In theory, is the position derived from accelerometer absolute?

In theory, is the position derived from accelerometer absolute?

Ok, so imagine you're a sensor. All you can sense is acceleration. You're an accelerometer.

Now you're at rest, or moving at a constant speed. You can't tell the difference, since Newton's laws don't allow that – an object at rest or in linear motion experiences no acceleration.

Obviously, since you might be moving (or not), you can't tell where you are, and whether you'll be at the same position in 10 seconds.

So, that answers your question. An accelerometer + signal processor can only tell the position relative to some starting position, and only if the starting speed is known.

Mathematically, you'd have to differentiate twice to go from position to acceleration. So you'd have to integrate twice to go back. Each integration step adds an unknown "offset" to your result.

I'm a bit surprised you didn't come up with either approach!