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.
