The fundamental goal of this work has been to extend the nonlinear state-space model (NSSM) and learning algorithm for it developed by Dr. Harri Valpola [58,60], by adding the possibility of several distinct states for the dynamical system, as governed by the HMM. The NSSM algorithm is an extension to earlier nonlinear factor analysis (NFA) algorithm [34].
In this section, some of the previous work on these models is reviewed briefly. This complements the discussion in Section 2.2.2 as the problem to be solved is essentially the same. But first let us begin with an introduction to linear state-space models (SSMs), a generalisation of which the nonlinear version is.