# Orientation determination using magnetometer data

I'm working on some of the math for rocket attitude determination based only on magnetometer data (and location on earth). I was hoping
to make some statements in hopes that some of the gurus in this area might be able to verify (or correct) these statements.
(note: a single vector includes both positive and negative directions)
If you have a single axis magnetometer parallel to the lengthwise axis (z-axis) of the rocket, with or without a spin rate, you have a cone of possible orientation vectors based on the magnetometer data.
With a 2-axis magnetometer (x and z axis), you can equate the possible attitude vectors of a non-spinning rocket down to a function of x-axis sensor orientation vectors (which is still an infinite number and pretty much useless in itself). If the rocket is spinning, you can reduce the possible attitude orientation vectors down to 4 based on the magnitude of the deviation during a revolution of the x-axis magnetometer data ... ?
Lastly, with a 3-axis magnetometer rocket, you could determine the exact attitude vector of the rocket regardless of spin...?
Any verification, corrections, or suggestions to my understanding is greatly appreciated.
Thanks! Dave
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David Harper wrote:

Yes, the axis of the rocket lies somewhere on a cone at a given angle with respect to the local magnetic field lines, but with totally unknown roll angle.

Yes, now for each point on the cone, there are two possible roll angles, but you still don't know where on the cone you are.

No, for each point on the cone, the magnitude of the magnetometer output vs time will be exactly the same. The timing of the peak output will tell you when the second sensor is pointed closest to the magnetic field lines but you still don't know where on the cone you are or what direction you are rotating in. However, the second sensor does give you a very good indication of the roll rate.

No, the third sensor only resolves the 2-possible angle ambiguity in the non-rolling case, but still does not tell you where on the cone you are. It can also tell you what direction your roll is.
Absolute orientation determination (angle in space and roll angle) is not possible because you only have one reference direction. For any magnetic sensor configuration, a rotation of your sensor about the magnetic field lines will keep your magnetic sensor outputs unchanged.

I hope this is helpful...
- Robert Galejs
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Gotcha... I had to rethink that a few times, but it makes sense. Now, if you had a sun sensor that gave you the angle between the rocket and the sun, coupled with single-axis magnetometer data, you could eliminate all but two possible orientation vectors.... (right?)
And with a 2-axis magentometer and a sun sensor that gave you both angular orientations with respect to the sun (not just a magnitude), you could determine the exact orientation... (right?)
Thanks for the help Robert, Dave
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