I am going to say this is the problem. Cyanogenmod IMO is one of the worst “custom” roms out there. I’d be interested to see if you put another ROM, like Paranoid Android, on there, if it made any difference.
I’m betting it would.
Also a quick google search returned many results with oneplus having GPS issues across the board.
I put these here to hopefully help you. It seems like aGPS does not work very well at all. Are you on “Battery Saving” mode for GPS? If so turn it on high accuracy and see if it gets better. From what i have read “Battery Saving” mode is basically useless on the OnePlus One. They will need to fix it with a software update.