In the wikipedia Kalman filter link, the state variable $x_k$ takes a continuous value say a floating point number, but what if the values are integer say symbols from an alphabet set, then how does one apply the Kalman filter? I have the following confusions and doubt and shall be obliged for an answer with some examples, if any.
DOubt 1: Kalman filter is called continuous filter because the state values and covariance etc all take real-valued numbers. But, these are discrete-in time $k$ varies from $1,2,\ldots$ and continuously. Is my understanding correct?
Doubt 2: I count not find any information or any working example on the case when the state variables take discrete values. What if they are symbols from DNA strings? Could somebody please throw some light into this case?