GPS理论与应用05

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1、GPS理论与应用（5.伪随机码测距原理）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5.伪随机码测距原理伪随机码测距原理授课内容授课内容1.GPS卫星的测距码信号卫星的测距码信号 2.GPS测距原理测距原理3.伪随机码基础伪随机码基础4.GPS中的伪码扩频中的伪码扩频5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n1.GPS卫星的测距码信号卫星的测距码信号nGPS卫星发送的信号采用卫星发送的信号采用L波段波段的两种的两种载频作载波，分别被称作载频作载波，分别被称作L1的主频率和的主频率和L2的次频率。的次频率。n这些载

2、波频率由这些载波频率由扩频码扩频码（每一颗卫星均（每一颗卫星均有专门的伪随机序列）和有专门的伪随机序列）和导航电文导航电文所调所调制。所有卫星均在这两个相同的载波频制。所有卫星均在这两个相同的载波频率上发射，但由于伪随机码调制不同，率上发射，但由于伪随机码调制不同，因此无明显的相互干扰。因此无明显的相互干扰。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nEach satellite transmits its ranging signal on two different radio frequencies:157

3、5.42 Megahertz(part of the so-called“L-Band”)which is referred to as the L1 Carrier,and 1227.60 Megahertz(also of the L-Band)designated as the L2 Carrier.nSuperimposed on these radio carrier wave signals are pseudo-random,binary,bi-phase modulation codes called PRN(Pseudo Random Noise)codes that are

4、 unique to each individual satellite.nThis simply means that the carrier signal is modulated(varied)by changing its phase(up-down position of the waves)back and forth(bi-phase)at a regular and programmed rate and interval.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nThis modulation of the signal,which is really

5、just a series of“dots and dashes,”is very long and complicated.So complicated,in fact,that if you were just to look at it without knowing what it was,it would simply look like a bunch of random noise that made no sense at all.But it really does make sense to those in the know.Thus the term pseudo-ra

6、ndom noise.nThere are two different pseudo-random code strings used by the GPS:the Coarse Acquisition Code (C/A-code),sometimes called the“Civilian Code”,and the Precise,or Protected Code (P-Code).GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n选择选择L波段的波段的优点优点是：是：n(1)减少拥挤，避免减少拥挤，避免“撞车撞车”。目前。目前L波段的频率占波段的频率占用率低于其他波段，

7、与其他工作频率不易发生用率低于其他波段，与其他工作频率不易发生“撞撞车车”现象，有利于全球性的导航定位测量。现象，有利于全球性的导航定位测量。n(2)适应扩频，传送宽带信号。适应扩频，传送宽带信号。GPS卫星采用扩频技卫星采用扩频技术发送卫星导航电文，其频带高达术发送卫星导航电文，其频带高达20 MHz左右，在左右，在占用率较低的占用率较低的L波段上，波段上，易于传送扩频后的宽带信号。易于传送扩频后的宽带信号。n(3)大气衰减小，有利于研制用户设备。大气衰减小，有利于研制用户设备。GPS卫星采卫星采用用L波段，避开了大气的谐振吸收，衰减较小，且电波段，避开了大气的谐振吸收，衰减较小，且电离层延

8、迟的影响小，有利于用较经济的接收设备测离层延迟的影响小，有利于用较经济的接收设备测量量GPS信号。而采用两个载频，目的在于测量出或信号。而采用两个载频，目的在于测量出或消除掉由于电离层效应而引起的延迟误差。消除掉由于电离层效应而引起的延迟误差。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nWhen a radio transmits a signal,it is in the form of a simple sine wave that has a particular frequency (the number of“humps”on the sine wave that

9、 pass a fixed point per unit of time-usually given as Hertz,or times per second),wavelength(the distance between“humps”or any matching successive point on the sine wave),and amplitude(the“height”of the“humps”).nRadio wavelengths can range from tens of kilometers down to tiny fractions of micrometer.

