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.