Likelihood computation stands at the heart of many statistical methods, e.g., maximum likelihood estimation and detection. Underlying statistical models can be viewed as factor graphs. This allows us to formulate likelihood computation from a message passing viewpoint. Thereby, scale factors of sum-product messages must, in general, not be neglected. We propose two dual definitions of such scale factors and provide corresponding message passing update rules. For signal processing applications, we consider linear state-space models, extended by the concept of a glue factor - a factor that connects the states of different state-space models. This leads to a generic algorithm that tracks a family of models and allows likelihood computation of each member in the family in the glue factor.