On complementary models and fixed-interval smoothing

Abstract

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Pi_{0}</tex> , since, unlike in existing algorifiuns, the relevant Riccati equation is entirely independent of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Pi_{0}</tex> . The derivation of the algorithm is based on properties of complementary models.