Chapter 12: Terrestrial Hyperbolic Systems
Loran-C and its modern descendant eLoran fix position from differences in time of arrival, producing hyperbolic lines of position independent of satellites.
How hyperbolic fixing works
A chain consists of a master and two or more secondary stations transmitting pulses at 100 kHz with a fixed group repetition interval. The receiver measures the time difference between master and each secondary; a constant time difference defines a hyperbola with the two stations as foci. Two such hyperbolas intersect at the fix. Accuracy is best where the LOPs cross near 90° and degrades near the baseline extensions where they become nearly parallel.
Errors and the eLoran case
Groundwave is used for navigation; skywave arriving later must be rejected by tracking the third cycle of the pulse, and cycle slip produces gross error. Propagation over land is slower than over seawater, requiring additional secondary phase factor corrections. Repeatable accuracy is far better than absolute accuracy, which is why Loran was prized for returning to a fishing ground. eLoran adds a data channel and differential corrections, giving 10–20 m accuracy and a high-power, hard-to-jam complement to GNSS for position, navigation and timing.
- Strength: high power, terrestrial, independent of GNSS
- Weakness: limited coverage, baseline extension geometry, land path corrections
Key takeaways
- • Time difference of arrival gives a hyperbolic line of position.
- • Avoid fixing on or near a baseline extension — geometry collapses there.
- • eLoran's role today is resilient PNT backup to GNSS, not primary navigation.
Knowledge check
Immediate feedback with rationales. Answer each question to see the explanation.
Chapter 12 quiz
0 of 3 answered
1.A constant Loran time difference defines:
2.Loran fix accuracy is poorest:
3.The principal modern argument for eLoran is: