How do GPS devices work?

How do GPS devices work? 

TWENTY FOUR SATELLITES make up the Global Positioning System.
NASA

The Global Positioning System (GPS) consists of 24 operating satellites and several spares. Some of these spare satellites are also in use or can readily be activated once an operating satellite becomes dysfunctional. Taking the specific orbits of this many satellites into consideration, an observer can see at least four satellites at any time from any location on the earth.

Methods to use GPS are more or less complicated depending on the desired accuracy and speed of positioning. For a simple example, assume that the orbital positions of the satellites can be accurately computed with respect to the earth at any time. Further assume that a GPS receiver on the ground can measure the distance between a receiver and a satellite for at least three satellites at the same time. By defining the receiver location with three coordinates, such as latitude, longitude and height, one can readily write three equations that relate the three distance observations to the known coordinates of the satellites and the unknown coordinates of the receiver. These three equations can be solved for the three unknowns.

The distance to the satellites is measured by timing signals transmitted by the satellites that travel with the speed of light toward a receiver on the ground. Because of the high speed of light, it is necessary that the instant of signal transmission at the satellite and the instant of signal reception at the receiver?s antenna be accurately registered in order for the distance and, consequently, the position calculation to be accurate. Satellites in fact carry atomic clocks. Receivers, in contrast, contain inexpensive and therefore less accurate clocks. As a result, we must allow for a timing error to occur as the arriving satellite signal is timed at the receiver. Because the signals arriving at a receiver from all satellites are measured at the same time, the distance measurements are all falsified by the same receiver clock error, which must be calculated in order to determine an accurate position. The complete position determination of the receiver consequently requires four unknowns: the receiver clock error and the three receiver coordinates. Measuring distances to at least four satellites allows one to set up four equations that can be solved for these four unknowns. This leads to the fundamental requirement for a truly global positioning system that at least four satellites be visible at any time from any location on the earth. In practice, receivers observe all visible satellites to determine the best estimates of both the receiver clock and location.

The solution described above is usually called the navigation solution. This type of calculation is implemented in virtually all receivers, including inexpensive handheld devices. In addition to determining position, the time is available to an accuracy of better than one microsecond. GPS receivers are therefore very valuable for time synchronization between remotely located clocks. Time synchronization is an important element in modern communication by Internet, telephone, TV broadcast and many other means.

A closer look at the underlying theories and techniques readily reveals that GPS positioning is not at all simple. This may be of little interest to hikers and motorists who use GPS to get from here to there. But for scientists, GPS is a utility with an endless list of applications, ranging from ionospheric and tropospheric studies to earth crust deformations. The list is equally long for engineering applications. GPS has truly become a national utility. 

Running fast

Running fast

China and India have much to offer the world of technology, argues Simon Cox, but more still to gain from it

TOWARDS the end of the 11th century, while tardy Europeans kept time with sundials, Su Sung of China completed his masterpiece: a water clock of great intricacy and accuracy. Standing almost 12 metres (40 feet) tall, Su's “Cosmic Engine” wavered, it is said, by only a few minutes in every 24 hours. From twin tanks filled by servants, a steady flow of water was cupped and spilled by a series of buckets mounted on a wheel. The rotation of the wheel turned the clock, as well as an astronomical sphere and globe that charted the movement of the sun, moon and planets. Drums beat 100 times a day; bells chimed every two hours. A replica, painstakingly built with contemporary methods, now turns in Taiwan's National Museum of Natural Science.

Clockmaking was only one scientific endeavour in which China and India comfortably led the world before the 15th century. China outstripped Europe in its understanding of hydraulics, ironsmelting and shipbuilding. Its machines for ginning cotton, spinning ramie and throwing silk seemed to lack only a flying shuttle and a drawbar to match the 18th-century contraptions that launched Britain's Industrial Revolution. Clean your teeth with a toothbrush, rebuff the rain with a collapsible umbrella, turn a playing card, light a match, write, pay—or even wipe your behind—with paper, and you register a debt to China's powers of invention.

India's genius, then as now, was in software not hardware. Its ancient civilisations ushered in a “mathematical revolution” from the fifth century, when Aryabhata devised something like the decimal system. In the seventh century Brahmagupta explained that a number multiplied by zero was zero. By the 15th century, Madhava had calculated pi to more than ten decimal places.

After the 15th century, however, the technological clock stopped in both countries, even as it accelerated in Europe. This peculiar loss of momentum, noted Joseph Needham, a great historian of Chinese science, takes some explaining. Why, he asked, did the science of Galileo emerge “in Pisa but not in Patna or Peking”?

In his book “The Lever of Riches”, Joel Mokyr settles on a simple explanation for China's technological stagnation: the country's imperial state lost interest. Its purposes were better served by continuity than by progress, and there was no rival source of power and patronage to pick up the threads it dropped. Roddam Narasimha of India's National Institute of Advanced Studies reaches a similar conclusion for India. “Up to the 18th century, the East in general was strong and prosperous, the status quo was comfortable, and there was no great internal pressure to change the global order,” he writes.

