What is the definition of a "complementary filter"? I'm writing my MSE thesis report on an inertial navigation problem I've been working on. In my work, I use a complementary filter to track the orientation of a device. Now, since my fellow students are likely not familiar with complementary filters or Kalman filters, I wish to give a brief description of what a "complementary filter" is, in general.

A definition, if you will.

So, what defines a complementary filter? Is it any filter on the form z = a * x + (1 - a) * y, where x and y are separate measurements of a single quantity?

It's fine to define it in terms of Kalman filters if that's appropriate.
Usually, a complementary filter (like a complementary function) complements another filter.  The two filters that are complementary to each other add to one.  Or, at least, add to an all-pass filter (which is what Linkwitz-Riley crossovers do.

so either

$$ H(f) + G(f) = 1 $$

or 

$$ H(f) + G(f) = A(f) $$

for $H(f)$ and $G(f)$ being complements of each other and $|A(f)|=1$ is an APF.