I recently run a Kalman Filter analysis for my own study, and meet something unclear about the technique.Basically a linear KF casts the problem into two equations: transition and measurement equations,Y(t) = alpha + beta * X(t) + error1X(t) = mu + F * X(t-1) + error2where X(t) is an unobservable latent series, alpha, beta, mu, and F are parameters to estimate. So far so clear, my question is can we still apply KF if X(t) is instead observable? for instance, I impose that X are for some macroeconomic variables, they may have some missing values (but not all are missing). So I'd like to apply KF filter which deals with missing value naturally.Could you please give me some hint? if yes, how can I do that? because for unobservable X, every step we need to update its value and variance, but for observable series, is the updating process still necessary?Thanks very much for your help in advance.

X is ergodic and stationary, so your Y is a trivial regression