GPS理論及應(yīng)用05

1、GPS理論與應(yīng)用（5.偽隨機(jī)碼測距原理）劉瑞華 教授中國民航大學(xué) 電子信息工程學(xué)院GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理授課內(nèi)容授課內(nèi)容1.GPS衛(wèi)星的測距碼信號衛(wèi)星的測距碼信號 2.GPS測距原理測距原理3.偽隨機(jī)碼基礎(chǔ)偽隨機(jī)碼基礎(chǔ)4.GPS中的偽碼擴(kuò)頻中的偽碼擴(kuò)頻5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n1.GPS衛(wèi)星的測距碼信號衛(wèi)星的測距碼信號nGPS衛(wèi)星發(fā)送的信號采用衛(wèi)星發(fā)送的信號采用L波段波段的兩種的兩種載頻作載波，分別被稱作載頻作載波，分別被稱作L1的主頻率和的主頻率和L2的次頻率。的次頻率。n這些載

2、波頻率由這些載波頻率由擴(kuò)頻碼擴(kuò)頻碼（每一顆衛(wèi)星均（每一顆衛(wèi)星均有專門的偽隨機(jī)序列）和有專門的偽隨機(jī)序列）和導(dǎo)航電文導(dǎo)航電文所調(diào)所調(diào)制。所有衛(wèi)星均在這兩個相同的載波頻制。所有衛(wèi)星均在這兩個相同的載波頻率上發(fā)射，但由于偽隨機(jī)碼調(diào)制不同，率上發(fā)射，但由于偽隨機(jī)碼調(diào)制不同，因此無明顯的相互干擾。因此無明顯的相互干擾。GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nEach satellite transmits its ranging signal on two different radio frequencies: 15

3、75.42 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) cod

4、es that are 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nThis modulation of the sign

5、al, which is really 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 k

6、now. Thus the term pseudo-random 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n選擇選擇L波段的波段的優(yōu)點優(yōu)點是：是： n(1) 減少擁擠，避免減少擁擠，

7、避免“撞車撞車”。目前。目前L波段的頻率占波段的頻率占用率低于其他波段，與其他工作頻率不易發(fā)生用率低于其他波段，與其他工作頻率不易發(fā)生“撞撞車車”現(xiàn)象，有利于全球性的導(dǎo)航定位測量?，F(xiàn)象，有利于全球性的導(dǎo)航定位測量。n(2) 適應(yīng)擴(kuò)頻，傳送寬帶信號。適應(yīng)擴(kuò)頻，傳送寬帶信號。GPS衛(wèi)星采用擴(kuò)頻技衛(wèi)星采用擴(kuò)頻技術(shù)發(fā)送衛(wèi)星導(dǎo)航電文，其頻帶高達(dá)術(shù)發(fā)送衛(wèi)星導(dǎo)航電文，其頻帶高達(dá)20 MHz左右，在左右，在占用率較低的占用率較低的L波段上，波段上， 易于傳送擴(kuò)頻后的寬帶信號。易于傳送擴(kuò)頻后的寬帶信號。n(3)大氣衰減小，有利于研制用戶設(shè)備。大氣衰減小，有利于研制用戶設(shè)備。GPS衛(wèi)星采衛(wèi)星采用用L波段，避開了大

8、氣的諧振吸收，衰減較小，且電波段，避開了大氣的諧振吸收，衰減較小，且電離層延遲的影響小，有利于用較經(jīng)濟(jì)的接收設(shè)備測離層延遲的影響小，有利于用較經(jīng)濟(jì)的接收設(shè)備測量量GPS信號。而采用兩個載頻，目的在于測量出或信號。而采用兩個載頻，目的在于測量出或消除掉由于電離層效應(yīng)而引起的延遲誤差。消除掉由于電離層效應(yīng)而引起的延遲誤差。 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nWhen a radio transmits a signal, it is in the form of a simple sine wave that has a particular frequency (t

9、he number of “humps” on the sine wave that 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

10、 of kilometers down to tiny fractions of micrometer. 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽

11、隨機(jī)碼測距原理GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nBy itself, the carrier 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 repres

12、ents a string of zeros (offs) and ones (ons) that we want to send on the carrier wave, much like Morse-code. nThere are several methods of transmitting that information on a carrier wave.GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nThe first is by varying (modulating) the amplitude, or how “high” and “l(fā)ow” the s

