Suppose the position of the satellite was measured by a ground-based
tracking station, which outputs the position in spherical coordinates
relative to the station's tracking antenna (spherical coordinates are
specified by a distance 
from an origin and two angles of
rotation 
and 
). This would be an example of a
non-linear dynamic system because the satellite's state vector
(which is represented in Cartesian coordinates) is no longer a linear
function of the measurement vector. This relationship can now be
expressed as
where
H is now a general vector-valued transfer function of
. In both the linear and non-linear cases, the noise is
assumed to be a property of the measurement process and not of
the system's state vector.