Copyright 1997, 2002

Chapter 5, Navigations in the Past, Present, and Future

Everybody knows that the global positioning system was developed for the purpose of navigation, but not many people realize that the clock was also developed for navigation.

Throughout history, it has been easy to determine latitude by measuring the angle between the Pole Star or the sun at noon and the horizon by a simple angle measuring device or an advanced sextant (see Appendix A). The early Phoenicians and Greeks learned to tell how far north they were by observing the height of the Pole Star above the horizon (or its angle of elevation). By the 15thcentury the Europeans generally believed that the earth was round, and Christopher Columbus (1451?-1506) set out to prove it. He used observation of the North Star to keep his course steadily toward the west; every night, he measured the North Star’s angle of elevation to tell whether his ship had drifted off course. But this method is of no help whatsoever in determining longitude, so Columbus did not know how far west he had gone. When he reached the New World, he thought he had arrived in India; because of this he named the inhabitants of this new land “Indians,” a name by which they are still known today. To his death, Columbus never realized that he had discovered a “New World.” But the famous Italian navigator Amerigo Vespucci (1454-1512), for whom the Americas are named, and others were convinced that what Columbus had achieved was the discovery of a previously unknown land.

The Longitude Problem

How to determine longitude at sea had been a serious problem for a long time. But it was known that local time could be ascertained by measuring the elevation of the sun at noon, or the stars, and then looking up the answer in a nautical almanac. By the seventeenth century astronomers had discovered that longitude could be calculated by comparing local time with the time shown on a clock at a known meridian. This reference meridian can be arbitrarily chosen; it can be, for example, the one passing through Greenwich, England. The French prefer to use the meridian that passes through Paris, and many ship's captains in the old days used their home port as the reference meridian.

The earth rotates 360 degrees in a day, or 15 degrees per hour. You can find your local time by celestial observation, as noted in the previous paragraph; if you find that your time is one hour ahead of the time at your reference meridian, then--since the earth rotates from west to east--you will know that you must be 15 degrees to the east of the reference meridian. So long as you carry the reference time with you, you will always be able to calculate your local longitude.

In the early days of sea navigation, though, no such precise time-keeping device was available. So, in the fifteenth, sixteenth, and seventeenth centuries, ship's captains had to use dead reckoning to guess their whereabouts--and, many cases, this method really did make them dead men. During the Age of Exploration ships were lost at an outrageous rate because they were unable to determine their longitude. Voyages were unpredictably long, supplies on board were insufficient, and sailors suffered terribly from the deadly disease of scurvy because their diets lacked fresh fruits and vegetables. For ships navigating by latitude alone, only a very few safe shipping routes were available.

Islands in the ocean became indispensable checkpoints, or way-points, in the shipping lanes. If a ship should waver from its route because of bad weather or some other reason like bad luck or navigation error, it might be lost forever. But human conflict was a much greater danger than natural disaster. All the whaling ships, merchant ships, warships, and pirate ships operated by the English, Spanish, Portuguese, French, Dutch, Germans, Italians, and others had to travel along the few narrow channels that were available for safe navigation; and since these nations were often at war with each other, chance meetings of ships could lead to fighting and killing. Romantic sea stories like Treasure Island, Robinson Crusoe, and Moby Dick are legacies of that era.

Many of the sea powers at that time offered rewards to anyone who could solve this tough navigation problem. Again and again the scientific elite turned to the heavens in the hope of finding an astronomical clock, and famous astronomers like Galileo, Werner, Newton, Halley, and Bradley all looked to the moon and starts for an answer. Observatories were built in London, Paris, Berlin, and other capitals for the purpose of finding longitude by studying heavenly bodies.

The Galileo Method

Galileo tried to solve the longitude problem by using his newly invented telescope to observe the periods of the moons of Jupiter. Eclipses of these moons occur around 1,000 times a year, and so they can be used as a clock. But Galileo's method was dismissed as not being very practical on the heaving sea; because, even on land, just the pounding of the observer's heart could throw Jupiter out of the telescope's field of view. Galileo's method was eventually accepted after his death in 1642, but for use on land only. Geographers used his method to redraw maps of the world, and found that earlier maps had greatly underestimated the distances between continents and misplaced the boundaries between nations by large distances. When the king of France saw the revised map of his domain, he complained that he was losing more territory to his astronomers than to his enemies!

