and satellite are synchronizedlWhole system depends on very accurate clocks lSatellites have atomic clocksAccurate but expensivelGround rece

12、ivers just need consistent clocksThe secret is in an extra satellite measurement that adjusts the receiver clock3The ideal situation (accurate clocks)In 2 dimensions for sake of drawing This is where we really are4 secs6 secsAdding a third measurement (accurate clocks) Third measurementwould go thru

13、 ourposition if correct4 secs6 secs8 secsWith fast clock Bad position becauseclock is off by one second5 secs wrong time7 secs wrong timeThird measurement (fast clocks) Wont go through the other two Now third measurement wont go thru the other two.7 sec (wrong)5 sec (wrong)9 sec (wrong)How Does GPS

14、Work?5 Steps to GPSTrilateration from satellites is basis of system.1 GPS measures distance using speed of light.2 Once GPS knows distance, it needs to know satellites position4 5Then correct for ionospheric and trospheric delays.3To measure thedistance GPS needsgood clocks anda fourth SVfrom the sa

15、tellites Knowing where the satellites areAfter all, theyre 12,600 miles uplHigh orbit Very stable orbitsNo atmospheric dragSurvivabilityEarth coveragelMonitored by Defense Departmentfly over US possession at least once a dayDoD transmits corrections back to satellite lCorrections transmitted from sa

16、tellites to usStatus message 4How Does GPS Work?5 Steps to GPSTrilateration from satellites is basis of system.1 GPS measures distance using speed of light.2 Once GPS knows distance, it needs to know satellites position4 5Then correct for ionospheric and trospheric delays.3To measure thedistance GPS

17、 needsgood clocks anda fourth SVfrom the satellites Atmospheric CorrectionsToo bad its not operating in a vacuumlIonosphere is a band of charged particleslTroposphere is our weather5由于地球本身就是一個(gè)球體，可以不需要觀測(cè)第四顆由于地球本身就是一個(gè)球體，可以不需要觀測(cè)第四顆衛(wèi)星，觀測(cè)三顆衛(wèi)星就可確定地面點(diǎn)位置（三球定位）衛(wèi)星，觀測(cè)三顆衛(wèi)星就可確定地面點(diǎn)位置（三球定位）232323322222222121211)()

18、()()()()()()()(jjjjPjjjjPjjjjPZZYYXXZZYYXXZZYYXXj1j2j3注意：但由于通過測(cè)定時(shí)間確定距離，必須保持衛(wèi)星和接收機(jī)時(shí)間嚴(yán)格同步，實(shí)際上無(wú)法精確已知接收機(jī)鐘差，需作為待定參數(shù)求解，于是必須觀測(cè)四課衛(wèi)星才能三維定位。j4GPS定位基本公式定位基本公式j(luò)jtttRRttt鐘面時(shí)衛(wèi)星和接收機(jī)間的準(zhǔn)確距離為： )(jRttCC實(shí)際上存在鐘差，只能測(cè)得鐘面時(shí)，那么星站觀測(cè)距離（偽距）為： RjjjjRjRjRjjjRRjRtcZZYYXXtctctctcttctcttttcttcc222)()()()()()(測(cè)定傳播時(shí)間來(lái)確定距離 ：=ct 式中： 未知數(shù)

19、為測(cè)站坐標(biāo)未知數(shù)為測(cè)站坐標(biāo)(X(Xj j,Y,Yj j,Z,Zj j) )和接收機(jī)鐘差和接收機(jī)鐘差t tR R Observe Equation1 21 21 21()()()jjjRXXYYZZc T 2 22 22 22()()()jjjRXXYYZZc T 3 23 23 23()()()jjjRXXYYZZc T 4 24 24 24()()()jjjRXXYYZZc T Linearization of Observe EquationXtXt Yt ZtjjjjT( )( ),( ),( )XX Y ZiiiiT, ,ijjitXtX( )( )XtXYtYZtZjijiji( )

20、( )( )22212XtXt Yt ZtjjjjT0000( )( ),( ),( )XXYZiiiiT0000,XtXtYtZtjjjjT( )( ),( ),( )XXYZiiiiT,lttXXtXtXtXijijjiijji( )( )( )( )( )000 m ttYYtYtYtYijijjiijji( )( )( )( )( )000 n ttZZtZtZtZijijjiijji( )( )( )( )( )000Linearization of Observe Equation|)(|)(000ijjiXtXtLinearization of Observe Equation(

21、 )( )( )( )( )( )ijijijijijjittltm tn tXtX0c ttttiji Igji Tj( )( )( ),( )( )( )( )( )ijijijijijittltm tn tX0 c ttttiji Igji Tj( )( )( ),Solve of Observe EquationVAXlnnnttttttl210122011)()()()()()(111222111nnnnmlnmlnmlATZYXXnVVVV21lAAAXTT1)(lQAAQAXTT111)(二、偽距測(cè)量原理 問題1：接收機(jī)如何測(cè)得衛(wèi)星至接收機(jī)的距離呢？回答：測(cè)定信號(hào)從衛(wèi)星傳播到接收

22、機(jī)天線所經(jīng)過的時(shí)間延遲回答：測(cè)定信號(hào)從衛(wèi)星傳播到接收機(jī)天線所經(jīng)過的時(shí)間延遲要求：衛(wèi)星和接收機(jī)必須在一致精確時(shí)間系統(tǒng)內(nèi)測(cè)定同一信號(hào)要求：衛(wèi)星和接收機(jī)必須在一致精確時(shí)間系統(tǒng)內(nèi)測(cè)定同一信號(hào)問題問題2：如何使得接收機(jī)與衛(wèi)星在相同時(shí)間內(nèi)產(chǎn)生相同碼信號(hào)呢？：如何使得接收機(jī)與衛(wèi)星在相同時(shí)間內(nèi)產(chǎn)生相同碼信號(hào)呢？回答：衛(wèi)星上有精確的原子鐘，接收機(jī)上雖然是石英鐘，但回答：衛(wèi)星上有精確的原子鐘，接收機(jī)上雖然是石英鐘，但多觀測(cè)一顆衛(wèi)星解算接收機(jī)鐘差作為替換多觀測(cè)一顆衛(wèi)星解算接收機(jī)鐘差作為替換問題問題3：相同信號(hào)衛(wèi)星的位置如何得到？：相同信號(hào)衛(wèi)星的位置如何得到？回答：衛(wèi)星軌道較高，有利于預(yù)報(bào)衛(wèi)星位置；接收機(jī)收到廣播回答：衛(wèi)星軌道較高，有利于預(yù)報(bào)衛(wèi)星位置；接收機(jī)收到廣播星歷，其中包含有衛(wèi)星位置，同時(shí)還有衛(wèi)星主要攝動(dòng)項(xiàng)改正星歷，其中包含有衛(wèi)星位置，同時(shí)還有衛(wèi)星主要攝動(dòng)項(xiàng)改正二、偽距測(cè)量原理 結(jié)果：衛(wèi)星至接收機(jī)距離=信號(hào)傳播時(shí)延光速問題4：如何測(cè)定衛(wèi)星至接收機(jī)時(shí)延？回答：接收機(jī)具有能生成與衛(wèi)星信號(hào)結(jié)構(gòu)、時(shí)序完全一致的回答：接收機(jī)具