Fast stable Kalman filter algorithms utilising the square root

Consideration is given to Kalman filtering algorithms from the viewpoint of fast and stable implementation. A number of authors have reformulated certain signal processing and linear algebra algorithms to be square-root-free in an effort to simplify parallel implementation. Following these derivations a number of Kalman filter algorithms and parallel array architectures have been realized that also avoid square-root computations. It is shown that, contrary to the motivation for realizing these algorithms, the standard algorithms (utilizing square roots) can be implemented more quickly than the square-root-free versions. Furthermore, the square-root-free versions suffer from overflow/underflow and in some cases are numerically unstable.<>