GPS理论与应用03

1、GPS理论与应用（3.工作原理与时间、坐标系统）刘瑞华 教授中国民航大学 电子信息工程学院GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统授课内容授课内容1.GPS定位原理定位原理2.时钟误差问题时钟误差问题3.GPS的时间系统的时间系统4.GPS参考坐标系参考坐标系5.坐标转换坐标转换GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统1.GPS定位原理定位原理GPS is a distance (ranging) system. This means that the only thing that the user is tryin

2、g to do is determine how far they are from any given satellite. There is no inherent vector information, which implies azimuth and elevation, in the GPS signal. All that the GPS satellite does is shoot out a signal in all directions, although there is a preferential orientation toward the Earth.GPS理

3、论与应用理论与应用 Introduction and Background(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统nGPS operates on the principle of trilateration(三边测量三边测量). The position of an unknown point is determined by measuring the lengths of the sides of a triangle between the unknown point and two or more known points.nThis is

4、 opposed to the more commonly understood triangulation(三角测量三角测量), where a position is determined by taking angular bearings from two points a known distance apart and computing the unknown points position from the resultant triangle.GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统nThe satellites do this by t

5、ransmitting a radio signal code that is unique to each satellite. Receivers on the ground passively receive each visible satellites radio signal and measures the time that it takes for the signal to travel to the receiver. GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统nDistance is then a simple matter of c

6、omputing D = V x T .nSince radio waves travel at the speed of light, the velocity is a given. Therefore, the only thing needed by the user to calculate distance from any given satellite is a measurement of the time it took for a radio signal to travel from the satellite to the receiver. GPS理论与应用理论与应

7、用 Introduction and Background(3)请注意，请注意，GPS是是单向测距单向测距系统，与声纳等的系统，与声纳等的双双向测距向测距系统不同系统不同GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统Single Range To A Single SV KnownnThe GPS Navstar satellite transmits a radio signal unique to each individual satellite. The signal is essentially omnidirectional, although th

8、ere is a preferential orientation toward the Earth since the satellites antennas aimed at the Earth. nIf we know that the range (distance) to a particular satellite is precisely 20,000 kilometers (for example), then the only place in the universe is somewhere on the surface of an imaginary sphere th

9、at has a radius of 20,000 kilometers.nWith only this amount of information there is no way to know where on the sphere we might be located.GPS理论与应用理论与应用 Introduction and Background(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统Two Ranges To Two SVs KnownnWe can narrow down this positional ambiguity consi

10、derably by adding a range to a second satellite. nWe already know that were 20,000 kilometers away from the first satellite ( “A”). If we determine that were also 22,000 kilometers from another, second satellite ( “B”), we find that the only place in the universe which is that distance away from sat

11、ellite “B,” andis still 20,000 kilometers away from satellite “A,” is located somewhere on a circle where the two respective spheres intersect.nWhile this has narrowed down our position considerably, we still dont know where on the sphere-intersection-circle we are.GPS理论与应用理论与应用 Introduction and Bac

12、kground(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统Three Ranges To Three SVs KnownnIf we add a third satellite with a known range of 21,000 kilometers, well almost be there. nNow, the only place in the universe is at the only two points where all three of the spheres happen to intersect.nWe now know w

13、here we are , at either one of two possible points. The receivers are smart enough to know the right one.nThree satellite ranges have given us our precise location in the universe. GPS理论与应用理论与应用 Introduction and Background(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统2.时钟误差问题时钟误差问题nWhy, when three satel

14、lites can determine our three-dimensional position so precisely, do we need four satellites? nTo keep very accurate time, each satellite carries four atomic clocks on board, two rubidium and two cesium. These clocks are accurate to within billionths of a second per month. nEach receiver, on the othe

15、r hand, only carries “inexpensive” quartz clocks with much lower accuracy. GPS理论与应用理论与应用 Introduction and Background(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统No Clock Timing Errornwe can look at the problem of clock timing error (clock bias error) as a two-dimensional problem by making several assum

