I was reading about subspace identification such as N4SID, MOESP and CVA. But they are so difficult and the education material I have does not teach those methods correctly. Always jumping over important stages and calculations.
Then I decided to go back and continue with estimation SISO system with ARX, ARMAX, BJ and OE metods.
Then I got the flashback:
$$G(s) = C(sI-A)^{-1}*B + D$$
It's possible to transform a state space model to a transfer function. And it's also possible to transform a transfer function to a state space model.
But how about a transfer function matrix $G_m(s) \in \Re^{nx1}$ to a state space model? It that possible?
Let's say that I have a system of a mechanical system. The mechanical system has two masses and that means that I can estimate two transfer function matrices.
$$G_m(s) = \begin{bmatrix} \frac{5}{s^2 + 3s +3}\\ \frac{0.1}{s^2 + 0.3s +6} \end{bmatrix}$$
Converting this to a state space will give me a SIMO state space model. But is this possible?
Yes it is. Although canonical realizations for SISO models are unique and straightforward, the equivalent theory for MIMO models, Brunovsky forms and the like, is somewhat more complex. The reason is, in general terms, that the connection between change of MacMillan degree and pole-zero cancellations is not as straightforward in the MIMO case as in the SISO case. I tend to agree with your impression that subspace identification is a complicated way to go about avoiding the issues created by multivariable models.
For the application you have in mind, system identification, I suggest you may want to use the work of yours truly. There's a learning curve related to realization theory, but if you trust our work cited below, and its references, you could go about implementing the methods without much fear.
Matchable-Observable Linear Models and Direct Filter Tuning: An Approach to Multivariable Identification. DOI: 10.1109/TAC.2016.2602891