The probabilistic interpretation of the dynamics of the sources in the standard NSSM is
The simplified model uses only one dynamical mapping but has an own covariance matrix for each HMM state . In addition to this, the innovation process is not assumed to be zero-mean but it has a mean depending on the HMM state. Mathematically this means that
Equation (5.50) summarises the differences between the switching NSSM and its components, as they were presented in Sections 5.1 and 5.2. The HMM ``output'' distribution is the one defined in Equation (5.50), not the data likelihood as in the ``stand-alone'' model. Similarly the model of the continuous hidden states in NSSM is slightly different from the one specified in Equation (5.25).