Navigation and the Global PositioningSystem (GPS):

Few changes of great importance to economics and safetyhave had more immediate impact and less fanfare than

GPS.

The Global Positioning System:

• GPS has quietly changed everything about how we locate objectsand people on the Earth.

• GPS is (almost) the final step toward solving one of the greatconundrums of human history.

Where the heck are we, anyway?

In the Beginning…….

• To understand what GPS has meant to navigation it is necessaryto go back to the beginning.

• A quick look at a ‘precision’ map of the world in the 18th century tellsone a lot about how accurate our navigation was.

Tools of the Trade:• Navigations early tools could only crudely estimate location.

• A Sextant (or equivalent) can measure the elevation of somethingabove the horizon. This gives your Latitude.

• The Compass could provide you with a measurement of yourdirection, which combined with distance could tell you Longitude.

• For distance…well counting steps (or wheel rotations) was the thing.

An Early Triumph:

• Using just his feet and a shadow, Eratosthenes determined thediameter of the Earth.

• In doing so, he used the last and most elusive of our navigationaltools.

Time

The early tools had many levels of uncertainty that werecumulative in producing poor maps of the world.

Plenty of Weaknesses:

• Step or wheel rotation counting has an obvious built-in uncertainty.

• The Sextant gives latitude, but also requires knowledge of theEarth’s radius to determine the distance between locations.

• The compass relies on the assumption that the North Magneticpole is coincident with North Rotational pole (it’s not!) and that it is aperfect dipole (nope…).

Navigation on land was helped by the availability of landmarks, placesthat could put context to a map and help calibrate a journey.

Such a technique is worthless at Sea….

Without any question THE most important maritime dilemma ofthe Renaissance world was how to determine Longitude.

Navigation at Sea:

• A sextant can be used to give latitude very effectively at sea.

• A compass can give you a good idea of your direction.

• But unless you can determine how far East/West you’ve gone….

This Will Eventually Turn into THIS!

• To determine one’s East-West position, the accepted method wascalled Dead Reckoning (perhaps aptly named).

• Dead Reckoning has many sources of error that add up over along journey. Even 95% accuracy in crossing from New York toLondon will accumulate to 175 MILES of error at the end of the trip.

Dead Reckoning:

• These kinds of error were a Serious problem for ships approachingrocky coasts or areas with submerged shoals and seamounts!

On October 22, 1707, a dead reckoning error by the fleet ofAdmiral Sir Clowdisley Shovel led to the death of 2000 sailors.

Longitude!

• In 1717, Queen Anne authorized a prize of 20,000 £ to anyone whocould maintain knowledge of longitude to ½ degree (the equivalent of30 miles on the equator).

• Almost all of the methods proposed for solving this problem centeredon the 4th element of navigation we haven’t talked aboutmuch…….TIME.

Why is Time so important?

• Your Meridian is nothing more than a circle on the Earth thatgoes through the North and South Poles and your position.

Meridians and Longitude:

• The Prime Meridian is the meridian thatgoes through an agreed upon zero point.

• The angle going west from Greenwich toyour meridian is your LONGITUDE!

• The Prime is locatedtoday in Greenwich,England.

Longitude and Time:

• It turns out that while there may be no landmarks on the ocean,there are fixed reference points…the stars.

• As the Earth turns, the stars pass by overhead. Each starcrosses every meridian on Earth exactly once each day.

So how do longitude and time relate?

• So the difference between the time astar crosses the prime and yourmeridian is your longitude.

• The problem then comes down toknowing what time it is…exactly.

• Every 4 minutes of error equals 1degree or 60 miles on the equator.

To win the longitude prize one had to be able to maintain accuratetime to within 2 minutes over a several months at sea.

John Harrison’s Clock:

• Galileo couldn’t win the prize (he was dead), but he had devised away of determining the time using the moons of Jupiter.

• The astronomers Tobias Mayer and Nevil Maskelyne proposedusing the predictable changes in the distance to the moon.

• John Harrison went after the prize by building accurate clocks thatcould survive the weather extremes and motion of ship travel.

• This actually worked well, but only for that part of theyear when Jupiter was visible at night!

• This also worked, but was VERY hard to docorrectly and didn’t work when the moon was lessthan ½ full.

