  This paper proposes the inertial localization problem, the task of estimating
the absolute location from a sequence of inertial sensor measurements. This is
an exciting and unexplored area of indoor localization research, where we
present a rich dataset with 53 hours of inertial sensor data and the associated
ground truth locations. We developed a solution, dubbed neural inertial
localization (NILoc) which 1) uses a neural inertial navigation technique to
turn inertial sensor history to a sequence of velocity vectors; then 2) employs
a transformer-based neural architecture to find the device location from the
sequence of velocities. We only use an IMU sensor, which is energy efficient
and privacy preserving compared to WiFi, cameras, and other data sources. Our
approach is significantly faster and achieves competitive results even compared
with state-of-the-art methods that require a floorplan and run 20 to 30 times
slower. We share our code, model and data at https://sachini.github.io/niloc.
