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--- datatrak:intro [2020/05/31 14:58] – [Three-step positioning process] philpem
+++ datatrak:intro [2023/01/03 22:55] (current) – [Three-step positioning process] philpem
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-====== Introduction to hyperbolic navigation and Datatrak ======
+====== Introduction to Datatrak and hyperbolic navigation ======
 Hyperbolic navigation is a means of navigation which works by measuring the difference in arrival time between two signals. This may be done by measuring either time-of-arrival or phase-difference. Phase difference is usually preferred as it removes the need to precisely synchronise many transmitting stations.
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 ^  Phase  ^  Frequency  ^  Wavelength (lane width)  ^  Resolution  ^
-|  "super-coarse"  |  $\Delta F = 80 Hz$  |  $\lambda \approx 3747 km (2329 miles)$  |  $\frac{3747 km}{1000} \approx 3.7 km$  |
+|  "super-coarse"  |  $\Delta F = 80 \mathrm{Hz}$         |  $\lambda \approx 3747 \mathrm{km} (2329 \mathrm{miles})$  |  $\frac{3747 \mathrm{km}}{1000} \approx 3.7 \mathrm{km}$  |
-|  "coarse"  |  $\Delta F \approx 13 kHz$  | $\lambda \approx 23 km (14.3 miles)$ |  $\frac{23 km}{1000} \approx 23 metres$  |
+|  "coarse"        |  $\Delta F \approx 13 \mathrm{kHz}$  | $\lambda \approx 23 \mathrm{km}    (14.3 miles)$           |  $\frac{23 \mathrm{km}}{1000} \approx 23 \mathrm{metres}$  |
-|  "fine"  |  $F \approx 130kHz$  |  $\lambda \approx 2.3 km (1.43 miles)$  |  $\frac{2.3 km}{1000} \approx 2.3 metres$  |
+|  "fine"          |  $F \approx 130 \mathrm{kHz}$        |  $\lambda \approx 2.3 \mathrm{km}  (1.43 miles)$           |  $\frac{2.3 \mathrm{km}}{1000} \approx 2.3 \mathrm{metres}$  |
 In practice, the total accuracy is limited by variations in propagation conditions and measurement error.