There are actually several ways to do this.

John Harrison’s Clock:

• Between 1736 and 1764 John Harrisonproduced 4 clocks for the Board ofLongitude (the group that held the prize).

• Because Nevil Maskelyne was chair of the Board of Longitude…

• Each clock was smaller and moreaccurate than the previous one. And theyALL met the condition for the longitudeprize. None were accepted!

• So why were they locked in an observatory instead of saving lives onships during this time?

• It would take an act of King George III to break the logjam and putchronometers into wide use.

Harrison’s clock changed navigation in a fundamental way.

The (FIRST) Global Positioning System:

• Anyone with a sextant and a chronometer could find their positionto within a few miles on the Earth.

• The clocks were incredibly expensive and in fairly short supply.

They weren’t perfect though

• Since they relied on Greenwich time, they had to be re-calibratedto Greenwich: Usually in Greenwich.

• Positions could only be determined at sunrise or sunset whenboth a star and the horizon could be seen.

• It didn’t work at all if the weather was cloudy…..

Harrison’s clock (and its successors) made navigationpossible for commercial shipping and the well to do, but it

wasn’t for the masses.

A Modern Solution:

• A universal navigation system would need the following.

• A way to tell time that isn’t expensive.

Enter the MODERN Global Positioning System (GPS):

• A set of references that didn’t disappear whenever it wascloudy

• A clock that can be calibrated anywhere, not just inGreenwich.

For all its complexity, GPS still comes down to the sameset of requirements that Harrison faced.

The Global Positioning System:

• Find out the time.

• The reference points also serve as the clock.

GPS adds a pair of twists:

• Find the reference points.

• Use the output to determine Longitude and Latitude to highprecision.

• Everyone uses the same system. The GPS network is effectivelya single device, like Harrison’s clock.

The GPS system consists of 3 elements.

Parts of the GPS Network:

• GPS ground support.

• GPS satellites.

• GPS receivers.

The first GPS Satellite was launched in 1978.

The GPS Satellite System:

• To function properly the network of satellites must contain 24 units.With GPS it is all about coverage.

• Each satellite has a 12 hour orbit, which means it passes over thesame place twice each day.

• There are 6 orbit ‘planes’ inclined by55° to the equator and rotated for a 60°spacing between them.

• Each plane contains 4satellites.

The first GPS Satellite was launched in 1978.

The GPS Satellite System:

• A Ground Track mapshows how this schemecovers the Earth.

The GPS satellites are nothing more than atomic clocks thatwork because we know where and when they can be found.

The GPS Ground Support:

• To maintain the satellites requires a ground support network (calledthe control segment - CS) that uplink time and radar tracking positiondata to the satellites (called the space vehicles – SV).

• There are 5 CS components that update satellites and alsocommunicate data to some advanced GPS reveivers

The receiver units are the backbone of the mass marketGPS. The receivers serve 3 purposes.

The GPS Receiver:

• Small handheld units receive signals from 4 or more SVs. Thereceivers are called the User Segment -US. Decoded signals provideX, Y, Z, and T. Everyone can find out where they are.

• Via SV-US communication, the exact time can be synchronizedworldwide in a matter of a few seconds.

• By combining signals from nearbyreceivers, very accurate navigationand surveying data can be obtained.

The Method of GPS:

• How does GPS work?.

• Your GPS receiver gets signals from satellites that are doing nothingmore than repeating the time over and over.

• Since light travels at a finite speed, there will be a differencebetween the instantaneous time on your receiver and the time youget from the satellite.

Time Difference = Speed of Light X distance

• The satellites know exactly where they are in X, Y, Z. So, if youhave a bearing to three of them, then you know as well.

• The time differences are small. 1000 feet of distance translates toonly a 1,000,000th of a second!

The Genius of GPS:• There’s a caveat to this. YOU don’t carry an atomic clock. Theyare expensive and heavy. YOUR receiver clock is going to be off asome random amount when it compares time with the satellites.

How do we get around this?

The Genius of GPS:

We add a 4th measurement!

• If we knew the time, a 4th

satellite would be redundant.

• However, the extra satellitecan ONLY match up with theother three at the CORRECTtime. It removes the error andcalibrates your receiver at thesame time!!!