10、Frequencies,intrinsically linked to wave-lengths,also have wide ranges,from only a few per hour(low frequency)to billions per second(high frequency).nA basic carrier sine wave is illustrated at the top of the diagram.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nBy itself,the carrie

11、r wave carries no information other than its frequency,wavelength,and amplitude.nIf we want to transmit any useful information on that carrier wave,we have to modulate or vary it at a regular rate.nThe second line in the diagram represents a string of zeros(offs)and ones(ons)that we want to send on

12、the carrier wave,much like Morse-code.nThere are several methods of transmitting that information on a carrier wave.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nThe first is by varying(modulating)the amplitude,or how“high”and“low”the sine“humps”go.If youve ever listened to AM radio,youve heard Amplitude Modulati

13、on.nYou could also vary,just slightly,the frequency of the carrier wave around a central“flat”frequency.That concept is illustrated by the line second from the bottom in the diagram.This is how FM,or Frequency Modulation,radio works.nFinally,you could modulate the phase of the carrier.The phase is t

14、he relative up/down position of the sine“humps.”By regularly reversing the ups and downs you can transmit your“Morse-code”information.This is how GPS transmits data on its two carriers.This is illustrated in the bottom line of the diagram.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nTwo Morse-code-like signal st

15、rings are transmitted by each satellite.They are the Coarse Acquisition,or C/A-code,and the Precise,or Protected Code-more commonly referred to as simply the P-Code.nGPS使用使用L频段的频段的两种载频两种载频为（其中为（其中f0是卫星是卫星信号发生器的基准频率）：信号发生器的基准频率）：L1载波：载波：fL1=154f0=1575.42 MHz，波长，波长1=19.032 cm；L2载波：载波：fL2=120f0=1227.6M

16、Hz，波长，波长2=24.42 cm。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nThe C/A-code is a sequence of 1,023 bi-phase modulations of the carrier wave.nEach opportunity for a phase-reversal modulation,or switch from a zero to a one,is called a “Chip (whether or not the phase is actually reve

17、rsed at that moment).nThis entire sequence of 1,023 chips is repeated 1,000 times each second,resulting in a“Chip-Rate”of 1.023 MHz or one(opportunity for a)phase switch(chip)every one-millionth of a second.nEach satellite carries its own unique code string.The C/A-code is the code used for the Stan

18、dard Positioning Service(PPS).GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nThe Precise(P)code is similar to the C/A-code,but instead of a sequence of 1023 chips,the chip-count runs to the millions.nAs a result,the complete sequence for the P-code takes 267 days to complete,rather than the one one-thousandth of a

19、 second for the C/A-code.One-week segments of the 267-day string are assigned to each satellite and are changed weekly.nThe P-code is the code used for the Precise Positioning Service(PPS).GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nThe chip rate of the P-code is an order of magnitude higher than for the C/A-co

20、de,running at phase-reversal chip rate of 10.23 MHz,or one phase switch(chip)opportunity every one ten-millionth of a second.This means that there are ten million individual opportunities for a phase reversal each and every second.nSince distance is a direct function of time,the radio wave clearly c

21、ant travel very far in only one ten-millionth of a second.Consequently,the P-code is considerably more precise than C/A-code.As well see,this fact is critical in understanding how GPS determines distance and why one service is so much more accurate than the other.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n2.GP

22、S测距原理测距原理nThe code is the key to understanding how GPS determines distance between the satellite and receiver,both for the Standard Positioning Service as well as the Precise Positioning Service.nBoth use their respective codes essentially the same way:they simply derive different levels of precisio

23、n by using different chip strings.Conceptually,both work identically.nThe basic concept is illustrated in the diagram.Each receiver has in its own memory each of the satellites unique codes.The receiver uses this information to internally generate an exact replica of the satellites code at the same

24、instant that the satellite generates its“real”code.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nBecause it took some finite amount of time for the signal from the satellite to reach the receiver,the two signals dont quite match up:theres a tiny delay,or lag time.Its that time delay

