GPS position slowly drifting

Hi,
I am working for a company that provides a GPS positioning service for our clients that buy the GPS devices we are selling.
But the device we are selling (it comes for Taiwan) has several bugs in it and we are searching another device.
The problem I am having right now is that the devices I am currently testing are giving positions with very bad accuracy when they are indoors. At first the GPS gives the actual location. Then it starts drifting in some direction for few meters, then several dozens of meters and even hundreds of meters (up to 1 km)!
If those positions were just jumping it would not be hard to filter them. But now the drifting is done is a specific direction and looks similar to good data.

The GPS module is U-BLOX.
I don't have the number of satellites or precision in the string sent by the device.

Does someone understands why it does this drift and if it can be corrected?
Thank you very much.
Raphael