Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. It is based on a variational principle of least action, formulated in generalized coordinates. Note that the concept of "generalized coordinates" as used here differs from the concept of generalized coordinates of motion as used in (multibody) dynamical systems analysis. Generalized filtering furnishes posterior densities over hidden states (and parameters) generating observed data using a generalized gradient descent on variational free energy, under the Laplace assumption. Unlike classical (e.g. Kalman-Bucy or particle) filtering, generalized filtering eschews Markovian assumptions about random fluctuations. Furthermore, it operates online, assimilating data to approximate the posterior density