5.5 Missing Data

Conceptually, missing data are easy to deal with in the framework of the Kalman filter. There are two steps to the process: (1) the prediction step, and (2) the updating step, which occurs when we observe the new data. If a data point is missing, we cannot do step 2, so we simply skip it. We retain the prediction made in step 1 and move on to the next time point.

Therefore, if \(y_t\) is missing, we can revise the update procedure to simply be

\[\begin{eqnarray*} x_t^t & = & x_t^{t-1}\\ P_t^t & = & P_t^{t-1} \end{eqnarray*}\]