On complementary models and fixed-interval smoothing

A new algorithm is derived for the standard fixed-interval linear smoothing problem in which the signal is generated by a state model. The structure of this new algorithm allows the smoothed estimate to be easily updated in response to a change in the initial state covariance matrix
\Pi_{0}
, since, unlike in existing algorifiuns, the relevant Riccati equation is entirely independent of
\Pi_{0}
. The derivation of the algorithm is based on properties of complementary models.