Kalman Filter (KF) uses a so-called Dynamic Shift matrix in the forecast step. The matrix is sometimes called Evolution or Propagator matrix, and is marked with D or M:
$ \mu_t = M_t \mu_{t-1} $
$ \Sigma_t = M_t \mu_{t-1} M_t' + Q_t $
In many implementations that I know about, M is just an Identity matrix. Can anyone provide an example and explanation of when that matrix is meaningfully more complex?
It is said that this matrix relates the state at the previous time step k – 1 to the state at the current step, k, in the absence of either a driving function or process noise, as well as that it can change with each time step (see Welch & Bishop 2001).
Here is a good video to explain what the shift operator matrix means. Hopefully that clarifies your doubt.Video by Professor Khaisare
Kalman Filter a priori state estimates can also be made by physics informed State Space models. For that you can refer to the book: Kalman Filtering by Grewal and Andrews.