  Based on Bellman's dynamic-programming principle, Lange (2024) presents an
approximate method for filtering, smoothing and parameter estimation for
possibly non-linear and/or non-Gaussian state-space models. While the approach
applies more generally, this pedagogical note highlights the main results in
the case where (i) the state transition remains linear and Gaussian while (ii)
the observation density is log-concave and sufficiently smooth in the state
variable. I demonstrate how Kalman's (1960) filter and Rauch et al.'s (1965)
smoother can be obtained as special cases within the proposed framework. The
main aim is to present non-experts (and my own students) with an accessible
introduction, enabling them to implement the proposed methods.