16、ptions: First, that the clocks onboard the satellites are absolutely, exactly right on. Another assumption is that the receiver clock and the satellite clocks are in perfect synchronization. nIn the two-dimensional diagram we know that, we can only be at the two possible points where the two circles

17、 intersect. GPS理论与应用理论与应用 Introduction and Background(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统Receiver Time One Second FastnThe fact is that the satellite and receiver clocks are never perfectly synchronized, and any error must be because of receiver clock(why?).nAssume that the receiver clock is f

18、ast by one second. This means that, it appears that the signal took one second longer than it really did(“seems” that much farther away than it really is ).nWith only two satellites, the receiver doesnt “see” a problem. Instead it calculates what it believes to be an accurate position based on the i

19、ncorrectly measured time/distance signals. GPS理论与应用理论与应用 Introduction and Background(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统nAddition Of Another SV Time/RangenThe problem becomes apparent to the receiver when an additional satellite is included in the calculations. There is no place where the thre

20、e radii intersect.nAs soon as the receiver recognizes this, it knows that the problem is with its own internal clock and so it “skews” its clock setting slightly forward and backward until all three ranges intersect. GPS理论与应用理论与应用 Introduction and Background(3)GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统

21、n接收机时钟误差对每次测量均是相同的，属接收机时钟误差对每次测量均是相同的，属于于公共时钟偏差公共时钟偏差。 这种偏差能够通过求解方这种偏差能够通过求解方程被消除或补偿掉，程被消除或补偿掉， 测距圆便会交于一点。测距圆便会交于一点。n在实际应用中，由于大气效应、各种干扰使在实际应用中，由于大气效应、各种干扰使信号传播受到影响，会导致测量值不准确。信号传播受到影响，会导致测量值不准确。这些误差称为这些误差称为独立测量误差独立测量误差，很难消除。，很难消除。n在独立测量误差存在的情况下，三个测距圆在独立测量误差存在的情况下，三个测距圆不相交于一点，而是一个三角区域，即存在不相交于一点，而是一个三角

22、区域，即存在定位误差定位误差。 GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统GPS测距定位原理测距定位原理 利用利用4颗卫星颗卫星的测的测量值，估计接收量值，估计接收机机时钟误差时钟误差，并，并对星对星-站距离值进站距离值进行补偿，通过求行补偿，通过求解方程确定用户解方程确定用户接收机接收机位置位置。GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统Levels Of GPS ServiceTwo levels of navigation and positioning are offered by the GPS: The Sta

23、ndard Positioning Service (SPS) and the Precise Positioning Service (PPS). nPPS is a highly accurate positioning, velocity and timing service that is designed primarily for the military and other authorized users.nSPS offers a base-line accuracy that is much lower than the PPS, but is available to a

24、ll users with even the most inexpensive receivers. There are various techniques available to increase the SPS accuracy.GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统nPublished specifications for the Precise Positioning Service are:17.8 meter horizontal accuracy27.7 me

25、ter vertical accuracy100 nanosecond time accuracynPublished specifications for the Standard Positioning Service are:100 meter horizontal accuracy156 meter vertical accuracy167 nanoseconds time accuracyGPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统3.GPS的时间系统的时间系统GPS disseminates a realization of coordinated

26、 universal time (UTC，世界协调时世界协调时) that provides the capability for time synchronization of users worldwide. Applications range from data time tagging to communications system packet switching synchronization.GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统1）UTC （世界协调时（世界协调时) nUTC is a composite time scale. Th

27、at is, UTC is comprised of inputs from a time scale derived from atomic clocks and information regarding the Earths rotation rate.nThe time scale based on atomic standards is called International Atomic Time (TAI). nTAI is a uniform time scale based on the atomic second, which is defined as the fund

28、amental unit of time in the International System of Units.GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统The other time scale used to form UTC is called Universal Time 1 (世界时，世界时，UT1). UT1 is a measure of the Earths rotation angle with respect to the Sun. It is one component of the Earth orientation paramet

