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 location if you drop your phone, so we pick an accelerometer with a maximum range of 50 m/s/s.
Now, how accurately can we measure acceleration? The raw image setting on a fancy digital camera is 14 bits, which gives 16384 levels. CD audio is 16 bit, so it has 65,536 levels. Assume you can come up with a design that offers a 32 bit range, for a full 4 billion levels.
That means your measurements will be precise to 0.0000000116 m/s/s - pretty accurate, right?
The thing is, after 24 hours your phone will have an inaccurate estimate of its speed (0.0000000116 m/s/s * 24 hours = 0.001 m/s) and after 24 hours with that inaccurate speed estimate you'll have an inaccurate position estimate (0.001 m/s * 24 hours = 86.4 m) and the longer you leave it going, the bigger the error can get.
TLDR: You need super-precise sensors to do dead reckoning that stays accurate for long periods.