Galaxy S3 Reports wrong location

I just got a Galaxy S3, upgrading from a Galaxy S (Captivate).

Overall, I like the phone better, but it tends to report me in completely wrong locations. When I first got the phone, it thought I was in Massachusetts instead of Kentucky. Yesterday, it decided that I travelled from Louisville, KY to Washington, DC and back, with my location history showing marked points in between. During that time, I was really only in a small, five-mile area in downtown Louisville.

This leads to lots of problems, especially with weather apps that use the phone's location to alert me of local weather problems.

As soon as I open an app that requires GPS to fix my location, the problem is resolved and all of my other apps that depend on location work correctly, so it seems to be related specifically to the LTE system. I also never had this problem with my old phone, which used 3G instead of LTE.

Kim