Variation of an inertial navigation system

I think everyone is thinking that what i'm trying to do is mission critical. It's far from it. I'm not trying to put a rocket into space. It exactly what arduino was meant for a hobby. If I can over come the basic math I'm sure I'll be more then able to get my readings where I'm happy with them. I gave the cave mapping as an example not as an exact. I appreciate all the people telling me why I can't do it but I'm an engineering and to some degree I'm sure everyone on this forum is an engineer. This is an exercise in learning and education. Here are the basics in the steps I need to over come and what i'm needing to find out.

  1. Filter the output of my sensor array to give a stable reading (done)
  2. Non-3D linearly calculate movement in the x, y, z direction. (This is where I'm at and need guidance on the math) ex. Based on a starting point of 0,0,0 where all measurements are in FT. put the circuit board on the ground and slide it 3ft in the x direction. Have it tell me my new position is 3,0,0. (ideal conditions are expressed here only)
  3. Determine attitude of measurement in respect to gravity. (easy to do)
  4. Take liner measurements and integrate them into 3D space using trig and calculus as needed (not a problem here).
  5. calculate long/latitude/altitude and display.

Step 2 is my big problem and the step that I am currently at.