Overview of Factorisation Methods in Kalman Filtering

The paper summarises and describes the most commonly used matrix factorisation methods applied in design of the Kalman filter in order to improve computational efficiency and avoid divergence issues caused by numerical round-off and truncation errors. Some forms of the Kalman filter are more prone to the growth of numerical error sand possible divergence than other implementations. In order to prevent the algorithm’s divergence additional processing is needed and this paper discusses pros and cons of different implementations and their numerical characteristics. Numerical issues still arise in finite word length implementations of algorithms, which frequently occur in embedded systems. This paper describes algorithms based on different factorisations such as Cholesky, U-D, SVD and their basic numerical properties.