Learner level information on Kalman filtering for different input kinds I am learning Kalman filters and have seen example on data as state varaibles that have real values / numeric. However, in digital communication the information is in digital - bits. So, can Kalman filter not work on bits?

I have not found this information in any text book, tutorials and other reading materials. In text books and in wikipedia, it says that the state $x$ of the system is represented as a vector of real numbers I want to know if Kalman filter and Ricatti Equations needs to modified if the input signal $x$ is a discrete, taking values from a symbol set. Examples of such input is the DNA genes, BPSK symbols, quantized pixel values. Is there a different Kalman filter for symbolic input? Or can we use the same Kalman filter and its equations. Thank you
I am most convinced you should try Hidden Markov Chains (which i am not explaining here), just justifying its use:

Kalman Filter: continuous state space, discrete observations

https://stats.stackexchange.com/questions/183118/difference-between-hidden-markov-models-and-particle-filter-and-kalman-filter