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

"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?

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.

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.