25、 that is used to determine the distance between the satellite and receiver.nThis method of range measurement by comparing the delay between two copies of the code is called“Code Correlation.”nDistances derived in this manner,before any kind of error correction is applied to the signal(which well tal

26、k about shortly)are called“Pseudo-Ranges.”GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nYou might ask“Why the ultra-complex chip string?Why not a simple,regular beep for example?Wouldnt that do the same thing?”nImagine for a moment that youre standing on the goal line of a football field and a colleague of yours

27、is standing 100 yards away at the other goal line.nAt the 50-yard line,theres a referee.Its agreed upon that at the exact moment the referee drops a flag,you and your colleague will begin yelling“HEY!”to each other at a pace of once per second.nWhat would you hear at your end?GPS理论与应用理论与应用5.伪随机码测距原理

28、伪随机码测距原理nObviously,you would hear yourself yell“HEY!”nA moment later you would hear your colleagues“HEY!”nYou could then measure how long after you yelled your“HEY!”that your colleagues“HEY!”got to you.nAssuming that you knew the speed of sound under your current conditions,calculation of your dista

29、nce from your colleague would be straightforward.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nBut there could be a problem here.nHow do you know that the“HEY!”you hear from your colleague is the right one to match your“HEY!”?In other words,what if,for example,it took 2 seconds for his “HEY!”to reach you?nYou wou

30、ldnt hear his“HEY!”until between your second and third one.You could quickly loose track and might even think that he was only second away because,after all,one of his“HEY!”did come only second after one of your“HEY!”s,just the wrong one!GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理

31、nNow imagine instead that at the same moment you both started yelling a count:“ONE!,TWO!,THREE!.”and so on.nNow when you heard any“number”that he yelled,youd instantly know which equivalent number of your own you would need to measure the time delay against.nThis would allow you to jump in anywhere

32、and know right away where you were in the count-string.nConceptually,thats how GPS measures distance with the C/A-and P-codes.Of course,GPS doesnt use numbers;instead,it uses those unique strings of ons and off s:zeros and ones.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nIn the“real”world of GPS,its easy to fin

33、d out where you are in the C/A-code string since the whole string“passes by”in only l/l,000 of a second.nTheres a problem,however,when trying to figure out where youre at in the 267-day long P-code string.nThus the term:Coarse Acquisition:because P-code receivers use the C/A-code to“get close”to whe

34、re they need to look in the P-code string,or to“ramp up”to P-code“lock-on.”nIf the C/A-code can tell the receiver where its at within a few hundred meters,then it only has to look at a very small part of the P-code.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nIt turns out that just knowing how far away you are f

35、rom the requisite four satellites isnt enough.nThe ranges to the satellites only tell you where you are relative to the satellites.But where are the satellites?It is also necessary to know where each satellite is in space.nFortunately,thats not too tough.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5

36、.伪随机码测距原理伪随机码测距原理nIn the first place,the military is very careful about where it sticks it very expensive space hardware.nOnce in place in space,the satellites orbits tend to be very stable through time because they are far above virtually all of the atmosphere and the drag that it can induce.nVaria

37、tions in orbits that are due to gravitational forces are fairly easy to predict and compensate for.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nTo compensate for the inevitable unpredictable perturbations in the satellites orbits,they are constantly monitored from the ground.nCorrections for any orbital variatio

38、ns that are identified are quickly uploaded from ground antennas to the satellites which then send the information back down to each receiver thats tuned in to them.nThis satellite position and orbital information is called the “Ephemeris,”or,as plural,“Ephemerides.”(Orbital position is constantly c

39、hanging,thus the term,based on the word“ephemeral,”meaning lasting only a short time.)GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nThe ephemeris is part of the Navigation/System data message(the“NAV-msg”)that is also superimposed on the L1 and L2 carriers,in a sense acting as a modulation of the modulation that

