Can any one explain Schuler cycle in Inertial Navigation System

[gkraju]

Can anyone please explain schuler cycle, please don not start explaining with same old pendulum with the length of radius of Earth stuff.
why is it required ?
what is that all about ?

 

[JLFarrell]

Sketch a circle and draw radii to each of two positions, true (T) and estimated (E). Let the angle between the radii be exaggerated but still narrow enough to allow small-angle approximation (sine=angle in radians).
Since accelerometers sense the NONgravitational part of acceleration, we have to supply the gravitational part ourselves -- vectorially. So:
Calling the chord distance "x" the radius "r" and gravity "g" note that
* the true gravity vector is vertical (down along the radius
from "T")
* the apparent gravity vector (down along the radius from
"E") has a small projection along the chord from "T" to "E"
producing a horizontal error in acceleration, OPPOSITE the
direction of position error.

By the small-angle approximation and the opposite sign, the acceleration error is then
(-x/r) g = (-g/r) x
i.e., the second time derivative of "x" equals (-g/r) times "x" -- that's the differential equation of a sinusoid. Plug in numbers for Earth radius and gravity -- you'll get an amount in radian/sec corresponding to a period between 83 and 84 minutes.
There's a little more to it but that explains the basics. For more info I'll cite a tutorial at http://www.ion.org/tutorials/

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