I should add something I did some time ago that worked great. I made a two arm Archimedian spiral using a piece of graph paper as a template.
The feed point is the center and you use a square, starting at the outer row (make sure the suare is an equal square meaning it shouldnt be larger on one side than another, (just rectangular), the number of boxes should be equal. Lots of different sizes "work" I have yet to work out how many work best. This is a largely frequency independent antenna and its virtually foolproof. Work your way inward skipping every alternating line, make a square archimedian spiral where 50% of the area is conductor, 50% is not. At the center you will have two squares diagonal from one another where you keep the copper from touching and feed it there. If you want you can short out the entire outer row to make a ring. (or use resistors, Ive heard this works better) Then the entire antenna will be at ground potential which prevents ESD. As you will be using this for GPS which usually is supplied with power, (but it doesnt need more signal, usually because its big. USE a DC block. (capacitor of adequate size in series with the antenna terminal so that it doesnt present what some GPS input stages will interpret as a short and raise an alarm. Ublox in particular does not like a short . The square shape electrically has the effect of a meander line which slightly reduces the size of the antenna, which you'll see is kind of a desirable property so dont worry about it. You should end up with a broadband circularly polarized, fairly low gain antenna that works great for GPS and similar kinds of signals. It offers excellent RHCP properties if its placed in the right handed orientation. The thumb of your right hand should be facing up, in the axis you are intending to receive from. (not left) Your fingers represent the arms of the antennas direction. If yoiu flip it over it will receive predominately LHCP. Some satellites use LHCP. Reflection reverses the polarization so you will want LHCP for the feed antenna if you want a parabolic dish, say, for RHCP. (or a GPS antenna intended to be placed to pick up reflections, say on the bottom of a car)
This square broadband archimedian spiral works well as a GPS (or Glonass, Beidou, QRZSS, or other GNSS system on any frequency.. within its frequency range.. Its a very decent antenna even one suitable for use in geodesy. Which would otherwise cost much more than one likes to pay for a GPS antenna. ($100 or often more)
The thumbnail below shows an example, that should be "RHCP" polarization, which is what one needs for GNSS systems like GPS and Glonass, etc. One could also short it around the exterior. Which might offer some advantages, extending the antenna that fills a certain amount of space a bit more low frequency range before it trails off.
This paper by Xiaoxing Zhang, Yefei Han, Wei Li, and Xuetao Duan explains many of the issues at play and the various tradeoffs one may want to play with. . It should be noted that this square shape lends itself to PCB use and also that its smaller than an equivalent antenna that is traditionally circular. The pattern may have very mild abnormalities but the symmetricity of the shape should make the pattern balance out somewhat. In any case it turns out better than one might expect...
If you use coax to feed it try putting ferrites on the feedline to get rid of the lump if you find you have one. If this antenna is implemented on PCB material, earth fulfills the function of a partial RF absorber beneath it well. The amount of water in the earth will change the reflectance and absorbtance of the earth, this can be used to measure the amount of moisture in soil with great precision by using the GPS satellites with their recisely known locations as an aid to this measure the ratio of LHCP to RHCP as a reflected signal will contain more LHCP than RHCP. That means the soil is wetter.
Thanks also to the ANTCAL friends for pointing this out!