That diffidence no longer hampers either state. Both China and India are now restless with technological ambition. China's government does not have the luxury of choosing between progress and stability; it cannot enjoy social peace without economic advance. For the past 30 years it has tried to turn the clock forward. By 2015 its research scientists and engineers may outnumber those of any other country. By 2020 it aims to spend a bigger share of its GDP on research and development (R&D) than the European Union.

India, for its part, surveys the future with uncharacteristic optimism. Its technological confidence has grown immeasurably thanks to the success of its software and IT firms. The heirs to Aryabhata and Brahmagupta, India's digital ambassadors have won acclaim for their mastery of ones as well as zeros.

But even as India's technological powers make a splash in the world, they stir only the surface of its own vast society. India produces more engineering graduates than America. But it has only 24 personal computers for every 1,000 people, and fewer than three broadband connections. India's billion-strong population cuts both ways. Whenever an Indian demographic appears as a numerator, the resulting number looks big. But whenever its population is in the denominator, the number looks small. It is like looking at the same phenomenon from opposite ends of a telescope. As of now, India matters more to technology than technology does to India.

This is a pity. India and China still have more to gain from the adoption and assimilation of technology than from invention per se. Some of their best minds are adding generously to the world's stock of knowledge, but the more urgent task for the countries themselves is to make wider use of know-how that already exists. Indeed, the World Bank has calculated that India could quintuple the size of its economy if it only caught up with itself—that is, if the mediocre firms in its industries closed the gap with the best. Both countries miss out when policies to promote invention, such as China's push for “indigenous” innovation or India's recent patent laws, serve to stymie diffusion.

A year in China, foreign residents say, is like ten years outside. Its clock is already turning rapidly. But the cogs and levers that drive technological progress are as intricate and delicate as Su Sung's mechanism. China's government is in danger of trying to do too much. Its monumental efforts to educate and train have filled the tanks of its innovation engine. Now it is time for it just to let the water flow.

 

Hrothgar's rheumy eyes

Hrothgar's rheumy eyes

Animation takes on a whole new reality

CAN created images seem more real than reality itself? Portrait artists from Roman times onwards have exploited optical effects to flatter their patrons as well as to push the boundaries of perception. Think of the roughly 70 self-portraits and etchings Rembrandt made during his lifetime—his dispassionate struggle to comprehend himself physically and psychologically. You only have to look at the puffy cheeks, bulbous nose and furrowed brows to appreciate the artist’s genius at creating a three-dimensional sense of volume on a two-dimensional canvas.

Remarkably, Rembrandt seems to have been born with an optical defect that prevented him from seeing the world in three dimensions. After studying 36 of his self-portraits, Margaret Livingstone, a neurologist at Harvard School of Medicine, believes he suffered from “stereo blindness”—a disability that prevents the eyes from aligning correctly. People who are blind in one eye suffer from this disability.

Perhaps because Rembrandt couldn’t see with normal binocular vision, Ms Livingstone suggests his brain may have automatically switched to one eye for many visual tasks. If so, stereo blindness could ironically have helped him to automatically “flatten” the images he saw—allowing him to visualise them, like Mercator projections, ready to be laid out on a two-dimensional canvas. Interestingly, art teachers often advise their students to close one eye in order to flatten what they see.

Fast forward from The Netherlands of 350 years ago to modern Hollywood. More than ever, it seems, the digital artists who produce today’s computer-generated blockbusters are bent on recreating a vision of reality that is likewise more vital and compelling than everyday life.

None are more imaginative than the animators at Sony’s Imageworks, a production house in Culver City that provides much of Hollywood’s special effects. Their reimagination of “Beowulf”, a tale of monsters, dragons and doomed heroes based loosely on the oldest epic poem in the English language, opened last week to global acclaim.

Though shown mostly on conventional two-dimensional screens, Imageworks actually created three different “3D” versions: one for big-screen IMAX theatres, another for cinemas equipped to handle the popular Real D format, and a third for those using the new Dolby 3D projectors. This represents Hollywood’s most ambitious venture into 3D film yet.

No question that 3D makes “Beowulf” spring to life. But that’s more because the film handles the depth effect adroitly. Apart from the odd spear shoved in the audience’s face, it has none of the clichés that gave 3D movies such a bad name in the 1950s.

Technological improvements have also helped. In all three versions of “Beowulf”, two slightly different views are projected onto the screen. The brain then adds the sense of depth, just as it would when seeing the real world from two slightly different perspectives. Alas, you still have to wear nerdish spectacles. But the old complaints about nausea and headaches seem to have been licked.

Instead of having spectacles with a crude red filter for one eye and green for the other, the Real D system relies on circularly polarised light—with one lens polarising the light to the left, and the other to the right. Polarisation is also used in IMAX theatres. In this case, however, the light is polarised in a different linear direction for each eye, so as to match the polarisation of the two side-by-side projectors used to show the film.

In the Dolby case, the glasses use multiple coatings on each lens to filter out different sets of frequencies of light. In front of the projector is a rapidly spinning filter wheel, half of which is coated to let through only frequencies for the left eye, and the other half admitting only frequencies for the right eye. The spinning wheel is synchronised with the projector to allow alternate images to be sent to each eye six times for every frame of film.