The success of this technique encouraged the scientific community to refine its prediction of eclipses of the moons of Jupiter and finally led to an answer to another of the great mysteries of science, the speed of light--which Galileo himself had tried and failed, to measure. By determining the regular changes in the periods (or phases) of the moons of Jupiter when the planet was at its nearest and farthest distances from earth during each half-year, the scientists were able to calculate the amount of time needed for light to travel through the diameter of the earth's orbit around the sun. The astronomers measured this diameter and calculated the speed of light to be nearly 300,000 kilometers per second. Until they made that breakthrough, it had been believed that light moved from one place to another instantly and had no finite speed that could be measured.

Figure 5-1. First time to determine the speed of light by astronomical method.

Despite these advancements in astronomy and science, how to determine the positions of ships at sea remained a puzzle. For a long time the quest for determination of longitude on the ocean was a synonym for "the ultimate illusion," like building a perpetual-motion machine, finding the Fountain of Youth, formulating a panacea to cure all diseases, or realizing the alchemists' dream of turning lead into gold. Even Newton was afraid it was an impossible dream.

The Chronometer

In 1714, the British Parliament offered a prize of 20,000 pounds to anyone who could devise a practical method of finding longitude at sea to an accuracy within 30 nautical miles. In those days, this was a huge amount of money. It was only in 1762, though, that an English clockmaker named John Harrison, fighting not only extreme technical difficulties but also the prejudice of the upper class of society against "that mechanic," won the prize by designing a chronometer. This is the kind of mechanical device that was refined and used as the standard timepiece until quartz and electronic clocks and watches became available not long ago.

The 24 time zones that we have around the world today, each one in principle occupying 15 degrees and referenced to Greenwich Mean Time (GMT), are derived from this old-time navigation and positioning technology. The standard time zones were established by international agreement in 1884 (see Fig. 5-2).

Fig. 5-2 Time Zones of the World

The global standard time zone system employs 24 standard meridians of longitude, each 15 degrees apart, beginning with the prime meridian that is referenced to Greenwich Mean Time. The system is based on the fact that the earth rotates at the rate of 15 degrees per hour. Aberrations in the zone borderlines--where they are curved--are established for the convenience of geographical regions. In some places, there are also half-hour time zones.

When the precise time-keeping device was invented, no one could have imagined the impact it would have upon the world--on the way we live, and on the new products and services which this new technology would make possible. The GPS is to precise position just as the chronometer was to precise time, and today we are in a similar position in regard to the initial development of GPS. Many still-unknown applications are just waiting for you to discover them once you understand this new technology.

We may need to be reminded just how dependent we have become on the precise timing we now take so much for granted. The millennium problem, or the year 2000 (Y2K) bug, caused a great deal of concern for business, industry, and the military. The GPS had its first week number rollover on Aug. 22, 1999. Some GPS receivers failed to function properly on that date, because their built-in software could not deal with this critical boundary condition.

The GPS Story

Throughout human history, navigation has always been a fascinating subject for every culture and every civilization. Chinese folklore tells of how 5,000 years ago, the Yellow Emperor discovered that a magnetic iron bar would always align in a north-south direction if allowed to hang freely. According to the legend, he mounted his device on a cart for use in the field; it helped him to defeat an invading barbarian army by allowing him to find his direction in the foggy battlefield so that he could command, dispatch, and supply his troops effectively. His victorious kingdom is thought to be the birthplace of Chinese civilization.

GPS, too, was originally designed and deployed for military use during the cold war. Remembering the surprise attack on Pearl Harbor on Dec. 7, 1941, as Franklin D. Roosevelt said “The day we will live in infamy”, U.S. military planners realized that if war should break out suddenly, America could lose its overseas navigational ground facilities in a matter of minutes. So, to assure that the navigation system would maintain its precision navigation capability for a reasonable period of time after such an attack, the architects of the GPS system made the most of the computing capability of user equipment--that is, the GPS receivers. This makes the system less reliant on the relatively vulnerable ground facilities; but it also makes receiver design more complicated, as described in previous chapters. Newer generations of GPS satellites will be able to carry out inter-satellite communications, making the system even less dependent on the ground facilities which are scattered all over the world. This helps to fulfill an important requirement for a military system, which is to eliminate any possible Achilles' heel.

