I've been doing a bit of research into antenna theory as I've never needed to learn it and after looking, a quarter wave whip is actually pretty plausible. Using 1.575GHz as the GPS frequency, I'm looking at an antenna length of 47.6mm. The problem I wonder though: How can I interface this with my GPS module? I could just solder a small SMA connector to some insulated copper wire and be done. Would this be the correct method of interfacing the antenna? If I'm using a module with a GPS module on a PCB, am I safe to assume that up to the SMA connector, all transmission line effects would have been solved by the module engineers?
EDIT: Also, isn't the ceramic antenna already a form of patch antenna or am I on the completely wrong end of the stick here? That little ceramic block seems pretty magic to me as it is!
The ceramic block thing most likely qualifies as a patch antenna, yes. The point is usually that you have a relatively wide radiating surface (a patch), to make up for the fact that you don't have any length behind it. You're coupling to electric field, but not magnetic field (indeed, most of the current flow and associated magnetic field may be trapped under the patch, via some short connecting wires or traces). Added capacitance (such as from a ceramic block) will act to shorten dimensions even further, but, the reactive current flowing through that capacitance is entirely internal, and does not couple into space. So you get an even lower resonant impedance (which makes things even worse against the already low inductance, necessitating some sort of matching network), more internal losses, and even lower radiation resistance. (The matching is usually on the part itself, so the transmission line sees 50 ohms or whatever as appropriate -- at least, at one narrow range of frequencies.)
The logical extreme of a very small antenna (patch or otherwise) is a resonator in a box: exclusively internal losses, with no radiation resistance whatsoever.
Electrically, the two cases are indistinguishable -- they both can be matched to 50 ohms at resonance, and have a narrow bandwidth; but one, the power just goes into heat, while the other actually communicates with the outside world.
As for 1/4 wave whip antennas, the problem is, to make a textbook case, you need the whip part to be vertical above a horizontal ground plane. Often, the ground is provided by an array of in-plane 1/4 wave grounding rods, or a PCB or something; solid ground is not required, but it does need to carry current radially.
The dipole replaces the ground plane restriction with a 1/4 wave in the opposite direction. Replaces one obstacle with even more length...
The free space you necessarily want around these antennas also ranges from 1/4 wave (can be helpful -- acts as a reflector) to 3/4 or more (avoid 1/2 or 1 wave, that's a null). You need volume as well as length to couple into space effectively.
You'll never be able to accommodate a proper, high efficiency antenna in a compact device, so you'll have to settle for something that's still close in (so it experiences proximity / loading capacitance, and has a smaller physical length, which means less to couple into space), and make it as much to the outside as possible. Hopefully, that's still good enough for useful GPS reception.
As for design or selection, that's really hard to say. Which is why the internals of cellphones are all so peculiar: they can afford the research. If you have a 1.5GHz signal generator and voltmeter, you can try testing it for resonance and matching, but it's just a shot in the dark* otherwise. You can get self-adhesive and patch antennas for various close quarters, but if they specify what proximity they are supposed to operate within... you really don't have much choice but to match your mechanicals. And if they say "keep clear up to at least X", it's probably because they're not trying any proximity at all, so have fun with that...
*Ha, because you don't know where the electromagnetic energy (light?) is. Get it?...
The one advantage your ceramic patch antenna has is, it's designed for board mounting, so one side should be in proximity to a board. The rest should be clear. But that's still better than trying to blindly fudge a more close fitting antenna.
Tim