13、ine “humps” go. If youve ever listened to AM radio, youve heard Amplitude Modulation.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 M

14、odulation, radio works.nFinally, you could modulate the phase of the carrier. The phase is the 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 illustrat

15、ed in the bottom line of the diagram.GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nTwo Morse-code-like signal strings 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頻段的頻段的兩種載頻兩種載頻為（其中為（其中

16、f0是衛(wèi)星是衛(wèi)星信號發(fā)生器的基準(zhǔn)頻率）：信號發(fā)生器的基準(zhǔn)頻率）： L1載波：載波：fL1=154f0=1575.42 MHz，波長，波長1=19.032 cm； L2載波：載波：fL2=120f0 =1227.6MHz，波長，波長2=24.42 cm。 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nThe C/A-code is a sequence of 1,023 bi-phase modulations of the carrier wave. nEach opportunity for a phase-re

17、versal modulation, or switch from a zero to a one, is called a “Chip (whether or not the phase is actually reversed 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

18、one-millionth of a second. nEach satellite carries its own unique code string. The C/A-code is the code used for the Standard Positioning Service(PPS).GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理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

19、millions. nAs a result, the complete sequence for the P-code takes 267 days to complete, rather than the one one-thousandth of a 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 Positi

20、oning Service(PPS). GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nThe chip rate of the P-code is an order of magnitude higher than for the C/A-code, 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 i

21、ndividual opportunities for a phase reversal each and every second. nSince distance is a direct function of time, the radio wave clearly cant 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

22、 in understanding how GPS determines distance and why one service is so much more accurate than the other. GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n2.GPS測距原理測距原理nThe code is the key to understanding how GPS determines distance between the satellite and receiver, both for the Standard Positioning Service as w

23、ell as the Precise Positioning Service. nBoth use their respective codes essentially the same way: they simply derive different levels of precision by using different chip strings. Conceptually, both work identically.nThe basic concept is illustrated in the diagram. Each receiver has in its own memo

24、ry each of the satellites unique codes. The receiver uses this information to internally generate an exact replica of the satellites code at the same instant that the satellite generates its “real” code.GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nBecause it took some finite amount

25、 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 that is used to determine the distance between the satellite and receiver. nThis method of range measurement by comparing the delay between two

26、 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 talk about shortly) are called “Pseudo-Ranges.”GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nYou might ask “Why the ultra-complex chip string? Why not a simpl

27、e, 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 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

28、 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nObviously, you would hear yourself yell “HEY!” nA moment later you would hear your colleagues “HEY!” nYou could then m

29、easure 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 distance from your colleague would be straightforward.GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nBut there could be a problem here.

30、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 wouldnt hear his “HEY!” until between your second and third one. You could quickly loose track and might even

31、 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nNow imagine instead that at the same moment you both started yelling a count: “ONE!, TWO!, THREE!

32、.” 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 and know right away where you were in the count-string. nConceptually, thats how GPS measu

33、res 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nIn the “real” world of GPS, its easy to find out where you are in the C/A-code string since the whole string “passes by” i

34、n 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 where they need to look in the P-code string, or to “ramp up” to P-code

35、“l(fā)ock-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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nIt turns out that just knowing how far away you are from the requisite four satellites isnt enough. nThe ranges to t

36、he 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nIn the first place, the military is very

37、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. nVariations in orbits that are due to gravitational forces ar

38、e fairly easy to predict and compensate for.GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nTo compensate for the inevitable unpredictable perturbations in the satellites orbits, they are constantly monitored from the ground. nCorrections for any orbital variations that are identified are quickly uploaded from grou

39、nd 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 changing, thus the term, based on the word “epheme

40、ral,” meaning lasting only a short time.)GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理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 weve already talked about.nIn addition to

41、 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理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n3.偽隨機(jī)碼基礎(chǔ)偽隨機(jī)碼基礎(chǔ)

