1 Introduction to GPS Mayur Shah (

2 Outline What is GPS? How does it work? Some Math Why is it ‘cool’? (Applications) What is ‘hot’? (New research frontiers) Where can I find more info?

3 What is GPS? GPS – Global Positioning System is a satellite based navigation system developed and maintained by US DoD Allows for positioning anywhere in the world, any time of the day, any weather condition Consists of 24+ satellites in 6 orbital planes 20,200 km orbits; period of ~12 hr

4 Components of the system

5 How does GPS work? We measure travel time (t) of signal from satellite. x = t*c (speed of light) give us distance from satellite Satellite location is known The distance (x) from one satellite tells us we're located somewhere on the surface of an imaginary sphere centered on that satellite with a radius of x. x miles

6 Distance measurements from two satellites limits our location to the intersection of two spheres, which is a circle. A third measurement narrows our location to just two points. One of the points is usually way off to be on earth

7 GPS Satellite Signals

8 GPS signal structure

9 How do we measure travel time? Receiver PRN Satellite PRN Time Difference

10 Clock bias unknown What about the synchronization of receiver and satellite clock? Satellites have very precise atomic clocks, but receiver clocks are inexpensive There is bias between receiver and satellite clock and this bias changes with time This adds a time (t) unknown in addition to (x,y,z) position unknown We require at least four measurements (satellites) to solve for 4 unknowns

11 Nonlinear pseudorange equations

12 Linearization and Taylor series Linearization around a point x means approximating the function at a very small distance from x Ignoring the higher order terms,

13 Least Squares

14 Taylor series Least Squares Weighted Least Squares

15 Applications of GPS Positioning – emergency E911, location based services, asset tracking, geo fencing Navigation – aerospace, marine, land based Surveying – uses carrier phase for mm level accuracy Farming

16 New applications Push for higher availability and accuracy Designs for high sensitivity GPS receivers which work indoor Anti-jamming and multi-path rejection Augment GPS signals with cellular signals Integrate GPS signals with inertial sensor measurements

17 The future…

18 Where can I find More info?