In a lot of modern airliners the Flight Management Computer will use the 3 DME method to keep the Inertial Navigation System position updated, though this is being superceded by GPS updating. It is fairly accurate and easy enough for the computer to keep channeling 3 different frequencies. This is known as rho-rho-rho navigation. The method described above with VOR radial and DME is known as rho-theta navigation.
Regards, Rob
VOR indicator in vc 10
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Rho-Rho-Rho Navigation
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