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Suppose that I am launching a cubesat into space. Let the cubesat be launched from the P-POD deployer. Since the satellite will have a huge velocity, hence the detumbling mode will be operating. As soon as the cubesat has completely detumbled, I wish to determine the initial quarternion of the cubesat with respect to an inertial frame of reference. How should I go about it?

I cannot determine it using TRIAD algorithm as the satellite will just immediately be launched, hence the sun sensors and magnetometers might not be active by the time the satellite has detumbled. Also how will I find the relation between the satellite frame of reference and the inertial frame of reference?

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    $\begingroup$ Seems to me that you your attitude will be totally unknown until you turn on at least one sensor. $\endgroup$ – Chris Jan 15 '18 at 0:18
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First, you will not be able to detumble without at least one sensor. For CubeSats the normal way to detumble is through the B-dot algorithm which measures the magnetic field change and turns on appropriate magnetorquers to slow down the motion. Since you have to measure the magnetic field to begin with, you've already established a rough attitude in two-axes. Utilizing more than one measurement can allow you to resolve the rotation around the third axis using well established algorithms. In fact the TRIAD algorithm does exactly that.

Without a magnetometer already on you will not detumble. (you could detumble using thrusters and a gyro, in which case you would not know your attitude, however that is not the usual approach for CubeSats as they normally don't have attitude thrusters)

This thesis covers a lot of the relevant math.

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