40、weve already talked about.nIn addition to the corrected satellite orbital and position data(the ephemeris data),the NAV-msg also carries a correction for any clock bias,or error in the atomic clocks,on board the satellites so that the receivers on the ground can compensate for these errors.GPS理论与应用理

41、论与应用5.伪随机码测距原理伪随机码测距原理n3.伪随机码基础伪随机码基础n从本质上讲，从本质上讲，GPS属于属于无线电无线电导航定位导航定位系统。系统。n用户只需要通过接收设备接收卫星播发用户只需要通过接收设备接收卫星播发的信号，就能测定卫星信号的传播的信号，就能测定卫星信号的传播时间时间延迟延迟或或相位延迟相位延迟，解算出接收机到卫星，解算出接收机到卫星间的距离（间的距离（伪距伪距），从而确定），从而确定接收机位接收机位置及时钟误差置及时钟误差。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n为了满足用户为了满足用户定位精度定位精度和和实时导航实时导航定位要求定位要求及军事

42、及军事保密保密的要求，的要求，GPS卫星信号采用了组卫星信号采用了组合码调制技术，即将卫星的导航电文（称为合码调制技术，即将卫星的导航电文（称为基带信号）经基带信号）经伪随机码伪随机码扩频为组合码，再对扩频为组合码，再对L频段进行频段进行BPSK调制。调制。n采用这种格式，不仅提高了系统导航的精度，采用这种格式，不仅提高了系统导航的精度，而且使系统具有很高的而且使系统具有很高的抗电子干扰抗电子干扰能力。为能力。为了达到这种目的，了达到这种目的，GPS中采用了伪随机码扩中采用了伪随机码扩频技术。频技术。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n1).二进制随机序列的二进制随

43、机序列的特点特点：nA.序列是非周期的，不能预先确定，不序列是非周期的，不能预先确定，不能复制；能复制；nB.序列中序列中1和和0出现的概率均为出现的概率均为1/2；n二进制随机序列二进制随机序列U(t)与其移位序列与其移位序列U(t-)模模2相加得到一个新的二进制随机序列。相加得到一个新的二进制随机序列。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理 二进制随机序列的二进制随机序列的自相关函数自相关函数定义为定义为:或简单写为或简单写为 01()()()TRU t U tdtT01()01R的个数的个数和的总个数GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理

44、由图可见，二进制随由图可见，二进制随机序列的机序列的自相关特点自相关特点为为1).1).=0=0时，时，R()=1;R()=1;2).|t2).|t0 0，时时R()=1;R()=1;3).|t3).|t0 0时时，R()R()与与 成线性变化成线性变化;GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n由于二进制随机序列是由于二进制随机序列是非周期非周期的，不能的，不能预先确定，也不能复制，其应用受到限预先确定，也不能复制，其应用受到限制。制。n在无线电通信中，利用在无线电通信中，利用多级反馈移位寄多级反馈移位寄存器存器产生具有周期性的、可以预见的、产生具有周期性的、可以预见的

45、、又具有良好相关性的二进制序列，称为又具有良好相关性的二进制序列，称为伪随机序列伪随机序列。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n下图为一个四级反馈移位寄存器下图为一个四级反馈移位寄存器原理图原理图。其。其中包括四级移位寄存器、模中包括四级移位寄存器、模2加法器、时钟发加法器、时钟发生器的反馈线路。而第生器的反馈线路。而第3、4两级经模两级经模2相加后相加后反馈到第反馈到第1级的输入端。级的输入端。2413脉冲发生器置1脉冲GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n移位寄存器开始工作时，在置移位寄存器开始工作时，在置1脉冲的作用下，各级脉冲的作用

