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!

  • $\begingroup$ so are you saying you have a black box with an input and output, you believe the relationship of the output to input is linear (and time-invariant), and you have the step response of this LTI system? (if you have the step-response, you can differentiate it to get the impulse response. and with the impulse response, you have everything you need to know about an LTI system from an input-to-output point of view.) $\endgroup$ Sep 1 '18 at 4:18
  • $\begingroup$ Along the lines of what robert said, but If you have a step input and the response is noisy, you can difference it and then use the identification algorithms for ARIMA models. These are time domain identification methods rather than DSP but they could still be useful particularly if system is linear but noisy. Google for "identification of arima models" and a lot should come up. Or, if you want references, there is the classic text of box-jenkins-reinsel and the text of boaz porat which is geared more towards DSP. Basically, any decent "intro to time series text " should have it. $\endgroup$
    – mark leeds
    Sep 1 '18 at 4:33

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