29、ers that define the actual orientation of the ECEF coordinate system with respect to space and celestial bodies and is treated as a time scale in celestial navigationGPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统UT1 remains a nonuniform time scale due to variations in the Earths rotation. Also, UT1 drifts

30、with respect to atomic time. This is on the order of several milliseconds per day and can accumulate to 1 second in a 1-year period.The International Earth Rotation and Reference System Service (IERS) is responsible for definitively determining UT1. GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统UTC is a ti

31、me scale with these characteristics（TAI和和UT1）. The IERS determines when to add or subtract leap seconds to UTC such that the difference between UTC and UT1 does not exceed 0.9 second. Thus, UTC is synchronized with solar time at the level of approximately 1 second.GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、

32、坐标系统2).GPS system timenGPS system time is referenced to UTC.nGPS system time is also “a paper time scale”; it is based on statistically processed readings from the atomic clocks in the satellites and at various ground control segment components. nGPS system time is a continuous time scale that is no

33、t adjusted for leap seconds. nGPS system time and UTC (USNO) were coincident at 0h January 6, 1980. GPS system time led UTC by 13 seconds(2006).GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统nThe GPS control segment is required to steer GPS system time within 1 s of UTC (modulo 1 second), but the difference

34、 is typically within 50 ns (modulo 1 second). nAn epoch in GPS system time is distinguished by the number of seconds that have elapsed since Saturday/Sunday midnight and the GPS week number.nGPS weeks are numbered sequentially and originate with week 0, which began at 0h January 6, 1980.GPS理论与应用理论与应

35、用3.工作原理与时间、坐标系统工作原理与时间、坐标系统3).接收机对接收机对UTC的计算的计算n在计算用户在计算用户PVT时确定其与时确定其与GPS系统时系统时的偏差的偏差tu，将这个偏差加到接收机时钟，将这个偏差加到接收机时钟的时间的时间trcv上便计算出上便计算出GPS系统时系统时。n在在GPS系统时与系统时与UTC之间的整数之间的整数闰秒值闰秒值tn由导航电文提供。由导航电文提供。n从而可以得到从而可以得到UTC时间：时间：tUTC=Trcv+tu+tn GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统4.GPS参考坐标系参考坐标系在在GPS应用中，接收机虽

36、然处于地球附近，应用中，接收机虽然处于地球附近，其位置随同地球的自转而运动，但其观其位置随同地球的自转而运动，但其观测目标却是受地球引力而绕地球运动的测目标却是受地球引力而绕地球运动的人造地球卫星。人造地球卫星。为了描述卫星的运动情况，并正确处理卫为了描述卫星的运动情况，并正确处理卫星的观测数据，需要采用星的观测数据，需要采用两种类型的坐两种类型的坐标系标系并实现坐标系之间的相互转换。并实现坐标系之间的相互转换。GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统一类是在一类是在空间固定空间固定的坐标系，该坐标系与的坐标系，该坐标系与地球自转无关，对描述地球自转无关，

37、对描述卫星卫星的运行位置的运行位置和状态极其方便。和状态极其方便。另一类是另一类是与地球体相固联与地球体相固联的坐标系统，该的坐标系统，该系统对表达系统对表达地面地面观测站的位置和处理观测站的位置和处理GPS观测数据尤为方便。观测数据尤为方便。可以通过坐标可以通过坐标平移平移、旋转旋转和和尺度变换尺度变换，将，将点的位置由一个坐标系变换到另一个坐点的位置由一个坐标系变换到另一个坐标系。标系。GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统坐标系统是由坐标坐标系统是由坐标原点位置原点位置、坐标轴指向坐标轴指向和和尺尺度度所定义的。所定义的。在在GPS定位中，坐标系原

