  The Kalman filter and its extensions are used in a vast number of aerospace
and navigation applications for nonlinear state estimation of time series. In
the literature, different approaches have been proposed to exploit the
structure of the state and measurement models to reduce the computational
demand of the algorithms. In this tutorial, we survey existing code
optimization methods and present them using unified notation that allows them
to be used with various Kalman filter extensions. We develop the optimization
methods to cover a wider range of models, show how different structural
optimizations can be combined, and present new applications for the existing
optimizations. Furthermore, we present an example that shows that the
exploitation of the structure of the problem can lead to improved estimation
accuracy while reducing the computational load. This tutorial is intended for
persons who are familiar with Kalman filtering and want to get insights for
reducing the computational demand of different Kalman filter extensions.
