Whenever I read something about GPS antenna's that teaches me something I usually file it away. Here are a few of the articles that I've looked at related to choosing a good GPS antenna. Not in any particular order and you might have to read the whole thing to get one good paragraph but that's the way it goes. I've got more but have to find them, I'll add them when I come across them in the future.
The ability to design and build a good antenna is formidable and would require some very expensive equipment. A new company RF Explorer has brought out signal generators and spectrum analyzer's that may do the job but you would need both units, a directional coupler and misc connectors that would be close to $750 USD to start playing with the design. A good background in working with microwave frequency's might help a lot.
Cheers
Steve