I'm wondering if we can measure 3-D length only by our smart-phone's accelerometer. And we all know these low cost IMUs are not accurate.
You can model accelerometer's error this way: $$ a = f*a' + g + b + \eta $$
where $a$ is the actual acceleration, $f$ is a 3x3 matrix modeling scaling, misalignments, cross-axis and ... errors. $g$ is gravity, $b$ is bias and $\eta$ is noise.
I'v found a good method to calibrate(compute $f$ and $b$) smart-phone's accelerometer: Estimate smartphone accelerometer bias
Now I have to:
1) remove $g$
2) remove $\eta$
How can I do that accurately? As I mentioned above, this problem requires good accuracy.
If you believe accelerometers are not accurate enough for this problem, and other sensors should be used (Sensor Fusion), please share your idea.