Kalman Filtering in the Theory of Gyroscopic Systems
Elena Gorelova, Vladimir Sobolev
The substitution of equations of motion of gyroscopic systems for
the so-called precessional equations is commonly used in
mechanics. This procedure gives, in many cases, favorably
compatible with the experiment results. This approach was
justified with the help of the method of integral manifolds. But
this very method reveals that the use of precessional equations
instead of original ones within calculating the filtering error
may lead to a intolerable error if the motion is performed by the
action of random forces of the Gaussian white noise type. This
conclusion is ascertained by the example analyzing the flow of the
plane gyroscopic pendulum on the moving foundation.