A navigation system that produces hyperbolic lines of position (LOPs) through the measurement of the difference in times of reception (or phase difference) of radio signals from two or more synchronized transmitters at fixed points. Such systems require the use of a receiver which measures the time difference (or phase difference) between arriving radio signals. Assuming the velocity of signal propagation is relatively constant across a given coverage area, the difference in the times of arrival (or phase) is constant on a hyperbola having the two transmitting stations as foci (see illustration). Therefore, the receiver measuring time or phase difference between arriving signals must be located somewhere along the hyperbolic line of position corresponding to that time or phase difference. If a third transmitting station is available, the receiver can measure a second time or phase difference and obtain another hyperbolic line of position. The intersection of the lines of position provides a navigational fix (see illustration). User receivers typically convert this navigational fix to latitude and longitude for operator convenience.
Typical grid of hyperbolic lines of position formed by a master (M) and two secondary stations (W and X).
The choice of frequency and locations of transmitters determines both the utility and the accuracy of hyperbolic navigation systems. In general, longer baselines (see illustration) enhance accuracy; however, transmitter power limitations may constrain a system to shorter baselines in order to maintain accurate synchronism.
