Define exactly what you mean by "a swarm of satellites"? Each satellite in a GPS style constellation (and I haven't looked into the details, but I believe that

Define exactly what you mean by "a swarm of satellites"? Each satellite in a GPS style constellation (and I haven't looked into the details, but I believe that all of the major GPS competitors use the same technique- Galileo, GLONASS, Beidou) has its own atomic clock in space and really can only do satellite navigation stuff[1]. Generally speaking, in the medium altitude orbits preferred for this mission, 24 is minimum for world-wide network. Having some more of these specific, large satellites is good: it helps you have more of them in sight at any given moment anywhere in the world, which should give you better accuracy, though having them too close to each other doesn't really help that much, and it helps to have some in reserve so if there is a problem with one you can activate another and quickly fill the gap. According to wiki there are 31 GPS sats operational (plus four in orbit but on reserve), 31 (plus five in orbit but on reserve) Beidou, 23 operational Galileo, and 24 GLONASS operational. So you can see that all of the major operations are at about the same number of satellites for a traditional global satellite navigation system. It might be possible to do a different technique and use a swarm of internet satellites: something like how the TRANSIT (aka NAVSAT) system could, in theory, provide navigation from satellite internet machines. In practice you'd need to know each member of the swarm's orbits very precisely to have sufficient accuracy with their Doppler shift, which means that you prefer station-keeping burns to be infrequent[2], and because they are in low orbit- lots of drag, so they need to regularly burn- that's harder to do (this is why the existing systems use medium orbits). Also, a TRANSIT style operation can't really give you turn-by-turn directions on your cellphone, it was about updating a very powerful submarine inertial guidance system with big honking mechanical gyroscopes every few days, the INS on your phone isn't nearly good enough to handle turn-by-turn directions with TRANSIT update rates. 1: Japan has their own Just Japan system, QZSS, which I have vague memories is different, but I don't remember enough to explain it. 2: The way these systems work, you can never really have more accuracy than you know the satellites location in space. In general, you want ground based systems to track and update orbital parameters after every satellite burn to get the necessary accuracy.