Standard filtering techniques operate under the assumption that the system is perfectly known: system matrices/functions, noise statistics and inputs. But such strong assumption does not typically hold in real-world applications. Indeed, when the assumed model does not perfectly align with the true system dynamics (i.e., model mismatch) the optimality properties of the Kalman filter and its nonlinear extensions are compromised, and the filter performance can be significantly degraded, reason why robust solutions must be accounted for. This contribution explores how a recently introduced adaptive robust regression framework can be adapted to the recursive filtering case, being then able to deal with time-varying outliers in the observation model. Methodological and practical insights are given regarding the design and implementation of the method. An illustrative navigation example is provided to highlight the filters' advantages and limits, and support the discussion.