## 3.5 Quaternion Error Display

The quaternion error display directly displays the elements of the
desired, estimated, and error quaternions. Even though at first
glance the quaternion appears to be a rather complex means for
attitude representation, it is actually fairly easy to extract some
information about system performance by simply observing its
individual elements directly.

Figure 3-5 Quaternion Error Display

The quaternion error display consists of two main sections. The
first simply prints the values of the elements of the desired and
estimated quaternions directly to the screen. Observing the value of
these elements is useful for determining if the quaternion has some
gross error in its formation (the magnitude must always be equal to
one). The second part provides a means for observing the long term
changes of the first three elements of the error quaternion. This
information is especially valuable because for reasonably small
angles, the first three elements of the error quaternion are nearly
proportional to the angular errors about the three vehicle axes. A
convenient rule of thumb typically used is that .01 quaternion unit
change is about the same as 1° of angular error about that axis.
For example, if the second element of the error quaternion is equal
to .03, then there is approximately a 3° pitch angle between the
desired and estimated vehicle attitudes. Using this basic rule, is
obvious how watching the convergence of the first three elements of
the error quaternion gives insight into the overall convergence of
the vehicle attitude. The first three elements may be displayed as
strip charts which can be scaled in time or magnitude. Alternatively,
they may be applied to the x and y axes of a chart and displayed
against each other, which yields insight concerning the path of
convergence.