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If the velocities measured by the IMU in the body-fixed reference frame are converted into earth fixed frame, are they equivalent to the ground velocity measured using the GPS?

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    $\begingroup$ You question is a good one but its writing makes it hard to follow. You should edit it to highlight why you think it may or may not be the same speed and what distrubs you enough to post this question. That way, the answer will be more specific and complete. $\endgroup$ – Manu H Nov 21 '16 at 9:24
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An IMU uses gyro and accelerometer measurements to calculate its velocity vector relative to the Earth. Similarly, a GPS uses range, range-rate, doppler, and/or carrier phase shift measurements to several satellites to calculate the same velocity vector. So, an IMU and a GPS calculate the same velocity vector, but use different measurements.

The difference between the IMU and GPS measurements are that, inherently, an IMU has very good short-term accuracy but drifts over longer periods of time; a GPS has very good long-term accuracy, but is very noisy over short periods of time. Therefore, IMU and GPS measurements are usually combined to provide a navigation solution that is accurate over both the short-term and the long-term.

The components of the velocity vector are usually given in a local-level, local-north reference frame; for example, the north- east, and down components: $v_N$, $v_E$, $v_D$. The ground speed is $v_H=\sqrt{v^2_N+v^2_E}$.

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    $\begingroup$ You are correct @mins. I will edit my answer, but still keep its simple. $\endgroup$ – Christo Nov 22 '16 at 9:31

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