Scattering theory and linear least-squares estimation, part III: The estimates

We extend our earlier work, [1], [2], on providing a scattering model for state-space estimation, by interpreting the smoothed state estimate as a propagating wave in a scattering medium, with the observed system outputs acting as internal sources in the medium. The value of this interpretation in providing simple pictorial derivations, in visualizing, and in organizing estimation results is demonstrated by obtaining several known forms of solution for the smoothed estimate, and equations for handling the effect of altered a priori information.