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You can only measure acceleration using an accelerometer. A gyroscope is technically still useful here for removing the gravity vector from the data accelerometer is reporting.

measured acceleration = true acceleration + accelerarion error

velocity = (true acceleration)t + (accleration error)t + v_0 + v_0's error

position = (true acceleration)t^2/2 + (acceleration error)t^2/2 + (v_0)t + (v_0's error)t + p_0 + p_0's error

The error grows quadratically meaning that this equation can only be used for a brief amount of time.




> You can only measure acceleration using an accelerometer. A gyroscope is technically still useful here for removing the gravity vector from the data accelerometer is reporting.

You can combine accelerometer and gyroscope data to give you a (position, orientation) signal that is more precise than either, using a Kalman filter. (You can add other sensors in like magnetometer too)

Unfortunately even with this technique there is still drift that over time accumulates without bounds (the error gets so larger you become completely lost). If you can navigate from known landmarks you can eliminate this drift however. Such landmarks include the stars (if you can see the night sky), buildings and topographic features like in this post, or GPS




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