State-Space Model with One Binary and One Continuous Observation

In this chapter, we will consider the case where \(x_{k}\) evolves with time following a slightly more complicated state equation and gives rise to both a binary observation \(n_{k}\) and a continuous observation \(r_{k}\) . Prior to looking into the equation derivations, however, as in the previous chapter, we will again first consider a few example scenarios where the need for such a model arises.