Earlier quoted context omitted.
To keep track of your position using inertial measurement you need two types of sensor - gyroscopes, to work out which way you're pointing, and accelerometers, to work out how fast you're going. An IMU in a smartphone would be subject to 10 m/s/s acceleration at all times under gravity, 50 m/s/s on a rollercoaster, and 100,000 m/s/s if you drop your phone on a hard surface. Let's say we don't mind losing your locatio…
One of the secrets of useful dead reckoning systems is damping which is basically reducing your velocity toward zero (or some expected value) by a measurement slightly greater than your error. The result is if your cellphone sit's on a table you don't accumulate errors. Coupled with the occasional calibration and you end up with some surprisingly accurate systems.
Inertial Navigation Systems like OxTS make [1] use GPS to get rid of this integration error that accumulates over time. For applications in vehicles you can also use the vehicle's speedometer, so you're measuring speed directly, which means fewer integration errors.