Accelerometer double integration error
I have tried to do this, with an iPhone’s accelerometer/gyroscope, and can empirically tell you there will be many orders of magnitude more error than that.

Your statement “without considering rotation” is an important one, as this is a huge factor. One of your difficulties will be removing the gravity vector from the integration. If the accelerometer is tilted even slightly, gravity will introduce a large error in each axis.

In my experiment, I was trying to make an iPhone into a 3D cursor a user can wave around in their hand for 3D modelling. It would drift off in random directions at a rate of centimetres per second. Lots of low pass filtering helped this a bit, but it was still way off.

My point is, even if your accelerometer has low noise, in the real world this is a very difficult problem to solve as there are many other sources of ‘noise’.

I recommend you go buy a commercially produced IMU if you want any chance of achieving this over 400m. I will be impressed if you can make an accelerometer work alone, over a distance of 400m with less than ±1km error.