The linear accelerometer does not output a signal that tells you how fast you are traveling in three directions, it would be great if it did. I am sure you know this, and since you covered so much in the video I understand the oversimplification. People who are new to accelerometers might not know this, however. Three axis linear accelerometers tell you how much you are accelerating in three axes. If you were in a spaceship in microgravity with your rocket motor off, you would expect a zero signal on each axis. If the rocket thrust is aligned with the x axis, turning the rocket on will make the x axis signal change to some value which is proportional to the thrust of the rocket. As long as the rocket puts out a constant thrust, this new value will be maintained, but your speed (velocity) is not maintained, it is ever increasing. If you now shut off the rocket motor, the x axis signal will return to zero, but your speed (velocity) will be equal to the speed when you shut the rocket motor off. On earth, you also must account for the direction and magnitude of the force of gravity, since at rest we are experiencing 1g of acceleration due to the force of gravity. So, to determine your vehicle velocity, you have to “add up” or integrate the instantaneous accelerations along all three axes and also keep track of any rotations of these axes due to the vehicle turning. This is where the fun starts. There are also bias errors, noise, and gain errors which can change over temperature. The point is that determining vehicle velocity in three axes is a challenge, which can be done, but not with only a three axis linear accelerometer for most situations.
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