Kalman filter: state update with some missing signals

[GF_London]

Hi,

I am trying to better understand how the Kalman filter updates the state variables when only some of the signal variables have been observed. To try this out, I have estimated a small state space model with just two signal variables. I have observations on the first through Jan-16 and on the second through Dec-15. I estimate the state space model through Dec-15 and then use makefilter and makestates to project forward the state variables from Jan-16 onwards. My understanding is that makestates does a partial update of the state variable forecasts in Jan-16 in response to the signal observation of the first variable. To do this, it seems to change the Kalman gain matrix by adjusting the values on the first half of the matrix and by setting the other half to zero. Do you have a simple explanation for how this adjustment of the Kalman gain matrix is actually carried out. I think I understand the intuition, but cannot quite replicate the calculation (I have looked at the references cited in the EViews manual but am still not entirely clear about this). Also, is my understanding of what the makestates function does correct, i.e., it does full updates of the state variables when all signals are observed, partial updates when only some signals are observed and skips the update completely when no signal is observed?

Thank you!!!