  This letter investigates relationships between iterated filtering algorithms
based on statistical linearization, such as the iterated unscented Kalman
filter (IUKF), and filtering algorithms based on quasi-Newton (QN) methods,
such as the QN iterated extended Kalman filter (QN-IEKF). Firstly, it is shown
that the IUKF and the iterated posterior linearization filter (IPLF) can be
viewed as QN algorithms, by finding a Hessian correction in the QN-IEKF such
that the IPLF iterate updates are identical to that of the QN-IEKF. Secondly,
it is shown that the IPLF/IUKF update can be rewritten such that it is
approximately identical to the QN-IEKF, albeit for an additional correction
term. This enables a richer understanding of the properties of iterated
filtering algorithms based on statistical linearization.