46、下，各级寄存器输出全为寄存器输出全为1。n在下一个脉冲作用下，各存贮单元将其内容移到下在下一个脉冲作用下，各存贮单元将其内容移到下一个单元，而一个单元，而3、4级的模级的模2和送入第和送入第1个单元，第个单元，第4级级同时作为输出。同时作为输出。n经过经过24-1=15个脉冲后，又回到个脉冲后，又回到2全全1状态，构成一个状态，构成一个周期周期。2413脉冲发生器置1脉冲GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n经过简单推算可知，上述经过简单推算可知，上述4级移位寄存器产生级移位寄存器产生的的状态表状态表如下所示如下所示 GPS理论与应用理论与应用5.伪随机码测距原理伪随

47、机码测距原理n由移位寄存器产生的二进制序列称为由移位寄存器产生的二进制序列称为m序列序列。n比较上表中各级移位寄存器的输出比较上表中各级移位寄存器的输出m序列可序列可见，这些序列的见，这些序列的结构相同结构相同，只是相互间移了，只是相互间移了一个码位。这些序列称为一个码位。这些序列称为平移序列平移序列。n对于对于r级移位寄存器，采用不同的反馈联接方级移位寄存器，采用不同的反馈联接方式，将产生不同的式，将产生不同的m序列，但其周期都是相序列，但其周期都是相同的。同的。nm序列的序列的周期周期为为 T=Nt0=(2r-1)t0GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nm序列可

48、用电路的序列可用电路的特征多项式特征多项式表示为表示为n其中，其中，1表示模表示模2加法器反馈到第加法器反馈到第1级的输级的输入端。入端。Ci=0表示第表示第i级输出不作为模级输出不作为模2加加法器的输入，法器的输入，ci=1表示第表示第i级输出作为模级输出作为模2加法器的输入。加法器的输入。n比如，对上述的比如，对上述的4位移位寄存器，其特征位移位寄存器，其特征多项式可表示为多项式可表示为1()1riiiF xc x 34()1F xxx GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n两个平移两个平移m序列模序列模2和所得到的和所得到的m序列结果不变，序列结果不变，只是码位

49、进行了只是码位进行了平移平移。可用下式表示。可用下式表示n例如，对上述的例如，对上述的4位移位寄存器的输出端，有位移位寄存器的输出端，有P(0)=111100010011010P(3)=100010011010111P(0)P(3)=011110001001101=P(14)00()()()P tP tKtP tLtGPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n2).伪随机码的特点伪随机码的特点n根据上述基本理论，可以总结出伪随机根据上述基本理论，可以总结出伪随机码的特点如下列码的特点如下列5点所示：点所示：nA.r级移位寄存器产生的级移位寄存器产生的m序列伪随机序列伪随机码

50、，码位宽度等于脉冲周期码，码位宽度等于脉冲周期t0，m序列序列的的周期周期为为T=(2r-1)t0；nB.伪随机码在一个周期内，伪随机码在一个周期内，0个数比个数比1少少一次一次；GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nC.伪随机码的伪随机码的自相关自相关函数为函数为 01(0,1,2,.,21)()1/,(0,)rnNt nNRNnt nnN，不为 的整数倍与 成线性关系，为其他值时GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n自相关举例自相关举例：n对于对于4位移位寄存器位移位寄存器 其输出端为其输出端为P(0)=111100010011010将输

51、出端向左移动将输出端向左移动4位，可以得到位，可以得到P(4)=000100110101111。该伪随机的自相关为该伪随机的自相关为R(4)=-1/1534()1F xxx GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n4).互相关函数：互相关函数：n2个不同的个不同的m序列之间的相关函数称为序列之间的相关函数称为互相关互相关函数，与自相关函数计算公式相函数，与自相关函数计算公式相同。同。n不同结构的不同结构的m序列的互相关函数具有多序列的互相关函数具有多种数值，随着级数的增加，互相关值种数值，随着级数的增加，互相关值迅迅速减小速减小。GPS理论与应用理论与应用5.伪随机码测

