English: This is the geometry of a basic hyperbolic navigation system. Hyperbolic navigation is a class of navigation systems based on the difference in timing between the reception of two signals, without reference to a common clock.

Here, the three ground stations are Stations A, B, C, whose locations are known. The times it takes for a radio signal to travel from the stations to the receiver are unknown, but the time differences are known. That is, ${\displaystyle t_{A},t_{B},t_{C}}$ are unknown, but ${\displaystyle t_{A}-t_{B}}$ and ${\displaystyle t_{A}-t_{C}}$ are known.

Then, each time difference locates the receiver on a branch of a hyperbola focussed on the ground stations. Then the ___location of the receiver is at one of the two intersections. Any other form of navigation information can be used to eliminate this ambiguity and determine a fix.

Created in GeoGebra. Permanent link here.

Additional note: We assume that the earth is approximately flat in this diagram. This assumption can be corrected. In general, the surface of equal time difference is a hyperboloid in space, and it intersects with a sphere (the surface of earth) at an ellipse. To see this, note that a hyperboloid

To locate a point uniquely in space, one must use at least least 4 ground stations. The receiver can then be located as one of the unique intersections of the 6 hyperboloids (one hyperboloid for each pair of the ground stations).