Abstract
A new approach to the derivation of square root forms for fixed-point and fixed-interval smoothers is taken and schemes different from those of Kaminski and Bryson are introduced. The square-root representation of Kalman filter is known to be effective in removing the numerical instability caused by poor observability in large scale systems. Particularly the square-root fixed-point smoother derived in this paper will reduce the number of triangularizing operations significantly, enhancing the computing efficiency over that of the Kaminski-Bryson square-root smoother.