After the tragic downing of Korean Airlines Flight 007 over Russian airspace in 1983, the Reagan administration announced that part of the navigational capability provided by GPS would be made available for civilian use. This would help ensure that navigational errors such as the one that allowed the Korean airliner to stray off course would not happen again. Since then, the U.S. government has been committed to providing GPS service free of charge, and this commitment has encouraged industry to make large investments in developing GPS receivers.

Over the years, great strides of progress have been made in miniaturizing the size, reducing the power consumption, and shortening the time-to-first-fix (TTFF)--that is, the time required for a receiver to produce the first position after power-on--of GPS receivers. Many new applications have also become feasible--for example, GPS capability for personal digital assistants (PDAs) and mobile phones. The Federal Communications Commission (FCC) has mandated that all mobile phones sold in the U.S. must have position reporting capability for emergency 911 calls by the year 2001, and other countries are expected to follow soon. This order has caused yet another fever of investment in GPS technology by telecommunications giants and venture capitalists.

The former USSR also offered free use of part of its GLONASS navigation capability, and the government of Russia reaffirmed this commitment following the USSR's breakup. A growing number of manufacturers are developing combined GPS/GLONASS receivers in order to increase the versatility and integrity of their products.

Differential GPS

After turning off the selective availability (SA) in May 2000, standalone GPS receiver can achieve an accuracy of approximately 30 meters horizontally. With SA, GPS offered civilian users an accuracy of about 100 meters horizontally and 156 meters vertically 95% of the time. Even better accuracy can be achieved by Differential GPS. The trick to differential GPS is to use a reference receiver station located at a precisely known position. The reference receiver, just like any other GPS receiver, knows where the satellites are supposed to be from the orbital data which we discussed in Chapter 2. Since the reference receiver also knows its own precise location, it can compute the distance to each satellite and divide that distance by the constant speed of light to get the delay time—that is, the amount of time it takes the signal to travel from the satellite to the receiver. The receiver compares this computed delay time with the measured delay time, and the difference between the two becomes the error estimate of the signal from the satellite. The reference station broadcasts this error estimate to GPS receivers in the vicinity, which use it to adjust their position calculations.

Most of the error sources we mentioned previously which affect both the reference station and the receivers—atmospheric delay, satellite clock error, and selective availability, among others—can be eliminated by this process. As a result, precision within one meter can be attained; for surveying receivers, the accuracy can even reach the centimeter level.


For many civilian applications, such as use as a primary navigation aid, GPS/GLONASS must meet certain stringent safety requirements such as improved availability and integrity. Neither GPS nor GLONASS provides users with timely notification of a satellite failure or excessive error. Also, if GPS and GLONASS are to be used together, compatibility issues like time standards and reference coordinate systems must be resolved. A geo-stationary augmentation service can make up for these shortcomings.

The Wide Area Augmentation System (WAAS) program, being implemented by the U.S. Federal Aviation Administration, is designed to provide just such a service. Under this system, GPS integrity and differential correction data are calculated by a network of ground reference stations. A corresponding network in space is made up of geo-stationary satellites like INMARSAT. The service provided by WAAS is for use primarily in the U.S.

Europe has a similar augmentation system called the European Geo-stationary Navigation Overlay Service, or EGNOS. To cover the Asia-Pacific region, Japan has its MTSAS program.

The Local Area Augmentation System (LAAS) is a ground-based system that provides additional navigational pseudo-satellite signals in a local area, usually near an airport, to enable aircraft to approach and land safely in almost zero-visibility conditions. Global interoperability of these systems is imperative. The space-based augmented GPS navigation systems will gradually replace the present ground-based aircraft navigation and air traffic control systems, which have remained basically unchanged since the end of World War II.

The benefits of this change are obvious (see Fig. 5-2). Present air routes have to pass over navigation facilities near populated areas, where electric power is available to run the equipment. Trans-oceanic flights must pass over islands that serve as way-points on which ground navigation facilities are located. The resulting air routes are often indirect, crowded, and inefficient. This is just like ocean shipping in pre-chronometer times, when shipping lanes were terribly constricted.

