  Typical iterated filters, such as the iterated extended Kalman filter (IEKF),
iterated unscented Kalman filter (IUKF), and iterated posterior linearization
filter (IPLF), have been developed to improve the linearization point (or
density) of the likelihood linearization in the well-known extended Kalman
filter (EKF) and unscented Kalman filter (UKF). A shortcoming of typical
iterated filters is that they do not treat the linearization of the transition
model of the system. To remedy this shortcoming, we introduce dynamically
iterated filters (DIFs), a unified framework for iterated linearization-based
nonlinear filters that deals with nonlinearities in both the transition model
and the likelihood, thereby constituting a generalization of the aforementioned
iterated filters. We further establish a relationship between the general DIF
and the approximate iterated Rauch-Tung-Striebel smoother. This relationship
allows for a Gauss-Newton interpretation, which in turn enables explicit
step-size correction, leading to damped versions of the DIFs. The developed
algorithms, both damped and non-damped, are numerically demonstrated in three
examples, showing superior mean-squared error as well as improved parameter
tuning robustness as compared to the analogous standard iterated filters.
