Signal Structure - Introduction to Global Navigation Satellite Systems | ASEN 5090, Study notes of Aerospace Engineering

Download Signal Structure - Introduction to Global Navigation Satellite Systems | ASEN 5090 and more Study notes Aerospace Engineering in PDF only on Docsity! Signal Structure Colorado University of Colorado at Boulder ASEN 5090 LECTURE NOTES - LARSON, AXELRAD ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 2  The position solution involves an equation with four unknowns:  Receiver position (x, y, z) (in what reference frame)  Receiver clock correction (correction to what?)  Position accuracy of ~1 m implies knowledge of the receiver clock to within ~3 ns  GPS accuracy is based almost entirely on knowing satellite orbits and satellite clocks.  Requires simultaneous measurements from at least four satellites  The receiver makes a range measurement to the satellite by measuring the signal propagation delay  A data message modulated on the ranging signal provides the precise location of the satellite and corrections for the satellite clock. GPS accuracy is based almost entirely on knowing these two things. Position Solution ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 5 SIGNAL COMPONENTS  Base frequency is f0 = 10.23 MHz = 10,230,000 Hz (cycles/sec)  L1 = 154 f0 = 1575.42 MHz  L2 = 120 f0 = 1227.6 MHz  L5 = 115 f0 = 1176.45 MHz (future)  C/A code chip rate = f0 /10 = 1.023 Mcps (MHz), 1 ms long  P code chip rate = f0 = 10.23 Mcps (MHz), 37 weeks long, each satellite gets a 1 week segment  Navigation Data rate = 50 bps, 20ms per bit, 6 s per frame, 30 s for individual satellite data, 12.5 min for all ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 6 PROPERTIES OF CODES  Protect against interference  Reduce noise effects  Permit many signals to be transmitted at the same frequency without interfering (known as : code division multiple access - CDMA)  Permit high resolution ranging  Enable communications security (known as : low probability of detection - LPD)  Key characteristics of codes are their type, length, chip rate. ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 7 PRN CODES (pseudo random noise codes)  In GPS, a pseudo random noise code used to modulate a carrier tone  Types of modulation: amplitude (AM), frequency (FM), phase (PM) Leick, GPS principles ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 10 CORRELATION FUNCTION - EXAMPLES 100111101110100010011011111111101 000010001010011100001110010010001 Every time the numbers agree, add 1. Every time the numbers disagree, subtract 1. ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 11 This example: codes for 2 different satellites 100111101110100010011011111111111 000010001010011100001110010010001 14 agree 11 disagree Total score: 3 Perfect agreement would be 35 ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 12 01100010101011001000100100000110000011110000 11000101010110010001001000001100000111100001 01100010101011001000100100000110000011110000 11000101010110010001001000001100000111100001 Agreement is perfect But if you recognize they are shifted by 1: This example: same satellite codes, but shifted Not so good - score of -3. ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 15 Satellite 10 compared to Satellite 10 code that has been shifted by 200. ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 16 I will not ask you to code up the GPS PRN sequences. Instead I will provide you with Matlab code I found on the web that does it for you. function g=cacode(sv,fs) % function G=CACODE(SV,FS) % Generates 1023 length C/A Codes for GPS PRNs 1-37 % g: nx1023 matrix- with each PRN in each row with symbols 1 and 0 % sv: a row or column vector of the SV's to be generated % valid entries are 1 to 37 % fs: optional number of samples per chip (defaults to 1), % fractional samples allowed, must be 1 or greater. % For multiple samples per chip, function is a zero order hold. ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 17 GENERATING PRN CODES  Tapped feedback shift register  Epoch state B A Y XOR Logic Table 11 10 01 00 YBA 1 0 0 11. . . 1 2 3 nn - 1 stage + output bitinput bit An n stage shift register PRN generator tapped at [3,n]. ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 20 -111 CodeRegister3Register2Register1 Start with all 1’s in your shift registers Add Register 1 and Register 3 The answer 0 goes into Register 1 and everything shifts to the right. Here is an example with 3 shift registers For this example, 1+1 =10 ==> 0 ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 21 Resulting in -111 CodeRegister3Register2Register1 0 11 1 ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 22 Next 0+1=1 1110 -111 CodeRegister3Register2Register1 1 0 1 1 ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 25 IMPACT OF CORRELATION PROPERTIES  What makes a useful code?  For ranging:  For CDMA:  For acquisition: ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 26 NAVIGATION MESSAGE Misra & Enge Fig. 4.13 ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 27 PRN CODE SPECTRUM  PRN codes have a sinc2 spectrum  Main lobe is 2x chipping rate  Side lobes are 1x chipping rate  Power density is very low ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 30 SIGNAL POWER  GPS Satellites transmit 27W toward the earth  GPS Signal level on the ground:  L1 C/A: -158.5 dBW ~10-16 Watts  L1 P(Y): -161.5 dBW  L2 P(Y): -164.5 dBW  Spread spectrum signal is “sub-thermal” or below the noise floor  After correlation in the receiver the recovered or despread carrier is above the noise (typical SNR’s 6-15 dB).  Processing gain for spread spectrum is signal BW/ data BW ASEN 5090 LECTURE NOTES – LARSON, AXELRAD 31 GPS SIGNAL GENERATION C/A CODE 1.023 Mcps NAVIGATION DATA 50 bps P(Y) CODE 10.23 Mcps L2 CARRIER 1227.6 MHz L1 CARRIER 1575.42 MHz 90 deg shift Σ Σ