New York to Hong Kong

________ Conventional ground-based route

………… Satellite-based GPS navigation route

Fig. 5-2 A restructuring of air routes based on GPS navigation can take advantage of great circle distance, which is the shortest distance between any two points on the globe. (From International Air Safety, LLC of Washington, DC; Fig. 5-2 is available in color at

Here is a pertinent quote from the Discovery channel program, Survival in the Sky: “Looking back 10 years from now, today may be the golden age of air travel. Casualties have stayed at the same level as in 1947 despite the fact that air traffic has grown a thousand-fold. If you were to take a random flight every day, it would take you 26,000 years before you encountered a major air accident, and chances are that even then you would survive the crash. In the next decade or so, our skies will be so crowded that the present air traffic control system won’t be able to handle the traffic growth. Experts are afraid that the casualty figures might double by that time.”

The ICAO, the FAA, and other civil aviation authorities around the world are pushing forward with new air traffic control and navigation systems based on GPS and communications applications.


Most stand-alone GPS receivers tell you your position by showing the latitude, longitude, and altitude of the receiver. From Chapter 1 and Appendix A, we are already familiar with latitude and longitude. But a display of coordinates like 24 degrees North, 121 degrees East, and 100 meters altitude might not be very helpful to you in locating your position. You need to find out where you are on the map.

The Geographic Information System, or GIS, is the database that stores maps in computers. The GIS can be much more sophisticated than a paper map; it can be three-dimensional to display the earth’s surface terrain, and it can include everything you need to know—a gas station, for example, or a picture of a tourist site. A car navigation system that combines GPS and GIS is expected to be the largest market sector for GPS applications in the 21stcentury.

We need to devote some additional attention to GPS elevation. This is not actual height above the ground, and it is not elevation above sea level either, because GPS receivers without GIS have no knowledge of the real world.

It is the software in your GPS receiver, remember, that computes your position, altitude, and speed. The software uses an ellipsoid model, called the WGS-84 (World Geodetic System 1984), to approximate the surface of the earth (see Fig. 5-3 and the Mathematical Model section of Chapter 2). Because of its rotation, the shape of the earth is that of a slightly flattened sphere. The calculated GPS height is the vertical distance above the imaginary, mathematical surface of this sphere. This is a smooth ellipsoid surface that carries no terrain information such as is provided by GIS. Unfortunately, this surface does not coincide with sea level, either. This fact combines with other GPS errors like selective availability and atmospheric delay to make things even worse.

There have been instances of pilots failing to use their GPS receivers properly, ignoring their baro-altimeters during low-latitude maneuvering, and ditching their aircraft into the sea.

Fig. 5-4

An ellipsoidal model of the earth (cross-section normal to the equatorial plane). GPS height is the height of a receiver above this imaginary mathematical model. To illustrate GPS height, this ellipsoid is much exaggerated.

It is important to learn the conditions under which a technology is supposed to work, and not to be trapped in a myth. Technology itself is not the Almighty; it needs to be applied with discipline. Accidents do happen, and ignorance can exact a heavy price. One striking example from history of this price is the “unsinkable” Titanic, which has provided synonyms for technological myth (unsinkable) and disaster (the Titanic).


One thing that makes GPS so exciting is that the theories involved stretch from Pythagoras down to Kepler, Newton, and Einstein, and cover the entire spectrum of physics and its practice including communications, computers, software engineering, semiconductors, microelectronic design, and automation--in fact, every discipline of modern technology.

It is said that GPS will be the next utility, and that it is provided free of charge. It will, like other utilities such as the time, electricity, running water, and the telephone, become a part of everyone's daily life. A GPS receiver will soon cost no more than a pocket radio or a watch, meaning that everybody will be able to afford one. And the applications of this new breed of high-tech capability are limited only by your imagination.

However, the satellite-based principles on which GPS receivers operate are considered so esoteric that most people don't bother with them or else misunderstand them. The purpose of this little book is to make the concepts behind the Global Positioning System easier to understand and more accessible so that you, the user, will be able to know exactly how the system works, what it can do, what its limitations are, and what kinds of GPS application are practical. This book is meant to serve as an introduction to the system; anyone who is interested in GPS can start here, and then, if interest provokes, go on to explore the vast territory that lies beyond. We hope that your understanding of this high-tech gadget will enable you to realize the new ideas and creative impulses that will inevitably come with your new knowledge.

Copyright 1997, 2002. All rights reserved.
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