How to track user's movements from one point to another without gps? (mobile devices) (Updated)

I want to create application which will navigate user at the shopping mall. So, I'll create a mall's map and I need somehow to track changes of user's location. Because of navigation in building, GPS is not a solution (low signal). So, I assume there is a way to track location changing (1-2 meters) with another module (maybe accelerometer?). Any ideas? Thanks

Update: I cannot use any additional devices such as iBeacons or so. I only can use device on which app is running. No access to wi-fi routers or so.

Example: I'm standing near Apple store(point A), and now I'm going to Samsung store(point B). The app should react that I started to move from point A, and know how much meters(accuracy may be not ideal) I walk from point A and in what side I'm going (east, west, south, north).