New square-root and diagonalized Kalman smoothers

Naive implementations of Kalman filters and smoothers often suffer from numerical problems. In this paper, we consider two Kalman smoothers that were proposed recently: (i) the adaptation of the MBF (Modified-Bryson Frazier) for input estimation and (ii) the BIFM (backward information filter, forward marginal) smoother. Even naive implementations of these smoothers are numerically rather robust because these smoothers require no matrix inversion. Nonetheless, additional measures are sometimes required. We present square-root versions for both these smoothers as well as state reparametrizations for improved numerical stability. The main novelty in this paper is the square-root version of the BIFM smoother, which can be used in numerically critical smoothing problems, as exemplified in a force estimation problem using a multi-mass resonator model of an industrial milling machine.