When I read the news about how expensive new GPS satellites are and how expensive Galileo became, I can't help thinking of a cheaper solution. Of course, nobody will ask me; one reason systems like GPS are so expensive is that the industry seeks to make profit from the state. They are not interested in making it cheap.
As usual, the price tag comes with the architecture. So what I'm sketching here is a cheap architecture, which allows to create a cheap positioning system with different approaches to make it more useful and more accurate. The target is clearly civil usage, there will be no means whatsoever intentionally added for military use.
The first take to make this cheap is to reduce load and costs of satellite starts. Anything that goes to space is extremely expensive. What absolutely needs to go up is a transponder that reflects a signal downwards, plus energy systems necessary for operation (solar panels and batteries). In many cases, this transponder should be an additional load to a commercial transponder (telco or TV), which would result in a geostationary position.
So the next question is: How many visible satellites do you absolutely need to obtain your position? The answer is: You need one. All the other stuff can be done on ground. If you only want a 2D position, you don't need any satellite at all, you can use the mobile phone systems installed in almost all inhabited areas of the world by now. It might not be as accurate, but if we are allowed to put some gadgets into the base stations, we can improve that by a vast amount. And it's still cheap, since we can install probably millions of units for the price of one satellite.
So our starting point is: we put one satellite into a geostationary orbit, which just has an added payload, the transceiver. This transceiver receives packets from ground stations, and retransmits them, spreading them over the globe. How many ground stations do you need? Four per satellite, if you want to find out the position of the satellite (if it is already known well enough, one ground station is sufficient). How many atomic clocks do you need on ground? One. All the other ground stations can just work like a satellite: Reflect the packet they receive, adding their position.
Satellites add their ID. Satellites can pingpong packets between them until the string of IDs exceeds the maximum capacity - all this ping-ponging back and forward, up and down adds information about the relative positions between the transceivers.
Having a geostationary orbit for at least one visible satellite is a good idea, for several reasons:
Of course, it also has downsides:
So after all, for a purely satellite driven system, you also need polar or at least highly inclined orbits. This is the more costly part, because there you can't just add the transceiver as another payload to a big telco/TV satellite. You still might find projects with polar orbits where an additional payload is feasible (earth observation satellites). So use geostationary orbits where possible, and add those other satellites only as necessary.
We have a number of requirements for the actual signal:
My conclusion is that pulse-ultra-wideband is the most appropriate modulation format fulfilling all these requirements. We get low energy by not sending the pulses very often, we get also low power in the receiver, which can turn of the amplifier when it doesn't expect a pulse. The stealth quality of pulse-UWB is well known; encryption can hide the signal completely in the noise, undetectable to anybody who does not know the complex pattern of the signal.
Pulses also have a high accuracy for time-of-arrival location systems, since the pulses themselves are very short (1GHz=30cm, 10GHz=3cm), thus the location obtained can be very precise. For multi-path situations, the first pulse received is used for timing; additional echos could be used to improve SNR, but in this case, the actual data is already known.
The actual frequency used should be well below the energy band absorbed by water.
The concept includes local stationary transceivers, e.g. in base stations. These are cheap to install and maintain, and they offer much higher precision than signals from the orbit. There's no ionosphere which bends the rays, there are usually no clouds tho shield them off, and since the stationary transceivers send mostly horizontal, no thick steel-reinforced concrete ceilings shield the signals (indoors). These transceivers can be integrated into the time-keeping system necessary for a base station.
I'm quite confident that this concept would reduce costs by about an order of magnitude compared to Galileo, while yielding better results. It can be installed incrementally, and it is possible to allocate at least some of the costs regionally (especially the geostationary satellites). Local base stations may give regions more control over the system.