Where on Earth am I? (Part II)

Wanderlust has kindled the human spirit for time immemorial. While a majority of humans live, work and die very close to where they were born, a significant number of us travel. In older days, travelers were the oddballs. They had uncanny methods of going from one place to the other with minimal knowledge of geography or navigation. We suspect they had some form of primordial skill that is often found in animals, birds or fish. Till today, scientists do not fully understand how migratory birds (or fish like Salmon and Hilsa) return year after year to the same breeding grounds with impeccable accuracy.

Humans devised navigation aids as very early. Around the 8^th century someone noticed that some stones keep pointing north and invented the first compass out of “lodestone”. Early travelers used the sun and the moon and the stars in intricate ways to judge their positions. Then Sextants and other gadgets followed (10^th century), making it possible to go further with less fear.

Pilotage (using landmarks) and Dead Navigation (using precalculated routes) have always been and still are well-established methods of getting around (both of these were discussed in this article, last week). Instruments for navigation make the journey safer and enhance the accuracy of tracking routes. The instruments used for navigation in the past century have all used two basic mechanisms, the gyroscope and radio waves.

The gyroscope is just a spinning wheel. The perfect gyroscope stays in exactly one position, pointing at a constant direction regardless where you take it. A gyroscope pointing north will always point north. A gyroscope pointing “down”, will point “up”, if you take it to the other side of the earth. In practice, it is difficult to keep a gyroscope accurate for a long time, due to friction on its bearings. Even then, “inertial guidance” systems use gyroscopes for long distance (intercontinental) navigation. A more common use for gyroscopes is to indicate “attitude” on aircraft. That is, it indicates whether the aircraft is level or banked or whether the aircraft is pointing up or down (at night or in fog, it is not possible to realize the attitude of an aircraft by visual cues).

Radio navigation is the final frontier. Radio navigation comes in many shapes and forms and works on varying principles. Radio navigation uses base (or transmitting) stations on the ground (or in space) and mobile (or receiving) stations on vehicles. The base stations differ in type and standards as these have been typically set up by governmental agencies. Currently US based standards such as VOR and LORAN are quite popular. The really modern navigation system is GPS, built by the US military.

VOR (VHF Omni-directional Range station) is the most common form of radio navigation used over land, especially in the United States. It is also the simplest form of radio navigation. Of course, its simplicity leads to its dependability, accuracy and popularity. A VOR navigation system consists of a large number of ground based VOR stations and a VOR receiver located onboard aircraft. A ground-based VOR station uses a frequency of about 100Mhz has a range of about 100 miles.

 The VOR station emits two kinds of signals—a burst of omni-directional radio pulse and a rotating, narrowly focused, radio beacon. The pulse is sent on a particular assigned frequency and contains the VOR identification data. Just as the pulse is emitted, the rotating beam starts sweeping the sky starting from the north. After the beam makes a full circle, the pulse fires again.

Suppose we are located due south of a particular VOR station and suppose the rotating beam takes a full minute to rotate from north back to north. Then, if we turn on our VOR radio, it would hear the pulse and 30 seconds later it would hear the rotating beam flash by. The time between the pulse and the beam, 30 seconds, would tell us that we are due south of the VOR station. That is exactly what a VOR station provides—a direction from a receiver’s current location to the VOR location. Now it would be easy to start walking towards the VOR station, using a compass to tell what is north. If the compass was inaccurate, we would detect the deviation from our subsequent VOR observations and then compensate for it. Lines connecting one VOR to another VOR are called Victor Highways, and they are the most heavily traversed roads in the sky. It is also possible to determine exact location using VOR—by using a more enhanced version.

Just as VOR is used over land, the LORAN (LOng Range Aid to Navigation) system is used over the high seas by ships and planes. LORAN is more complex than VOR. LORAN uses clusters of transmitters sending out powerful pulses (800KW) of low frequency (100KHz) radio waves, which can then be analyzed and the position of the receiver calculated using triangulation (using observed delays in the LORAN pulses received from different transmitters in the cluster).

The mother of all navigation systems is GPS (Global Positioning System). GPS works in every corner of the world with uncanny accuracy. Originally GPS was built by the US military, but its civilian and commercial uses has far outstripped military uses. GPS is pure high-tech. GPS uses 24 satellites circling the earth at about 10,000 miles up there, and has been working since 1995. Each satellite contains an ultra-accurate atomic clock and broadcasts a signal that is synchronized with the atomic clock. That is, each satellite tells you the time.

If I had an atomic clock, and listened to one particular satellite, I would see that the satellite’s time is a bit delayed (due to the time taken for the signal to reach me from the satellite). From this delay I could calculate how far the satellite is from me. Suppose I found the satellite is 11,034.8 miles from where I am. Then I calculate the exact position of the satellite in the sky (from its trajectory and the time of day). Given the location of the satellite I draw a circle on the earth’s surface, exactly 11,034.8 miles from the satellite. I am located somewhere on this circle.

Using a second satellite I get another circle. Hence I must be at the intersection of these two circles—but the circles intersect in two places. Where am I? That is easy, I use a third satellite and the third circle must intersect the first two at one of the two points they intersect, telling me my exact location.

Of course, if the three circles do not intersect at any one point, that would tell me that (1) my calculations are goofy or (2) my atomic clock is broken or (3) I have had a martini too much. Oh, by the way, did I say “atomic clock”? Of course I do not have an atomic clock, those things are doggedly expensive, not to mention that they are highly illegal to possess.

Since we do not have an atomic clock, we use a fourth satellite as a source of time. Now we will find that the four circles that do not intersect at one point at all! So I keep adjusting my time value, till all four circles intersect—and voila I have my exact position and a free atomic clock.

In reality GPS location finding is a little more difficult than the explanation above.  The GPS system uses a plethora of computations to correct for satellite position deviation, atmospheric delays and many other sources of errors. The final result is that commercial GPS receivers can display my position on the mother earth, at an accuracy of about 50 feet. That is right, 50 feet is uncannily small when you consider the signals are originating in deep space.

What does a GPS receiver cost? Far less than you expect. They range in price between $100 and $300 depending on brand and features. The $300 model has a lawn mower built in. What does a GPS receiver look like? About the size of two packs of playing cards. The price and size is expected to come down and applications are expected to skyrocket. Currently GPS is heavily used in traveling, hiking, camping, oil exploration, trucking, car navigation, treasure hunting and a huge amount of commercial and recreational activities. Within a year, cell phones will have a GPS built in so that the phone’s location can be determined. The use of GPS in aviation is surprisingly limited. Aviation folks are very paranoid of any new technology whose failure modes are not well understood. However, all recently manufactured planes are equipped with GPS and their use for flying is slowly becoming acceptable.

Differential GPS is yet another form of GPS that has an accuracy of about 5 feet. Differential GPS can automatically land planes—that is, given the exact location (latitude, longitude and elevation) and the direction of the runway, a plane with differential GPS on board can land itself. Just by ensuring the wheels touch the earth at the exact specified position, plus or minus 10 feet. Pilots do not believe this will ever by used in real life. Remember, “ever” is always a few years around the corner.

Partha Dasgupta is on the faculty of the Computer Science and Engineering Department at Arizona State University in Tempe. His specializations are in the areas of Operating Systems, Cryptography and Networking. His homepage is at http://cactus.eas.asu.edu/partha.