52、距原理伪随机码测距原理n互相关举例互相关举例：n对于对于4位移位寄存器，位移位寄存器，P1(0)=111100010011010P2(0)=111100101110010P2(4)=001011100101111P2(5)=010111001011110其互相关分别为其互相关分别为5/15，-7/15，1/15n可见，可见，m序列之间的互相关是不同的。序列之间的互相关是不同的。341()1F xxx 232()1F xxx GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nE.截短和复合：截短和复合：n对于周期性对于周期性m序列，可以截取其中一部序列，可以截取其中一部分组成一个新

53、的周期序列，称为分组成一个新的周期序列，称为截短序截短序列列（截短码）；也可以将多个周期较短（截短码）；也可以将多个周期较短的序列按照一定的规则合成为一个序列，的序列按照一定的规则合成为一个序列，称为称为复合序列复合序列（复合码）。（复合码）。n截短序列和复合序列均具有伪随机序列截短序列和复合序列均具有伪随机序列的特点。的特点。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n对于上述的对于上述的4位移位寄存器位移位寄存器n将各级移位寄存器的输出同时送至状态检测器。将各级移位寄存器的输出同时送至状态检测器。若设定当检测状态为若设定当检测状态为0110令置令置1脉冲输出，则脉冲输出

54、，则原来的伪随机码序列由原来的伪随机码序列由15位截短为位截短为10位。位。34()1F xxx GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n4.GPS中的伪码扩频中的伪码扩频nGPS信号的信号的调制波调制波，是，是卫星导航电文卫星导航电文和和伪随伪随机噪声码机噪声码（Pseudo Random Noise Code，简称简称PRN码，或称伪噪声码）的组合码。码，或称伪噪声码）的组合码。n卫星导航电文是一种不归零二进制码组成的卫星导航电文是一种不归零二进制码组成的编码脉冲串，称之为数据码，记作编码脉冲串，称之为数据码，记作D(t)，其，其码率为码率为50 b/s。n对于距离

55、地面对于距离地面20000 km之遥的之遥的GPS卫星，卫星，扩扩频技术频技术能有效地将很低码率的导航电文发送能有效地将很低码率的导航电文发送给用户。给用户。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n扩频方法是用很低码率的数据码作扩频方法是用很低码率的数据码作二级调制二级调制（扩频）。（扩频）。n第一级第一级，用，用50 Hz的的D码调制一个伪噪声码，码调制一个伪噪声码，例如调制例如调制P码的伪噪声码，其码率高达码的伪噪声码，其码率高达10.23 MHz。D码调制码调制P码的结果，便形成了一个码的结果，便形成了一个组合码组合码P(t)D(t)，使得，使得D码信号的频带宽码

56、信号的频带宽度从度从50 Hz扩展到扩展到10.23 MHz，也就是说，也就是说，GPS卫星从原来要发送卫星从原来要发送50 b/s的的D码，转变为码，转变为发送发送10 230 b/s的组合码的组合码P(t)D(t)。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n在在D码调制伪噪声码以后，再用它们的组合码去码调制伪噪声码以后，再用它们的组合码去调制调制L波段的载波，实现波段的载波，实现D码的码的第二级第二级调制，而调制，而形成向广大用户发送的已调波。形成向广大用户发送的已调波。n即即D码的数据首先同伪噪声码码的数据首先同伪噪声码C/A码和码和P(Y)码模码模二相加后，形成组

57、合码二相加后，形成组合码C/A(t)D(t)和和P(t)D(t)，然，然后才调制后才调制L1载波。载波。n在在L1载波上，载波上，C/A(t)D(t)调制和调制和P(t)D(t)调制在相调制在相位上是正交的，位上是正交的，L1载波频率上的两个调制之间载波频率上的两个调制之间有有90的相移。的相移。nL2载波上的调制过程与载波上的调制过程与L1载波大致相同，不同载波大致相同，不同的是的是L2载波可以用载波可以用C/A(t)D(t)码、码、P(t)D(t)码或者码或者P(Y)码来调制。码来调制。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n根据无线电通信中的根据无线电通信中的仙农