42、n從本質(zhì)上講，從本質(zhì)上講，GPS屬于屬于無線電無線電導(dǎo)航定位導(dǎo)航定位系統(tǒng)。系統(tǒng)。n用戶只需要通過接收設(shè)備接收衛(wèi)星播發(fā)用戶只需要通過接收設(shè)備接收衛(wèi)星播發(fā)的信號，就能測定衛(wèi)星信號的傳播的信號，就能測定衛(wèi)星信號的傳播時間時間延遲延遲或或相位延遲相位延遲，解算出接收機(jī)到衛(wèi)星，解算出接收機(jī)到衛(wèi)星間的距離（間的距離（偽距偽距），從而確定），從而確定接收機(jī)位接收機(jī)位置及時鐘誤差置及時鐘誤差。GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n為了滿足用戶為了滿足用戶定位精度定位精度和和實時導(dǎo)航實時導(dǎo)航定位要求定位要求及軍事及軍事保密保密的要求，的要求，GPS衛(wèi)星信號采用了組衛(wèi)星信號采用了組合碼調(diào)

43、制技術(shù)，即將衛(wèi)星的導(dǎo)航電文（稱為合碼調(diào)制技術(shù)，即將衛(wèi)星的導(dǎo)航電文（稱為基帶信號）經(jīng)基帶信號）經(jīng)偽隨機(jī)碼偽隨機(jī)碼擴(kuò)頻為組合碼，再對擴(kuò)頻為組合碼，再對L頻段進(jìn)行頻段進(jìn)行BPSK調(diào)制。調(diào)制。n采用這種格式，不僅提高了系統(tǒng)導(dǎo)航的精度，采用這種格式，不僅提高了系統(tǒng)導(dǎo)航的精度，而且使系統(tǒng)具有很高的而且使系統(tǒng)具有很高的抗電子干擾抗電子干擾能力。為能力。為了達(dá)到這種目的，了達(dá)到這種目的，GPS中采用了偽隨機(jī)碼擴(kuò)中采用了偽隨機(jī)碼擴(kuò)頻技術(shù)。頻技術(shù)。GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n1).二進(jìn)制隨機(jī)序列的二進(jìn)制隨機(jī)序列的特點特點：nA.序列是非周期的，不能預(yù)先確定，不序列是非周期的，不

44、能預(yù)先確定，不能復(fù)制；能復(fù)制；nB.序列中序列中1和和0出現(xiàn)的概率均為出現(xiàn)的概率均為1/2；n二進(jìn)制隨機(jī)序列二進(jìn)制隨機(jī)序列U(t)與其移位序列與其移位序列U(t-)模模2相加得到一個新的二進(jìn)制隨機(jī)序列。相加得到一個新的二進(jìn)制隨機(jī)序列。 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理 二進(jìn)制隨機(jī)序列的二進(jìn)制隨機(jī)序列的自相關(guān)函數(shù)自相關(guān)函數(shù)定義為定義為: :或簡單寫為或簡單寫為 01( )( ) ()TRU t U tdtT01( )01R的個數(shù)的個數(shù)和的總個數(shù)GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理 由圖可見，二進(jìn)制隨由圖可見，二進(jìn)制隨機(jī)序列的機(jī)序列的自相關(guān)特

45、點自相關(guān)特點為為1). 1). =0=0時，時，R()=1;R()=1;2). |t2). |t0 0，時時R()=1;R()=1;3). |t3). |t0 0時時，R()R()與與 成線性變化成線性變化; ;GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n由于二進(jìn)制隨機(jī)序列是由于二進(jìn)制隨機(jī)序列是非周期非周期的，不能的，不能預(yù)先確定，也不能復(fù)制，其應(yīng)用受到限預(yù)先確定，也不能復(fù)制，其應(yīng)用受到限制。制。n在無線電通信中，利用在無線電通信中，利用多級反饋移位寄多級反饋移位寄存器存器產(chǎn)生具有周期性的、可以預(yù)見的、產(chǎn)生具有周期性的、可以預(yù)見的、又具有良好相關(guān)性的二進(jìn)制序列，稱為又具有良

46、好相關(guān)性的二進(jìn)制序列，稱為偽隨機(jī)序列偽隨機(jī)序列。 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n下圖為一個四級反饋移位寄存器下圖為一個四級反饋移位寄存器原理圖原理圖。其。其中包括四級移位寄存器、模中包括四級移位寄存器、模2加法器、時鐘發(fā)加法器、時鐘發(fā)生器的反饋線路。而第生器的反饋線路。而第3、4兩級經(jīng)模兩級經(jīng)模2相加后相加后反饋到第反饋到第1級的輸入端。級的輸入端。 2413脈沖發(fā)生器置1脈沖GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n移位寄存器開始工作時，在置移位寄存器開始工作時，在置1脈沖的作用下，各級脈沖的作用下，各級寄存器輸出全為寄存器輸出全為1。

