The current GPS system uses a number (currently about 28) satellites in low earth orbit that broadcast time pulses. These sats were originally put up to provide early warning and precise location of the electro-magnetic pulses generated by detonating nuclear bombs. They listen for the EMP and mark its arrival time down to under a billionth of a second. That time is then transmitted to a base station that can calculate the exact location of detonation. Since the sats have a good clock, they were simply provided with a few transmitters and that data an be used on the ground to determine position.
Since the EU has no need to the large spy sats that need good clocks, their Galileo system is going to cost the users much more than the Navstar system which begs the question, why put clock in orbit when there are already many there in the form of Pulsars?
Pulsars are neutron stars that are spinning very quickly in such a way that their magnetic field emits a radio (or light) beam much like a lighthouse when observed form earth. The ones we know about are from about 50 light years to 35,000 light years away. They tend to move at speed up to 1000km/sec (2 million miles an hour) and are very precise.
For example the first known millisecond Pulsar (B1937+21) rotates with a period of .001557806468819794+/-.000000000000000004 hz. It is 31474 light years away and moving at 22 km/s and has spinning spinning for about 250 million years. The rate at which its spinning has changed is is about the same order as atomic clocks on earth. Older pulsars have much more stable rotation times.
Why is this already being done?
The Navstar GPS system was launched in 1978 but had been designed earlier. The first pulsar was discovered in 1967 but it took years to discover more of them. It wasn't until the 1990's when large numbers of them had been found and their properties quantified.
Other problems will need to be solved as well. The current GPS sats are orbiting and the GPS receivers have to take into account such things as Doppler shift from the signals, orbit changes because of the sun moon and even Jupiter and Saturn. The time signals then have to be adjusted because of Relativistic effects and there are still a few factors that are unknown. A Pulsar based system would have to take all these into account in addition to the relative orbit around the sun, as well as the suns orbit in the solar system.
The receiving antenna and circuits would also require solving some new problems. Pulsars tend to be observed in the 1.4, 2.4 and 4.85 GHz bands. The 2.4 GHz band is very close to commonly used bands and may result in excessive interference. 1.4 GHz detection systems are similar to the 1.6 GHz Navstar GPS receiver but the signals being searched for are different.
A typical GPS receiver made today will have more processing power and memory than an IBM XT. With the proper receiver, a device could be built today to do the needed calculation and display a position with the same or better precision than the Navstar GPS system.
Pulsar is a trademark of Expert Automation dealing with global positioning systems and products.