1 Introduction to GPS Mayur Shah ( [email protected]) [email protected].

18
1 Introduction to GPS Mayur Shah ([email protected] )

Transcript of 1 Introduction to GPS Mayur Shah ( [email protected]) [email protected].

Page 1: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

1

Introduction to GPSMayur Shah ([email protected])

Page 2: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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?

Page 3: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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

Page 4: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

4

Components of the system

Page 5: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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 m

iles

x m

iles

Page 6: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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

Page 7: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

7

GPS Satellite Signals

Page 8: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

8

GPS signal structure

Page 9: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

9

How do we measure travel time?

Receiver PRN

Satellite PRN

Time Difference

Page 10: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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

Page 11: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

11

Nonlinear pseudorange equations

Page 12: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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,

Page 13: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

13

Least Squares

Page 14: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

14

Taylor series

Least Squares

Weighted Least Squares

Page 15: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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

Page 16: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

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

Page 17: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

17

The future…

Page 18: 1 Introduction to GPS Mayur Shah ( Mayur.Shah@gmail.com) Mayur.Shah@gmail.com.

18

Where can I find More info?

• http://www.trimble.com/gps/ • http://www.ion.org/

• http://www.gpsworld.com/ • http://www.gmat.unsw.edu.au/snap/gps/gps_links.htm• http://www.snaptrack.com/