Invisible Stars - GPS Declassified: From Smart Bombs to Smartphones - page 80

Fig. 5.2. Instantaneous navigation math. Mathematicians at the Naval Research Laboratory
formulated this solution to the problem of two-, three-, and four-dimensional instantaneous
navigation using passive ranging signals from satellites. (Courtesy Naval Research Laboratory)
effects and receiver quality, but the accuracy of the Standard Positioning Ser-
vice offered to civilians is generally three meters or less—under ten feet—99.99
percent of the time. Various techniques used today, including augmentation
systems discussed in later chapters and high-end receivers that measure the
carrier wave itself, can improve that accuracy to a few millimeters. 49
Before gps receivers display latitude, longitude, and altitude figures or a
moving dot on a map, computer chips inside them perform an astonishing
number of mathematical calculations. For a glimpse at the type of formulas
involved, consider figure 5.2, which shows how Naval Research Laboratory
mathematicians in 1971 formulated a solution for instantaneous navigation
by satellites in four dimensions.
After locking onto a satellite signal the gps receiver begins repeating the
signal's digital navigation sequences the way people sing “Row, Row, Row Your
Boat” in the round. It then delays its own sequences until they synchronize
with the incoming signal. The amount of delay equals the signal's travel time
from satellite to receiver, which, multiplied by the speed of light, yields the
satellite's distance. With computed distances from three satellites and the
accurate time from a fourth satellite's clock to synchronize the battery-powered
quartz clock in the receiver, the receiver's computer can perform the geomet-
ric calculations (variously called trilateration, trilateralization, or triangula-
tion) to determine a three-dimensional position as it moves in real time.
Society has become habituated to inexpensive portable computing power.
Without it, satellite navigation would be unavailable to everyday users. Many