On the Relationship Between Iterated Statistical Linearization and Quasi–Newton Methods
Anton Kullberg, Martin A. Skoglund, Isaac Skog, Gustaf Hendeby · IEEE Signal Processing Letters · 2023
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 theqniterated extended Kalman filter (qn–iekf). Firstly, it is shown that theiukfand the iterated posterior linearization filter (iplf) can be viewed asqnalgorithms, by finding a Hessian correction in theqn–iekfsuch that theiplfiterate updates are identical to that of theqn–iekf. Secondly, it is shown that theiplf/iukfupdate can be rewritten such that it is approximately identical to theqn–iekf, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.