47、n在下一個脈沖作用下，各存貯單元將其內(nèi)容移到下在下一個脈沖作用下，各存貯單元將其內(nèi)容移到下一個單元，而一個單元，而3、4級的模級的模2和送入第和送入第1個單元，第個單元，第4級級同時作為輸出。同時作為輸出。n經(jīng)過經(jīng)過24-1=15個脈沖后，又回到個脈沖后，又回到2全全1狀態(tài)，構(gòu)成一個狀態(tài)，構(gòu)成一個周期周期。 2413脈沖發(fā)生器置1脈沖GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n經(jīng)過簡單推算可知，上述經(jīng)過簡單推算可知，上述4級移位寄存器產(chǎn)生級移位寄存器產(chǎn)生的的狀態(tài)表狀態(tài)表如下所示如下所示 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n由移位寄存器產(chǎn)生的二進(jìn)制

48、序列稱為由移位寄存器產(chǎn)生的二進(jìn)制序列稱為m序列序列。n比較上表中各級移位寄存器的輸出比較上表中各級移位寄存器的輸出m序列可序列可見，這些序列的見，這些序列的結(jié)構(gòu)相同結(jié)構(gòu)相同，只是相互間移了，只是相互間移了一個碼位。這些序列稱為一個碼位。這些序列稱為平移序列平移序列。n對于對于r級移位寄存器，采用不同的反饋聯(lián)接方級移位寄存器，采用不同的反饋聯(lián)接方式，將產(chǎn)生不同的式，將產(chǎn)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為為 T=Nt0=(2r-1)t0GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nm序列可用電路的序列可用電路的特征多項式特征多

49、項式表示為表示為n其中，其中，1表示模表示模2加法器反饋到第加法器反饋到第1級的輸級的輸入端。入端。Ci=0表示第表示第i級輸出不作為模級輸出不作為模2加加法器的輸入，法器的輸入，ci=1表示第表示第i級輸出作為模級輸出作為模2加法器的輸入。加法器的輸入。n比如，對上述的比如，對上述的4位移位寄存器，其特征位移位寄存器，其特征多項式可表示為多項式可表示為1( )1riiiF xc x 34( )1F xxx GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n兩個平移兩個平移m序列模序列模2和所得到的和所得到的m序列結(jié)果不變，序列結(jié)果不變，只是碼位進(jìn)行了只是碼位進(jìn)行了平移平移?？捎?/p>

50、下式表示?？捎孟率奖硎緉例如，對上述的例如，對上述的4位移位寄存器的輸出端，有位移位寄存器的輸出端，有P(0)=111100010011010P(3)=100010011010111P(0) P(3)=011110001001101=P(14) 00( )()()P tP tKtP tLtGPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n2).偽隨機(jī)碼的特點偽隨機(jī)碼的特點n根據(jù)上述基本理論，可以總結(jié)出偽隨機(jī)根據(jù)上述基本理論，可以總結(jié)出偽隨機(jī)碼的特點如下列碼的特點如下列5點所示：點所示：nA.r級移位寄存器產(chǎn)生的級移位寄存器產(chǎn)生的m序列偽隨機(jī)序列偽隨機(jī)碼，碼位寬度等于脈沖周期碼，碼

51、位寬度等于脈沖周期t0，m序列序列的的周期周期為為T=(2r-1)t0 ；nB.偽隨機(jī)碼在一個周期內(nèi)，偽隨機(jī)碼在一個周期內(nèi)，0個數(shù)比個數(shù)比1少少一次一次；GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nC.偽隨機(jī)碼的偽隨機(jī)碼的自相關(guān)自相關(guān)函數(shù)為函數(shù)為 01(0,1,2,.,21)( )1/,(0,)rnNt nNRNnt nnN ，不為 的整數(shù)倍與 成線性關(guān)系， 為其他值時GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n自相關(guān)舉例自相關(guān)舉例：n對于對于4位移位寄存器位移位寄存器 其輸出端為其輸出端為P(0)=111100010011010將輸出端向左移動將輸出端

