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While reading about IMU on wikipedia I found this about its disadvantages:

"A constant error in attitude rate (gyro) results in a quadratic error in velocity and a cubic error growth in position."

How is Gyro drift error related to error in velocity and position?

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In a typical pure inertial nav solution, you must cancel out the acceleration due to gravity by subtracting it out. If the vehicle's down vector is incorrect, this error appears as a lateral acceleration that is equal to \$\sin \theta_{error}\$ -- and for small angles is close to \$\theta_{error}\$ itself. So if the gyro has an offset, \$\theta_{error}\$ grows linearly and therefore acceleration error grows linearly (at first).

Since velocity is the integral of acceleration, and position is the integral of velocity, a constant, linear acceleration drift (1st order polynomial) will result in a quadratic velocity error (2nd order polynomial) and cubic position error (3rd order polynomial).

If all you have is a 6-DOF IMU and a model of the earth's gravity, then both the IMU and the gravity model have to be perfect.

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Drift adds an moving offset to the angular velocity which is an error. Then if you time integrate that to get angular position the error gets transferred over and accumulates.

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