Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter

An unclear treatment is corrected of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren (1986). It shows that the habitual implementation of the Kalman filter makes it extremely sensitive to the so-called loss-of-symmetry phenomenon. Furthermore, it is also demonstrated that an exact implementation of the conventional Kalman filter removes this sensitivity. >