1. Connectivity Lab University of California, Berkeley Location and Timing with C/A code in GPS Wanbin Tang Jan 24, 2007

2. Connectivity Lab University of California, Berkeley Outline GPS Signal Structure  Overview  C/A code  GPS Time GPS receiver  Acquisition  Tracking  Subframe identification  Pseudorange Calculation  Satellite position calculation  User position calculation Conclusion

3. Connectivity Lab University of California, Berkeley Overview of Satellite Transmissions All transmissions derive from a fundamental frequency of 10.23 MHz L1 = 154 * 10.23 = 1575.42 MHz L2 = 120 * 10.23 = 1227.60 MHz All codes initialized once per GPS week at midnight from Saturday to Sunday Chipping rate for C/A is 1.023 MHz Chipping rate for P(Y) is 10.23 MHz

4. Connectivity Lab University of California, Berkeley GPS Signal Characteristics

5. Connectivity Lab University of California, Berkeley Codes on L1 and L2

6. Connectivity Lab University of California, Berkeley Coarse/Acquisition Codes

7. Connectivity Lab University of California, Berkeley PRN Cross-correlation Correlation of receiver generated PRN code (A) with incoming data stream consisting of multiple (e.g. four, A, B, C, and D) codes

8. Connectivity Lab University of California, Berkeley GPS Data Format

9. Connectivity Lab University of California, Berkeley GPS Time GPS time is referenced to a universal coordinated time (UTC). The GPS zero time is defined as midnight on the night of January 5/ morning of January 6, 1980. The largest unit used in stating GPS time is one week, defined as 604,800 seconds (7 × 24 × 3600).

10. Connectivity Lab University of California, Berkeley GPS Time The GPS timing information transmitted in the air interface includes :  17-bit truncated version of the TOW count covers a whole week and the time unit is 6 sec (1.5 sec * 4), which equals one subframe time.  the 10 most-significant bits (MSBs) as the week number

11. Connectivity Lab University of California, Berkeley GPS Time

12. Connectivity Lab University of California, Berkeley Outline GPS Signal Structure  Overview  C/A code  GPS Time GPS receiver  Acquisition  Tracking  Subframe identification  Pseudorange Calculation  Satellite position calculation  User position calculation Conclusion

13. Connectivity Lab University of California, Berkeley A fundamental GPS receiver

14. Connectivity Lab University of California, Berkeley Acquisition Requirement:  Search over a frequency range of ±10 KHz to cover all of the expected Doppler frequency range for high-speed aircraft.  The resolutions of the two important outputs of acquisition, the beginning of the C/ A code period and the carrier frequency, should reach the requirement of the tracking circuits. Methods:  Conventional correlation  Fast Fourier transform (FFT)  Delay and multiplication

15. Connectivity Lab University of California, Berkeley Acquisition

16. Connectivity Lab University of California, Berkeley FFT (5MSamples/s,1ms Received data) 1.Perform the FFT on the 1 ms of input data x(n) and convert the input into frequency domain as X(k) where n=k=0 to 4999 for 1 ms of data. 2.Take the complex conjugate X(k) and the outputs become X(k)*. 3.Generate 21 local codes lsi(n) where i=1, 2,... 21, using equation given in blow. The local code consists of the multiplication of the C/A code satellite s and a complex RF signal and it must be also sampled at 5 MHz. The frequency f i of the local codes are separated by 1 KHz. lsi = Cs exp( j2pif it) 4.Perform FFT on lsi(n) to transform them to the frequency domain as Lsi(k). 5.Multiply X(k)* and Lsi(k) point by point and call the result Rsi(k). 6.Take the inverse FFT of Rsi(k) to transform the result into time domain as rsi(n) and find the absolute value of the |rsi(n)|. There are a total of 105,000 (21  5,000) of |rsi(n)|. 7.The maximum of |rsi(n)| in the nth location and ith frequency bin gives the beginning point of C/A code in 200 ns resolution in the input data and the carrier frequency in 1 KHz resolution.

17. Connectivity Lab University of California, Berkeley Fine frequency estimation Strip the C/A code from the 1ms input signal; At time m, the highest frequency component in 1ms of data is X m (k),then the initial phase: At time n, a short time after m, the phase is: Fine frequency is:

18. Connectivity Lab University of California, Berkeley Tracking

19. Connectivity Lab University of California, Berkeley How to get fine timing resolution Correlation output within 1chips in ideal conditions

20. Connectivity Lab University of California, Berkeley Curve Fitting Correlation output within limited bandwidth

21. Connectivity Lab University of California, Berkeley Basic Simulation Results 1 satellite ; Raise cosine filter; AWGN channel; 1ms received data processing; Oversample rate = 5; Delay between the early and ontime tracking branch = one sample Quadratic curving fitting

22. Connectivity Lab University of California, Berkeley Subframe identification Convert tracking output to nevigation data; Using the preamble of pattern(10001011) in the first word and parity code (00) to identify subframe.

23. Connectivity Lab University of California, Berkeley Psedurange calculation In collecting the digitized data there is no absolute time reference and the only time reference is the sampling frequency. As a result, the pseudorange can be measured only in a relative way. prange = (const + diff of dat + finetime) * c where c=299792458 m/s is speed of light; const is an arbitrarily chosen constant to make all the pseudoranges positive; and the fine time is obtained from the tracking program. the relative transit time (diff of dat) is calculated according to:  the beginning points of the C/A code  the beginning of the first navigation data  the beginning of subframe 1

24. Connectivity Lab University of California, Berkeley Calculate the satellite position Calculate the coarse time of the transmission of satellite: t c = TOW − relative transit time Using the navigation data and t c, the user can determine the satellite position in earth-center earth-fixed coordinate system.

25. Connectivity Lab University of California, Berkeley Calculate the satellite position

26. Connectivity Lab University of California, Berkeley Calculate the satellite position Calculate the mean motion: Calculate the mean anomaly: M=M0 + n(tc −t oe ) Calculate the eccentric anomaly: E = M + e s sin E Calculate the overall time correction: Calculate the true anomaly: Calculate the angle

27. Connectivity Lab University of California, Berkeley Calculate the satellite position Calculate the following correction terms: Calculate the angle between the accenting node and the Greenwich meridian : Find the position of the satellite and adjust the pseudorange:

28. Connectivity Lab University of California, Berkeley Calculate user position a minimum of four satellites is required to solve for the user position: where b u is the user clock bias error expressed in distance.

29. Connectivity Lab University of California, Berkeley Iterative method to update the transmit time The time used to calculate the position of a satellite and the time used to calculate user position are different. The time used to calculate the satellite position should be adjusted to be the same time for calculating user position. Update the satellites position with t t and get a updated user position. iterative calculae until the changes in x, y, z (or x u, y u, z u ) are below a predetermined value. In the end, the absolute position and timing of user is determined.

30. Connectivity Lab University of California, Berkeley Outline GPS Signal Structure  Overview  C/A code  GPS Time GPS receiver  Acquisition  Tracking  Subframe identification  Pseudorange Calculation  Satellite position calculation  User position calculation Conclusion

31. Connectivity Lab University of California, Berkeley Conclusion The complexity of GPS receiver is mostly determined by baseband digital signal processing:  acquisition  tracking  multi satellite signal receiving The absolute time can be determined after the accurate position of user is get. The timing resolution and position resolution are highly correlated. Roughly to say, if position resolution is less than 30m, the timing resolution is less than 100ns.

32. Connectivity Lab University of California, Berkeley Thanks !