Can any one explain Schuler cycle in Inertial Navigation System

gkraju

Can any one 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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