On Computational Complexity Reduction Methods for Kalman Filter Extensions

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.