58、定理仙农定理，在高斯白，在高斯白噪声干扰条件下，通信容量噪声干扰条件下，通信容量c与带宽与带宽B、信、信号号S和噪声和噪声N之间的关系为之间的关系为 n可见，当可见，当c一定时，扩大带宽，可以降低一定时，扩大带宽，可以降低对对信噪比信噪比的要求。的要求。n利用伪随机码的相关性及可复制性，对扩利用伪随机码的相关性及可复制性，对扩频信号进行相关接收，可以大大改善接收频信号进行相关接收，可以大大改善接收信号的信噪比。信号的信噪比。2log(1/)cBS NGPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n扩频信号扩频信号接收电路接收电路如下图所示。如下图所示。GPS理论与应用理论与应用

59、5.伪随机码测距原理伪随机码测距原理n图中，电路输入端除有用信号图中，电路输入端除有用信号D(t)P(t)外，还有干扰信号外，还有干扰信号N(t)。本地码。本地码P(t)经经过移相器与过移相器与P(t)码对齐，有码对齐，有P(t)P(t)=1。于是于是D(t)P(t)P(t)=D(t)。n然后经过带宽为然后经过带宽为F=50Hz的滤波器可的滤波器可以提取出以提取出D(t)，从而可以，从而可以恢复导航电文恢复导航电文。n这个过程称为这个过程称为解扩解扩。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n而对噪声信号而言，而对噪声信号而言，N(t)与本地码相乘，得到与本地码相乘，得到

60、N(t)P(t)，带宽被到扩展到，带宽被到扩展到f=10.23MHz，于，于是干扰能量分布在是干扰能量分布在 f中。中。n经过带宽为经过带宽为F 的滤波器后，输出的能量仅为输的滤波器后，输出的能量仅为输入端的入端的f/F。n在在GPS系统中，系统中，F=50Hz，f=10.23MHz。经过计算可知，信噪比的改善程度可高达经过计算可知，信噪比的改善程度可高达53dB。n因此，利用因此，利用伪码扩频技术伪码扩频技术可以极大地提高可以极大地提高GPS信号的信号的抗干扰能力抗干扰能力。GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理n5.伪随机码测距原理伪随机码测距原理nThe diag

61、ram at next page graphically illustrates the various codes that are transmitted on the two carrier frequencies.nThe 1575.42 MHz L1 carrier wave(top of the diagram)carries the C/A-code,the P-code,and the NAV-msg.nThe 1227.6 MHz L2 carrier wave(bottom of the diagram)only carries the P-code and the NAV

62、-msg.nTherefore,while the P-code is available on both Ll and L2 frequencies,the C/A-code is only available on the Ll.The NAV-msg is transmitted on both carriers.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nActually,the strength of the GPS signal is very small,equivalent to the tail

63、 light of a car seen from 2,500 kilometers away-halfway across the U.S.!Weaker,in fact,than the ordinary background radio noise thats all around us all of the time.nHow to isolate a coherent signal from a louder background noise can be solved by an interesting little concept discovered in informatio

64、n theory.nBecause the background noise is truly random,you can take random segments of that noise and repeatedly“lay”them on top of each other.Because they are random,they would eventually cancel,or zero themselves out.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nThe pseudo-random

65、code,while seemingly random,is not.So if you do the same thing with the code as you did with the random noise,youll get a very different result.nThe receiver has an internal copy of the satellites PRN(pseudo-random noise)code.The receiver can take its copy of that code and“lay it down”over the incom

66、ing noise(which contains the satellite code signal),and then“slew”its replica slightly back and forth.nWhen the replica code and“hidden”satellite code align,they will reinforce each other resulting in a slightly stronger code signal.The receiver can then lay another copy of the code string and again slew it slightly back and forth until it lines up with the now slightly stronger satellite signal,and so on.GPS理论与应用理论与应用5.伪随机码测距原理伪随机码测距原理nGPS卫星发射的信号采用卫星发射的信号采用直接序列直接序列扩频扩频调制，扩频序列中提供了调制，扩频序列中提供了测距信号