The nonlinear switching state-space model is a combination of two well known models, the hidden Markov model (HMM) and the nonlinear state-space model (NSSM). In this chapter, a brief review of previous work on these models and their combinations is presented. Section 4.1 deals with HMMs and Section 4.2 with NSSMs. Section 4.3 discusses some of the combinations of the two models.
The HMM and linear state-space model (SSM) are actually rather closely related. They can both be interpreted as linear Gaussian models . The greatest difference between the models is that the SSM has continuous hidden states whereas the HMM has only discrete states. Roweis and Ghahramani have written a review  that nicely shows the common properties of the models. This thesis will nevertheless follow the more standard formulations, which tend to hide these connections.