Estimation of Position, Velocity and Time Accuracy of the estimates of position, velocity and time (PVT) obtained from GPS can vary widely with time, place and—most important—a user’s resources. The SPS performance specifications (e.g., the oft-quoted x-meter horizontal accuracy better than 95% of the time, where the value of x was 100 in the days of SA and is about 10 now) are a conservative estimate of the GPS performance available in real time with a minimum-capability receiver operating in an autonomous mode. A resourceful user can do much better.
Navigation is the art and science of charting a course from point A to point B and staying on that course. The subject has a long and fascinating history, what with some of our forebears crossing vast oceans guided only by the stars. But these were brave souls for the stars couldn’t be counted upon to be visible. The technology of the twentieth century has now solved this problem nearly completely by placing artificial stars in the sky. These stars shine all the time, radiating extraordinarily faint radio signals. What the signals lack in raw power, however, they make up in cleverness of design, and provide far more information than the sailors of old ever got from the stars on the clearest of nights.
The NAVSTAR Global Positioning System (GPS) is the first of this new breed of global navigation satellite systems to become operational. Buy a $100 GPS receiver and a map, and you wouldn’t be lost as long as you have a clear view of the sky. Or, buy a pair of more capable receivers for about $5000 each and, with a careful analysis of the measurements, you would be able to tell if the earth under your feet moved a few millimeters while you weren’t looking.
The GPS signals travel 20,000 kilometers from a medium earth orbit and arrive at the earth’s surface with a power density of only 10–14 to 10–13 watts/m2. Even so, these electro-magnetic whispers:
• Enable high-precision ranging even in the presence of natural noise and modest amounts of man-made interference. Indeed, the precision of the pseudorange measurements is approximately 0.5 meters for the civilian code. This remarkable ability derives from the auto-correlation properties of the spread spectrum codes that modulate the signal from each satellite.
• Distinguish the direct (desired) signal from reflected signals. This handy property also derives from the auto-correlation properties of the codes.
• Allow the satellites to simultaneously use the same transmission frequencies. The satellites do not offset their carrier frequencies. Nor do they use a time sharing scheme, where each satellite must transmit only during a prescribed time slot. As we shall discover, this multiple-access property derives from the crosscorrelation properties of the GPS codes.
• Carry all the ancillary data required for position fixing. each satellite sends an estimate of its ephemeris and clock offset relative to GPS time.
The GPS signal and user receivers act in concert to achieve these goals. Both are carefully crafted and well worth our study. To enable this study, Chapter 8 provides a review of the signals and systems tools that we will need in the remainder of this book. It includes an introduction to convolution, Fourier series, Fourier transforms, and Laplace transforms.