Effect of station angle on location errors

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Problem 7.2

If the error in Shoran time measurements is , what is the the size of the parallelogram of error in Figure 7.2a when (a) and (b) ? Take the velocity of radio waves as km/s.


Shoran is a radio-navigation device which measures the 2-way traveltime between the point of observation and a fixed station. Using two fixed stations, the point of observation can be located by swinging arcs centered at the two stations; for large distances the arcs become nearly straight lines.

The traveltimes are subject to error , so the ranges are , , 2. Swinging the four arcs corresponding to these time values, we get a parallelogram of error such as that in Figure 7.2a; the location lies somewhere inside this parallelogram.


In Figure 7.2a, the error in range

Figure 7.2a  Parallelogram of error for traveltime uncertainty of


The long diagonal m.

The short diagonal m.

To get the figure for we merely reverse the arrow on or ; therefore the error values are the same as for .

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