DSP Applied to GPS Algorithms

1. DSP Applied to GPS Algorithms DSP Applied to GPS Algorithms

2. References • Understanding GPS Principles and Applications, 1996, Elliott D. Kaplan • Digital Signal Processing – A Practical Approach, 1993, Emmanuel C. Ifeachor, Barrie W. Jervis • ADSP-TS101 TigerSHARC Processor Programming Reference, Rev 1, January 2003, Analog Devices DSP Applied to GPS Algorithms

3. Introduction • GPS traditionally done with ASIC/Processor combination • Looking at FPGA/DSP combination for low end GPS receivers • Technological interest in software radio • Cheaper, quicker development cycle. • Customizations for special applications DSP Applied to GPS Algorithms

4. What is GPS? Global Positioning System 24 satellite (SV) constellation Orbiting 20,000 km from the surface of the Earth in 12 hour cycles Orbits are set-up to give global coverage 24 hours a day Need at least 4 satellites in view to calculate a position (1) DSP Applied to GPS Algorithms

5. GPS Positioning Concepts • For now make 2 assumptions: • We know the distance to each satellite • We know where each satellite is • Require 3 satellites for a 3-D position in this “ideal” scenario (1) DSP Applied to GPS Algorithms

6. GPS Signal Structure • Each satellite transmits 2 carrier frequencies referred to as L1 (1575 MHz) and L2 (1227 MHz) • Each carrier frequency is BPSK modulated with a unique PRN (pseudo random number) code • The PRN code on L1 is called CA code (coarse acquisition), The PRN code on L2 is called P code (precise) • CA code takes 1 ms for full PRN transmission at 1MHz chip (bit) rate. P code takes 1.5 s for full PRN transmission at ~10MHz chip rate • Also modulated on each carrier is 50 Hz data that includes the current position of the satellite DSP Applied to GPS Algorithms

7. Determining Time • Use the PRN code to determine time • Use time to determine distance to the satellite distance = speed of light * time (1) DSP Applied to GPS Algorithms

8. Algorithms to Find PRN Phase N-1 • Cross correlation: 1/N∑x1 (n) * x2(n) • n = 0 • Correlation of perfectly matching signals gives a maximum value • Correlation of 2 random data sequences tends to 0 • Frequency domain correlation: 1/N F-1[X1(k)X2(k)] where F-1 is the inverse Discrete Fourier Transform and the X’s are the Discrete Fourier Transforms of two sequences D DSP Applied to GPS Algorithms

9. Timing • Frequency Domain 1/N F-1[X1(k)X2(k)] • 1024 point FFT (NLOG2N) • 1024 MULTS (N) • 1024 point INV FFT (NLOG2N) • Time Domain 1/N∑x1 (n) * x2(n) • n = 0 • 1024 MACs (N) • 1024 Phases (N) 21504 operations N-1 1048576 operations (N2) DSP Applied to GPS Algorithms

10. Tiger SHARC TS101 Cummunications Operations • Despreading • Needs lots of shifts 2 bit at a time DSP Applied to GPS Algorithms

11. Xcorr operation DSP Applied to GPS Algorithms

12. TigerSHARC TS201 • XCORR operation • Combines 16 despreading instructions in a single cycle. With both X and Y working we get 512 Multiplies and 512 additions in a single cycle • Need to consider end effects DSP Applied to GPS Algorithms

13. Project Plan • Compare optimized frequency domain (FFT based) and time domain (XCORR based) algorithms on the TigerSHARC • Determine method of testing the algorithms to relate results back to GPS signals • Use canned data sample from actual GPS receiver? • Use Matlab modeled data • Use a second TigerSHARC development board to produce data DSP Applied to GPS Algorithms

14. Conclusions • Introduced basic concepts of GPS • Introduced cross correlation algorithms • Introduced TigerSHARC features to support implementation of cross correlations • Project plan DSP Applied to GPS Algorithms