38、点一般取定位中，坐标系原点一般取地球质心地球质心，而坐标轴的指向具有一定的选择性，为了使而坐标轴的指向具有一定的选择性，为了使用上的方便，国际上都通过协议来确定某些用上的方便，国际上都通过协议来确定某些全球性坐标系统的坐标轴指向，这种共同确全球性坐标系统的坐标轴指向，这种共同确认的坐标系称为认的坐标系称为协议坐标系协议坐标系。协议天球坐标系和协议地球坐标系是两种常见协议天球坐标系和协议地球坐标系是两种常见的协议坐标系。的协议坐标系。GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统1).协议天球坐标系协议天球坐标系 天球天球：以地球质心为球心，半径为无限大的假：以地

39、球质心为球心，半径为无限大的假想球体。想球体。 天极天极：地球自转轴与天球面的交点，有北天极：地球自转轴与天球面的交点，有北天极和南天极这两个天极。和南天极这两个天极。 天球赤道面天球赤道面：通过地球质心与天轴垂直的平面。：通过地球质心与天轴垂直的平面。 黄道黄道：地球公转轨道面与天球相交的大圆。即：地球公转轨道面与天球相交的大圆。即地球上的观测者所见到的太阳在天球上的运动地球上的观测者所见到的太阳在天球上的运动轨迹。黄道面与赤道面的夹角称为黄赤交角，轨迹。黄道面与赤道面的夹角称为黄赤交角，约约23.50。 春分点春分点：当太阳在黄道上从天球南半球向北半当太阳在黄道上从天球南半球向北半球运行时

40、，黄道与天球赤道的交点球运行时，黄道与天球赤道的交点。GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统 在天文学和卫在天文学和卫星大地测量学星大地测量学中，中，春分点和春分点和天球赤道面是天球赤道面是建立参考系的建立参考系的重要基准点和重要基准点和基准面基准面。天球示意图天球示意图GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统天球坐标系天球坐标系 在天球坐标系中，任一天体的位置可用天球空在天球坐标系中，任一天体的位置可用天球空间直角坐标系和天球球面坐标系来描述。间直角坐标系和天球球面坐标系来描述。天球空间直角坐标系天球空间直角坐标系

41、的定义：原点位于地球的的定义：原点位于地球的质心，质心，z轴指向天球的北极轴指向天球的北极Pn，x轴指向春分轴指向春分点点 ，y轴与轴与x、z轴构成右手坐标系。轴构成右手坐标系。天球球面坐标系天球球面坐标系的定义：原点位于地球的质心，的定义：原点位于地球的质心，赤经赤经 为含天轴和春分点的天球子午面与经过为含天轴和春分点的天球子午面与经过天体天体s的天球子午面之间的交角，赤纬的天球子午面之间的交角，赤纬 为原为原点至天体的连线与天球赤道面的夹角，向径点至天体的连线与天球赤道面的夹角，向径r为原点至天体的距离。为原点至天体的距离。GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时

42、间、坐标系统 天球空间天球空间直角坐标直角坐标系与天球系与天球球面坐标球面坐标系的系的定义定义GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统2).地心惯性（地心惯性（ECI）坐标系）坐标系For the purposes of measuring and determining the orbits of the GPS satellites, it is convenient to use an Earth-centered inertial (ECI) coordinate system. A GPS satellite obeys Newtons laws

43、 of motion and gravitation in an ECI coordinate system.定义定义：原点：原点-地球质心；地球质心；X轴轴-由地心指向春分由地心指向春分点；点；Z轴轴-由地心指向北极；由地心指向北极；Y轴：轴：XY平面与平面与赤道面重合，构成右手坐标系。赤道面重合，构成右手坐标系。GPS理论与应用理论与应用3.工作原理与时间、坐标系统工作原理与时间、坐标系统3).地心地球固连（地心地球固连（ECEF）坐标系）坐标系For the purpose of computing the position of a GPS receiver, it is more convenient to use a coordinate system that rotates with the Earth, known as an Earth-centered Earth-fixed (ECEF) system. In ECEF system, it is easier to compute the latitude, longitude, and height p