Forward-pass bryson-frazier smoother in discret-time systems

An algorithm is described for the standard fixed-interval smoothing problem in which the system is linear, time-varying discrete-time. The present smoother which is called the forward-pass Bryson-Frazier smoother here is shown to be a dual version of the well-known Bryson-Frazier smoother. The algorithm is less attractive in the numerical implementation of time-varying systems than that of Bryson and Frazier, because it involves inversion of the state transition matrix. However, the mechanization of this new algorithm allows the smoothed estimate or error covariance to be readily updated in response to a change in the initial statistics. A numerical example of a fourth-order tracking system illustrates the characteristics of both Bryson-Frazier smoothers. Thus, the present result together with the usual Bryson-Frazier smoother give a set of two solutions to the fixed-interval smoothing problem using a Lagrange multiplier method.