My GPS is working quite well either in sport tracking programs as well as osm navigation. Please keep in mind, the problem about wrong speed and distance calculation is most likely a bug in a system library and has nothing to do with the gps system, hopefully we will see a rom update to 4.2.2 or 4.3 with a fix.
Having said as much, currently I sit in the basement, around 1m away from the window and get a fix in gps test in roundabout 10s with 13 satellite in sight, even though we have a solid overcast.
If your phone is rooted, you could try do the following steps, maybe this will help a bit.
- First geht the app "Mobiluncle MTK Tools" in your play store.
- Open the tool, allow superuser access and choose "Engineer Mode".
- Next "Engeneer Mode ( MTK ).
- Swipe to right for "Location"
- Choose Location Based Services
- In the menu bar on top choose AGPS
- Enable A-Gps
- In the menu bar on top choose EPO
- Enable EPO
- Enable Auto Download (this will use a bit of data, for me around 4Mb per month)
- Touch EPO button to download the needed files
- In the menu bar on top choose GPS
- Touch Button "GPS (OFF)" to start GPS
- Wait till you get a lock (maybe you'll need to get outside for that)
- Touch Button "Ref Position"
- New window opens, touch "Apply Last Location"
- Leave the window, if you like to you can test with "YGPS" how fast your phone gets a lock