There are three general categories of radionavigation: long range, short range, and satellite. Long range radionavigation (OMEGA/VLF, LORAN) is useful for ships and international flights, and effectively covers the entire world at the expense of accuracy. Short range radionavigation (VOR, TACAN, DME, ILS) provides reasonably accurate position fixes within 10 to 100 miles of a station. Satellite radionavigation (GPS, GLONASS) can generally nail positions anywhere on the globe within a few meters.
LORAN (LOng RAnge Navigation) is based on groups ("chains") of 100 kHz transmitters in various parts of the world. Each chain has one master and several slaves. The master transmits a pulse, followed by the slaves at predetermined intervals. By measuring the propagation delay between the master pulse and the slave pulses, a LORAN receiver can construct hyperbolic position lines, and hopefully intersect enough of them to determine a position. The delay between master pulses is called the Group Repetition Interval (GRI). It is possible to identify a LORAN chain by its unique GRI. LORAN power output is usually on the order of 500 kilowatts.
OMEGA was a worldwide navigation system based on phase differences between very low frequency (VLF) radio signals (approximately 10.2 kHz). There were eight OMEGA stations throughout the world, each putting out a 10 kilowatt CW (continuous wave) signal through a large, vertical mast. OMEGA stations were also known to blast massive amounts of ground wave RF energy through buried radials, probably for the benefit of submarines. Of course the probability that this increased the risk of cancer for nearby residents was heavily downplayed.
The US Navy also used the OMEGA frequencies to send VLF command signals to its submarines. Although not really intended for navigation, they worked just as well as the actual OMEGA transmissions. Many OMEGA receivers also supported Navy VLF reception.
Although officially OMEGA was accurate to only a four nautical mile radius (partly to address concerns that OMEGA could be used for ballistic missile navigation), it is likely that military equipment was able to obtain much higher accuracy. Theoretically, with good equipment and using all available OMEGA frequencies, the system could resolve positions down to just a few meters. Not bad for a system built in the 1960's.
In contrast to LORAN and GPS, OMEGA was a relative system, based on counting iso-phase lanes (circles of equal radius from the transmitter site; as far as I can tell, a "lane" was simply the span of one wavelength, which was pretty long at VLF frequencies). The practical result was that OMEGA was useless if you didn't know your starting position. Power losses could really screw OMEGA up, because the receiver would lose track of its lane crossings.
OMEGA was shut down in September, 1997 due to the wide acceptance of GPS technology. Many consider it a good riddance. LORAN is still active and is widely used for aircraft and ship navigation, often as a backup to GPS.
Short range navigation systems are generally based on low-power transmitters in the VHF and UHF bands.
The most common short range radionavigation system is VOR, the VHF Omni Range. VOR stations transmit two signals: a constant, omnidirectional reference signal and a directional, phase-shifting signal. When the directional signal is aligned with magnetic north (a 0-degree heading), the signals are in phase, and when it is aligned with magnetic south (a 180-degree heading), the signals are completely out of phase. By calculating the phase difference between these two signals, a VOR receiver can determine its bearing relative to the ground station. This is displayed with a simple needle as a deviation from a pilot-selected heading. The needle is called the Course Deviation Indicator (CDI), and the heading to track is selected with the Omni Bearing Selector (OBI) knob. With a little practice, VOR tracking requires almost no thought.
DME, Distance Measuring Equipment, is a very simple but precise method for measuring the distance to a VOR station. The onboard DME transmits a pair of radio pulses with a particular timing and waits for the ground VOR/DME station to respond with pulses of the same timing. The DME receiver determines distance from the delay between transmitting the pulses and receiving the correct response. DME is unique in that it requires two-way communications between the aircraft and a ground station. A common use of DME is to fly a circular arc around a VOR/DME station. This is very difficult to do without the direct distance reference.
TACAN, TACtical Aid to Navigation, is a military spinoff of VOR/DME that operates in the L-band (1 GHz) range. Same basic idea. Many VORs are actually VORTACs, since they transmit both VOR and TACAN signals. TACAN-equipped VOR stations have a special symbol on aeronautical charts. VORTACs also support DME.
A localizer is essentially a very narrow slice of a VOR signal aimed along a runway's approach path. Combine this with a glideslope signal (same thing, but turned vertically) and a few other components, you have an ILS (instrument landing system). The localizer and glideslope needles are usually located in the same instrument display, providing a nice crosshair that you can just follow down to the runway. Whereas taking off is optional, landing is unfortunately mandatory, and the ILS is good to have if you can't see the runway due to clouds. Of course this requires an instrument rating, special equipment, and quite a bit of practice.
Finally, I'd be amiss if I didn't point out ADF, the Automatic Direction Finder. ADF is an aircraft instrument that simply points a needle in the general direction of a MF (medium frequency) radio signal, such as an AM broadcast station. ADF is very occasionally useful. At least 50% of ADF units in rental aircraft seem to be broken, simply because nobody cares. I'm told that ADF is more popular outside the US. Eeh, another panel instrument, more blinkenlights!
GPS (NAVSTAR) solves for position by timing the differences between predictable (pseudorandom) signals from multiple satellites. A full 3D position fix requires four satellite signals, and of course the accuracy depends on the relative positions of those satellites. GPS uses L-band (microwave) radio frequencies (1575.42 MHz and 1227.6 MHz). There are two sets of signals, an open one for civil use and an encrypted one for military use. Following a presidential order on May 1st, 2000, the civil signal is no longer intentionally degraded by the insertion of random errors ("Selective Availability"), but it is fundamentally not as accurate as the military code.
Differential GPS (DGPS) enhances GPS accuracy by measuring the error of the GPS system at known positions on the ground and transmitting correction signals to mobile GPS receivers. Individual users of the GPS service are responsible for maintaining their own DGPS correction stations. However, there are lots of DGPS stations out there, and many commercially available GPS receivers are able to find and integrate these correction signals. The Department of Transportation's WAAS (Wide Area Augmentation System) is simply a large network of DGPS stations designed to improve GPS accuracy within the borders of the US enough to perform precision aircraft approaches.
GLONASS (GLobal Orbiting Navigation Satellite System) is a Russian equivalent to GPS. It differs in some technicalities (FDMA across about 12 MHz rather than CDMA on a single frequency, different orbits, unstable funding, etc), but it is still available for use. New GLONASS satellites have been launched as recently as 2003. Some GPS receivers also offer the ability to track GLONASS satellites.
A healthy dose of conspiracy theory:
Lots of good info on various radionavigation systems:
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