52、向左移動4位，可以得到位，可以得到P(4)=000100110101111。該偽隨機(jī)的自相關(guān)為該偽隨機(jī)的自相關(guān)為R(4)=-1/1534( )1F xxx GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n4).互相關(guān)函數(shù)：互相關(guān)函數(shù)：n2個不同的個不同的m序列之間的相關(guān)函數(shù)稱為序列之間的相關(guān)函數(shù)稱為互相關(guān)互相關(guān)函數(shù)，與自相關(guān)函數(shù)計算公式相函數(shù)，與自相關(guān)函數(shù)計算公式相同。同。n不同結(jié)構(gòu)的不同結(jié)構(gòu)的m序列的互相關(guān)函數(shù)具有多序列的互相關(guān)函數(shù)具有多種數(shù)值，隨著級數(shù)的增加，互相關(guān)值種數(shù)值，隨著級數(shù)的增加，互相關(guān)值迅迅速減小速減小。GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距

53、原理n互相關(guān)舉例互相關(guān)舉例：n對于對于4位移位寄存器，位移位寄存器，P1(0)=111100010011010P2(0)=111100101110010P2(4)=001011100101111P2(5)=010111001011110其互相關(guān)分別為其互相關(guān)分別為5/15，-7/15，1/15n可見，可見，m序列之間的互相關(guān)是不同的。序列之間的互相關(guān)是不同的。 341( )1F xxx 232( )1F xxx GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理nE.截短和復(fù)合：截短和復(fù)合：n對于周期性對于周期性m序列，可以截取其中一部序列，可以截取其中一部分組成一個新的周期序列，

54、稱為分組成一個新的周期序列，稱為截短序截短序列列（截短碼）；也可以將多個周期較短（截短碼）；也可以將多個周期較短的序列按照一定的規(guī)則合成為一個序列，的序列按照一定的規(guī)則合成為一個序列，稱為稱為復(fù)合序列復(fù)合序列（復(fù)合碼）。（復(fù)合碼）。n截短序列和復(fù)合序列均具有偽隨機(jī)序列截短序列和復(fù)合序列均具有偽隨機(jī)序列的特點。的特點。 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n對于上述的對于上述的4位移位寄存器位移位寄存器n將各級移位寄存器的輸出同時送至狀態(tài)檢測器。將各級移位寄存器的輸出同時送至狀態(tài)檢測器。若設(shè)定當(dāng)檢測狀態(tài)為若設(shè)定當(dāng)檢測狀態(tài)為0110令置令置1脈沖輸出，則脈沖輸出，則原來的

55、偽隨機(jī)碼序列由原來的偽隨機(jī)碼序列由15位截短為位截短為10位。位。 34( )1F xxx GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n4.GPS中的偽碼擴(kuò)頻中的偽碼擴(kuò)頻nGPS信號的信號的調(diào)制波調(diào)制波，是，是衛(wèi)星導(dǎo)航電文衛(wèi)星導(dǎo)航電文和和偽隨偽隨機(jī)噪聲碼機(jī)噪聲碼（Pseudo Random Noise Code，簡稱簡稱PRN碼，或稱偽噪聲碼）的組合碼。碼，或稱偽噪聲碼）的組合碼。n衛(wèi)星導(dǎo)航電文是一種不歸零二進(jìn)制碼組成的衛(wèi)星導(dǎo)航電文是一種不歸零二進(jìn)制碼組成的編碼脈沖串，稱之為數(shù)據(jù)碼，記作編碼脈沖串，稱之為數(shù)據(jù)碼，記作D(t)，其，其碼率為碼率為50 b/s。n對于距離地面對

56、于距離地面20000 km之遙的之遙的GPS衛(wèi)星，衛(wèi)星，擴(kuò)擴(kuò)頻技術(shù)頻技術(shù)能有效地將很低碼率的導(dǎo)航電文發(fā)送能有效地將很低碼率的導(dǎo)航電文發(fā)送給用戶。給用戶。GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n擴(kuò)頻方法是用很低碼率的數(shù)據(jù)碼作擴(kuò)頻方法是用很低碼率的數(shù)據(jù)碼作二級調(diào)制二級調(diào)制（擴(kuò)頻）。（擴(kuò)頻）。 n第一級第一級，用，用50 Hz的的D碼調(diào)制一個偽噪聲碼，碼調(diào)制一個偽噪聲碼， 例如調(diào)制例如調(diào)制P碼的偽噪聲碼，其碼率高達(dá)碼的偽噪聲碼，其碼率高達(dá)10.23 MHz。 D碼調(diào)制碼調(diào)制P碼的結(jié)果，便形成了一個碼的結(jié)果，便形成了一個組合碼組合碼P(t)D(t)，使得，使得D碼信號的頻帶寬碼

