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I'm trying to use an accurate FOG gryo for tracking heading in a moving platform. The FOG gyro has two rate errors, Faraday (fixed amount regardless of alignment to the earth) and the 15.04 degrees per hour of the earths rotation (function of my alligmnet to the rotation).

I know the attitude of the gyro ring.. Roll,Pitch,Yaw and Latitude,Longitude.. If the gyro is exactly aligned with the rotation I will see all of the 15.04 deg/hr superimposed, none of it if I'm perpendicular to the rotation. Now I need mapping/function that will give me a number between -1 to 1 giving me the amount of the earths rotation imparted at a given roll,pitch and yaw on the surface of the earth.. Where roll=pitch=0 level with the surface, yaw=0 pointing true north. The gyro (yaw axis) is mounted flat in the plane of the earth.

This will allow me to remove the Faraday drift (constant) and then calculate the amount of the earths rotation projected into this gyro at this roll,pitch, yaw, latitude.

Can someone help with this transformation or point me to a document that can help?

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2 Answers 2

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Your second "drift" term is not an error term at all, it's the FOG measuring the actual sidereal rotation of the Earth. Some systems use this to get an absolute orientation reference; this is known as "gyrocompassing".

When you're working with systems that have this level of accuracy, it would be better to treat this term for what it is, and do an explicit transformation between the Earth-centered nonrotating coordinate frame (which is what the FOG is measuring) and the Earth-centered, Earth-fixed (rotating) coordinate frame you want for your answers.

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  • \$\begingroup\$ How well are cheap gyros able to ascertain absolute orientation within a certain length of time? There is mathematically enough information for a device which is fixed to the Earth to determine its orientation relative to the earth's axis, but the Earth's rotation is pretty slow, so I don't know how well one can separate out changes in measured rotational velocity which stem from the Earth's rotation from sensor drift. \$\endgroup\$
    – supercat
    Commented Nov 26, 2013 at 0:45
  • \$\begingroup\$ Cheap (e.g., most MEMS) gyros have inherent bias and noise levels that make it impossible to resolve the Earth's rotation. Most MEMS-based systems use magnetometers, plus accelerometers to measure the gravity vector, to get some sort of absolute orientation reference. \$\endgroup\$
    – Dave Tweed
    Commented Nov 26, 2013 at 11:56
  • \$\begingroup\$ That's what I would have expected; I should perhaps have phrased my question as, "how does the level of accuracy and precision required to detect the earth's rotation in various lengths of time compare to what's available from various gyros?" For example, if one wanted a device which could report its latitude if left at in a fixed earth-relative position, in a temperature-controlled space, for 48 hours, would such a device require $1, $10, $100, $1000, or more worth of sensors? \$\endgroup\$
    – supercat
    Commented Nov 26, 2013 at 16:09
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simple solution, use the gyros to stop the earths rotation... then you know it is 0.

Joking aside, you will need access to good gyros to measure anything with any degree of certainty and frankly your easier option is to look at the stars... they are far enough away and offer enough data points that you can consider them stationary and get a better gauge than a gyro will give you.

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