I am fairly new to system identification (some background in DSP), and I am trying to use a linear black-box system identification procedure. I am specifically looking for recommendations of sources with a well-described procedure on how to implement black-box system ID and criteria for a properly identified black-box system. I am currently using the method described in "Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains" by Billings, but I am not having much luck. Basically any good starting place would be helpful!
More possibly relevant info about my project: I have a system that I am reasonably confident is linear. I only have data for a step input and I do not have a way of generating other kinds of responses. Signal to noise ratio is extremely high. The manufacturer of the system has purported a simple model. It is clearly an erroneously low order, but is this enough to use a gray-box system ID? I know even less about that, so if I have it all backwards, just ignore this part of the question.
Thanks for the help!