57、信號的頻帶寬度從度從50 Hz擴(kuò)展到擴(kuò)展到10.23 MHz，也就是說，也就是說， GPS衛(wèi)星從原來要發(fā)送衛(wèi)星從原來要發(fā)送50 b/s的的D碼，轉(zhuǎn)變?yōu)榇a，轉(zhuǎn)變?yōu)榘l(fā)送發(fā)送10 230 b/s的組合碼的組合碼P(t)D(t)。 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n在在D碼調(diào)制偽噪聲碼以后，再用它們的組合碼去碼調(diào)制偽噪聲碼以后，再用它們的組合碼去調(diào)制調(diào)制L波段的載波，實現(xiàn)波段的載波，實現(xiàn)D碼的碼的第二級第二級調(diào)制，而調(diào)制，而形成向廣大用戶發(fā)送的已調(diào)波。形成向廣大用戶發(fā)送的已調(diào)波。n即即D碼的數(shù)據(jù)首先同偽噪聲碼碼的數(shù)據(jù)首先同偽噪聲碼C/A碼和碼和P(Y)碼模碼模二相加后，形

58、成組合碼二相加后，形成組合碼C/A(t)D(t)和和P(t)D(t)，然，然后才調(diào)制后才調(diào)制L1載波。載波。n在在L1載波上，載波上，C/A(t)D(t)調(diào)制和調(diào)制和P(t)D(t)調(diào)制在相調(diào)制在相位上是正交的，位上是正交的，L1載波頻率上的兩個調(diào)制之間載波頻率上的兩個調(diào)制之間有有90的相移。的相移。nL2載波上的調(diào)制過程與載波上的調(diào)制過程與L1載波大致相同，不同載波大致相同，不同的是的是L2載波可以用載波可以用C/A(t)D(t)碼、碼、P(t)D(t)碼或者碼或者P(Y)碼來調(diào)制。碼來調(diào)制。GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n根據(jù)無線電通信中的根據(jù)無線電通信中的

59、仙農(nóng)定理仙農(nóng)定理，在高斯白，在高斯白噪聲干擾條件下，通信容量噪聲干擾條件下，通信容量c與帶寬與帶寬B、信、信號號S和噪聲和噪聲N之間的關(guān)系為之間的關(guān)系為 n可見，當(dāng)可見，當(dāng)c一定時，擴(kuò)大帶寬，可以降低一定時，擴(kuò)大帶寬，可以降低對對信噪比信噪比的要求。的要求。n利用偽隨機(jī)碼的相關(guān)性及可復(fù)制性，對擴(kuò)利用偽隨機(jī)碼的相關(guān)性及可復(fù)制性，對擴(kuò)頻信號進(jìn)行相關(guān)接收，可以大大改善接收頻信號進(jìn)行相關(guān)接收，可以大大改善接收信號的信噪比。信號的信噪比。 2log (1/)cBS NGPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n擴(kuò)頻信號擴(kuò)頻信號接收電路接收電路如下圖所示。如下圖所示。 GPS理論與應(yīng)用

60、理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n圖中，電路輸入端除有用信號圖中，電路輸入端除有用信號D(t)P(t)外，還有干擾信號外，還有干擾信號N(t)。本地碼。本地碼P(t)經(jīng)經(jīng)過移相器與過移相器與P(t)碼對齊，有碼對齊，有P(t)P(t)=1。于是于是D(t)P(t)P(t)=D(t)。n然后經(jīng)過帶寬為然后經(jīng)過帶寬為F=50Hz的濾波器可的濾波器可以提取出以提取出D(t)，從而可以，從而可以恢復(fù)導(dǎo)航電文恢復(fù)導(dǎo)航電文。n這個過程稱為這個過程稱為解擴(kuò)解擴(kuò)。 GPS理論與應(yīng)用理論與應(yīng)用5.偽隨機(jī)碼測距原理偽隨機(jī)碼測距原理n而對噪聲信號而言，而對噪聲信號而言，N(t)與本地碼相乘，得到與本地