I am try to use Linear Kalman to do time series prediction. I understand that I have to define a model process matrix which indicate how system state evolve, and a measurement matrix H which convert state variable to measurement space. However in my problem, there is no clear relationship between my measurement and state, so there is no way to just give 1 to some element in H to pick up the same physical meaning in state variable X, and 0 to other irrelevant component. Under this situation, how do I design H matrix? I have read a paper, it propose method below which use some data to train all the matrix, including H. But I don’t understand how to deduce? can some one shed light on this? Also there is another post about how to calculate these matrix, but I don’t understand, https://towardsdatascience.com/the-kalman-filter-a… . So either https://towardsdatascience.com/the-kalman-filter-a… or the paper I posted will do.

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