Technology aside, the cinematic language has improved as well. Film-makers have always relied on tools like lighting and depth-of-field to shift the audience’s perspective, but the convergence of animation and 3D has made them pay greater attention to detail.

Using a lens with too long a focal length, for instance, makes the image appear flat. A wide-angled lens with too short a focal length can cause the image to become distorted and lurch unpleasantly out of the scene. From their work on films like “The Polar Express” and “Monster House”, both of which combined live action with digital imagery, the digital animators at Imageworks have learned to use their tools with restraint.

In one memorable scene in “Beowulf”, when the computer-generated character drawn from Angelina Jolie’s heavenly form and voice emerges naked from a pool, the focal length is suddenly reduced by five degrees. The difference is sufficient to make the image “pop” enough to draw a collective gasp from the (predominantly male) audience.

Even in two dimensions, “Beowulf” is still impressive. Nowadays, hybrid movies that merge live action with computer animation to produce three-dimensional digital maps of their real-life actors’ body movements include lots of fine-grained information about expression. Actors on whom the animated characters are based rehearse their lines over and over again with dozens of reflective dots stuck over their faces and bodies, while hundreds of infrared cameras record their every twitch.

For “Beowulf”, Imageworks even measured the electric currents in the actors’ eye muscles. That allowed them to take into account the way the eyeball, which is actually more pear-shaped than spherical, drags the eye’s lids and brows slightly when the gaze swivels. Similar computer controls were developed to make the animated characters’ cheeks puff and lips narrow according to the vowel sounds uttered. 

Without such detailed controls, facial expressions can appear as blank as a doll’s. With them, computer-generated characters suddenly become unnervingly real.

“Beowulf” is the most successful attempt yet to combine live action, animation, special effects and 3D techniques to create a world that is more real than any of the individual components could achieve alone. The result is so engrossing—especially in 3D—that the animated characters quickly demand your total attention and sympathy.

With a whole slate of similar 3D productions due for release next year, “Beowulf” could well mark the beginning of a new era for film. Even Rembrandt would have approved.

Radiant Information

Radiant Information

State-of-the-art light microscopy illuminates the exquisite details of life 

BRIGHT BRAINS: Thomas Deerinck of the University of California, San Diego, captured fine anatomical details of a 400-micron sample of rat cerebellum, coloring the Purkinje neurons green, the glial cells red and the nuclei blue (2-photon microscopy).

For all the delights and horrors human vision provides, it has only one way of collecting information about life: cells in the retina register photons of light for the brain to interpret into images. When it comes to seeing structures too small for the eye to resolve, ones that reflect too few photons for the eye to detect, microscopy must lead the way. The images displayed here, honored in the 2007 Olympus BioScapes Digital Imaging Competition for both their technical merit and their aesthetics, represent the state of the art in light micro­scopy for biological research.

Call it a renaissance, call it a revolution; in the field of light microscopy, it is well under way. Palettes of light are diversifying as scientists develop new fluorescent markers and new genetic techniques for incorporating them into samples, throwing open doors to discovery. For example, the researchers responsible for this year’s first-prize image employed a new technique, called Brainbow, to turn each neuron in a mouse’s brain a distinct color under the microscope. The method allows them to trace individual axons through a dizzying neuronal mesh and to map the wiring of the brain in a way that was impossible using earlier imaging techniques.

The precision of the tools is changing, too. Individual proteins can be tagged to watch how a molecule walks, and the minute details of cell division and differentiation can be witnessed live. Microscopists can paint fast in broad strokes of light to capture ephemeral events or more slowly in tiny strokes of light to see a piece of life in exquisite detail. And with new innovations in microscope technology, the lacuna between imaging speed and resolution continues to narrow.

The ability to see even the smallest biological structures with a range of techniques and to manage the massive amounts of resulting data builds a powerful, intimate portfolio of life—accessible to all and deeply meaningful to those who understand and wonder at its details.

The Semantic Web In Action

The Semantic Web In Action

Corporate applications are well under way, and consumer uses are emerging

SLIM FILMS

Six years ago in this magazine, Tim Berners-Lee, James Hendler and Ora Lassila unveiled a nascent vision of the Semantic Web: a highly interconnected network of data that could be easily accessed and understood by any desktop or handheld machine. They painted a future of intelligent software agents that would head out on the World Wide Web and automatically book flights and hotels for our trips, update our medical records and give us a single, customized answer to a particular question without our having to search for information or pore through results.

They also presented the young technologies that would make this vision come true: a common language for representing data that could be understood by all kinds of software agents; ontologies—sets of statements—that translate information from disparate databases into common terms; and rules that allow software agents to reason about the information described in those terms. The data format, ontologies and reasoning software would operate like one big application on the World Wide Web, analyzing all the raw data stored in online databases as well as all the data about the text, images, video and communications the Web contained. Like the Web itself, the Semantic Web would grow in a grassroots fashion, only this time aided by working groups within the World Wide Web Consortium, which helps to advance the global medium.