GPS Wrap Up

How GPS Works in a nutshell

• ~24 satellites are in orbits around the earth such that 6-12 are usually above the horizon of any given location.

• Timing information from each satellite tells us our distance from each one since we know the speed of light.

• Since we know the location of each satellite, we use these distances to solve for our location.

Orbits• 6 orbital planes

inclined at 55o with respect to equator

• 12 hr orbital period• 4 satellites in each

• (Not geosynchronous)

• Do Question 1

Finding our location• If we know the location of each satellite and

we know our distance from each one, we can solve for our location if we can see at least 3 satellites

Even better if we see at least 4

Timing and Uncertainty

• Your GPS receiver will tell you the uncertainly in your position (can be ~15 feet).

• This means that, at least:– We must know the location of each satellite to

better ~15 feet.– We must know the time of the satellites clock to

better than about ~15 ns.– Do questions 2 & 3.

Signal Arrival Time:• Spread Spectrum Transmission does it all:

This pseudorandom code is 1023 bitslong and is differentfor each satellite.

Technique is calledCDMA (code divisionmultiple access)and is used by cell phones etc.

1575.42 MHz = 10.23 MHz × 154

This pseudorandom code is 1023 bitslong and is differentfor each satellite.

Each bit takes 1/f = 1/106 Hz = 10-6 s.

For a long string of bits like this one the overall phase (time) can be determined to around 1% ~ 10-8 s = 10ns.

If the uncertainty in time is about 10ns, the uncertainty is distance is about 10 feet.

Sources of Error

(Wikipedia)

Relativistic Effects (Stuff we understand and can correct for)

• Special Relativity (moving clocks run slow)– About 7x10-6 s/day

• General Relativity (clocks high up run fast)– This is ~6x bigger than SR

• Overall effect, the satellite clock runs fast.– Compensate for this by running the satellite clocks a bit slow

(10.229999995453 Mhz instead of 10.23 Mhz )

http://www.kowoma.de/en/gps/errors.htm

How this course tied in to GPS• Classical Mechanics

– Forces and acceleration determine orbits– Accelerometers illustrate equivalence principle

• E&M– Speed of light– Maxwell’s equations, static fields & waves.– Transmission of information, 2.4GHz microwaves

• Special Relativity– Moving clocks run slow, lengths shrink.– In a moving reference frame E looks like B

• Spectroscopy & atomic clocks– Saturation absorption spectroscopy– How to build a state of the art atomic clockWe have had time for just a taste - there must be lots of questions

Things we might do before lunch ?

Some possible suggestions:• Prepare for your Friday Presentations• Further discussion of GPS.• Discussion of any of the many activities from

the last two weeks (most went by quite fast).• Anything other activities you thought up.

– For example, using your MSP430 hardware to build a wireless ECG unit.

Lab Tours after Lunch

• 12:30-12:50 Brian Demarco 329 LLP• 12:55-1:15 Charles Gammie 251 LLP• 1:20-1:40 Russ Giannetta 129 LLP• 1:45-2:05 Laura Greene 114 MRL • 2:10-2:30 Nadya Mason B46 MRL • 2:35-2:55 Lance Cooper 226 MRL• 3:00-3:20 Yann Chemla 57-59 LLP