I tried a little experiment with my new phone. I did not update the phone immediately. Using 10.0.1, I used google map and here maps. It worked very well. Google map was routing and rerouting perfectly. Here maps was able to find and route me too. The blue dot is not moving around in maps and it is steady in my location. In short, it worked as it should.
Then I updated to 10.1.1. Here I noticed that the gps is acting strange again. Not as worst as before, which is jumping from my location to a far away place. Now it's slightly moving, slowly, around my location. Also, the blue circle goes big then small more often. Here maps when I try it goes to "looking for gps" again, but wait a little while and it will be able to go find a gps.
My conclusion, I think it's a software bug. I got a new phone but upgrading to the latest OS shows signs of the previous problem. I hope it does not go as worst as before. But the signs are there. Hope apple has an update soon to solve this.