Sorry if that came across as overly critical ykh, it was not meant to be.
"Patch" is the oh-so-technical term for the small (20mmx20mmx2-4mm) ceramic GPS antenna. Generally, it needs to be mounted with clear PCB space around it (ground plane) to improve reception. They tend to be directional (they have gain-lobes or something) so will receive signals best from perpendicular to the mounting surface. Because the GPS signal is so weak (much weaker than the cellphone or wireless net signals) if you cover them with anything more than air and thin plastic (2-3mm) they don’t work very well at all. Anything metallic over the path will shield the signal; this includes anything like LED, LCD or OLED displays.
When I talk about the small arc or line of sight, I'm talking about the line of sight from the GPS receiver to the satellite overhead. If anything solid gets in the way (building, big trees etc) the signal is lost. A GPS receiver needs to "see" three satellites minimum to work. If you are surrounded by lots of tall buildings, there is only a small area of sky in which to see the satellites, and since there are a limited number of them up there, the chances of being able to see three or more is reduced.
The other option is to use a more conventional non-directional antenna (old cellphone style), but this would ruin the dog-tag idea.
Phew. I've been hangin around the engineers too long