How to get the trajectory of an android device with accelerometer and gyroscope?

Question

Android

Tell me if I understand everything correctly?
Let's say we have an ideal accelerometer. It measures, roughly speaking, the acceleration vector.
If I remember physics correctly, then acceleration is the derivative of speed. So, having two acceleration readings, we add them up and divide them by two and get one speed reading?
And having two speed readings and knowing the sampling frequency, can we calculate the path traveled during the sampling period in three-dimensional space? And so with each count you can get the trajectory of movement, right?
Is there any library for android that would do this?

Answer 1

Need to integrate. Twice. Don't take the arithmetic mean.
http://ru.wikipedia.org/wiki/Numerical_integration
Moreover, the acceleration vector must not be forgotten to transform taking into account the orientation of the device, which can be found by integrating the angular accelerations in a similar way. And do not forget about the accumulated error. In general, this is a real Inertial Navigation System.

Answer 2

In! Thank you. I couldn't remember what it's called (INS). I once read a textbook on missile navigation...
And why and how to transform the acceleration vector?
Do you know if there are libraries for creating ANN for android?
Isn't the integral in the discrete form calculated as mean in the simplest case?

Answer 3

Double integration gives a monstrous error - the accuracy falls in proportion to the square of time. :(
www.youtube.com/watch?v=C7JQ7Rpwn2k&feature=youtu....

Answer 4

https://www.youtube.com/watch?v=C7JQ7Rpwn2k