How do we determine the position of an object with accelerometer and gyroscope sensor data?

Hello,

the problem you are referring to usually receives the name of "inertial navigation" or "dead reckoning". It is something I am currently working on, and is a problem whose solution is not direct.

The method I am using is:

1. Obtain a good "orientation estimation" or "attitude estimation". This is, find the best guess of the rotation transformation that relates two reference frames: the one attached to your sensor, and other one usually taken to be an inertial reference frame (or approximately inertial) as one whose z-axis points in a direction orthogonal with the Earth surface. The accelerometers sense the gravity accelerations, so it gives you information about "where it is down". Gyroscopes help predict orientation. A common approach is to use a Kalman filter:

although others use gradient descent techniques and also obtain good results:

2. Transform the acceleration measurements (taken in a non inertial reference frame: the one attached to your sensor) to the inertial reference frame using the rotation transformation obtained with orientation estimation.

3. Subtract the acceleration due to gravity.

4. Integrate the resulting acceleration twice to obtain position.

This is what you usually obtain when you perform this process:

If you have seen those videos you will have begun to think that it is not possible. However, in certain scenarios you can use pseudo-measurements to improve your estimation:

I would conclude that depending on your application, you should use pseudo-measurements, or include more sensors to estimate the position. In other case, as far as I know, it is not possible to obtain a good position estimation.