卫星定位理论与方法-第13次课-伪随机码测距原理

1、 测量与导航工程系导航与定位教研室陈明剑第第1212次课次课 伪随机码测距原理伪随机码测距原理 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个球体，可以不需要观测第四颗由于地球本身就是一个球体，可以不需要观测第四颗卫星，观测三颗卫星就可确定地面点位置（三球定位）卫星，观测三颗卫星就可确定地面点位置（三球定位）232323322222222121211)()

18、()()()()()()()(jjjjPjjjjPjjjjPZZYYXXZZYYXXZZYYXXj1j2j3注意：但由于通过测定时间确定距离，必须保持卫星和接收机时间严格同步，实际上无法精确已知接收机钟差，需作为待定参数求解，于是必须观测四课卫星才能三维定位。j4GPS定位基本公式定位基本公式jjtttRRttt钟面时卫星和接收机间的准确距离为： )(jRttCC实际上存在钟差，只能测得钟面时，那么星站观测距离（伪距）为： RjjjjRjRjRjjjRRjRtcZZYYXXtctctctcttctcttttcttcc222)()()()()()(测定传播时间来确定距离 ：=ct 式中： 未知数

19、为测站坐标未知数为测站坐标(X(Xj j,Y,Yj j,Z,Zj j) )和接收机钟差和接收机钟差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、伪距测量原理 问题1：接收机如何测得卫星至接收机的距离呢？回答：测定信号从卫星传播到接收

22、机天线所经过的时间延迟回答：测定信号从卫星传播到接收机天线所经过的时间延迟要求：卫星和接收机必须在一致精确时间系统内测定同一信号要求：卫星和接收机必须在一致精确时间系统内测定同一信号问题问题2：如何使得接收机与卫星在相同时间内产生相同码信号呢？：如何使得接收机与卫星在相同时间内产生相同码信号呢？回答：卫星上有精确的原子钟，接收机上虽然是石英钟，但回答：卫星上有精确的原子钟，接收机上虽然是石英钟，但多观测一颗卫星解算接收机钟差作为替换多观测一颗卫星解算接收机钟差作为替换问题问题3：相同信号卫星的位置如何得到？：相同信号卫星的位置如何得到？回答：卫星轨道较高，有利于预报卫星位置；接收机收到广播回答：卫星轨道较高，有利于预报卫星位置；接收机收到广播星历，其中包含有卫星位置，同时还有卫星主要摄动项改正星历，其中包含有卫星位置，同时还有卫星主要摄动项改正二、伪距测量原理 结果：卫星至接收机距离=信号传播时延光速问题4：如何测定卫星至接收机时延？回答：接收机具有能生成与卫星信号结构、时序完全一致的回答：接收机具