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I'm a physics Phd student and just have a self-taught knowledge about lti-systems. After a while I found out that several techniques such as heat capacity or thermal-conductance measurements can be modeled as lti-systems. The current approach to estimate the physical quantities is a nonlinear fit of the solution of the differential equations to the data.

But knowing that the system can be modeled as an lti-system, it's equivalent to estimating the state space matrices A, B, C, D. After some research I found out there are several techniques such as subspace identification which do not need non linear regression.

My question is what are the state of the art techniques for identifiing low dimensional models with only a few in- and outputs?

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