Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 21

CHAPTER 2
Fundamentals of Satellite Navigation

Elliott D. Kaplan and Joseph L. Leva
The MITRE Corporation
Dennis Milbert
NOAA (retired)
Mike S. Pavloff
Raytheon Company

2.1 Concept of Ranging Using TOA Measurements

GPS utilizes the concept of TOA ranging to determine user position. This concept
entails measuring the time it takes for a signal transmitted by an emitter (e.g., fog-
horn, radiobeacon, or satellite) at a known location to reach a user receiver.
This time interval, referred to as the signal propagation time, is then multiplied
by the speed of the signal (e.g., speed of sound or speed of light) to obtain the emitter-
to-receiver distance. By measuring the propagation time of the signal broadcast from
multiple emitters (i.e., navigation aids) at known locations, the receiver can deter-
mine its position. An example of two-dimensional positioning is provided next.

2.1.1 Two-Dimensional Position Determination
Consider the case of a mariner at sea determining his or her vessel's position from a
foghorn. (This introductory example was originally presented in [1] and is con-
tained herein because it provides an excellent overview of TOA position determina-
tion concepts.) Assume that the vessel is equipped with an accurate clock and the
mariner has an approximate knowledge of the vessel's position. Also, assume that
the foghorn whistle is sounded precisely on the minute mark and that the vessel's
clock is synchronized to the foghorn clock. The mariner notes the elapsed time from
the minute mark until the foghorn whistle is heard. The foghorn whistle propaga-
tion time is the time it took for the foghorn whistle to leave the foghorn and travel to
the mariner's ear. This propagation time multiplied by the speed of sound (approxi-
mately 335 m/s) is the distance from the foghorn to the mariner. If the foghorn sig-
nal took 5 seconds to reach the mariner's ear, then the distance to the foghorn is
1,675m. Let this distance be denoted as R 1. Thus, with only one measurement, the
mariner knows that the vessel is somewhere on a circle with radius R 1 centered
about the foghorn, which is denoted as Foghorn 1 in Figure 2.1.

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