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I would like to study time series modeling and state space modeling for the purpose of modeling a complex physical system (vibrations of an industrial machine). The system is mostly linear (small deformation hypothesis applies), but there could be nonlinearities due to coupling with the operating fluid. I had a look at the available books, but there's a huge number of them and I don't know how to choose. Can you point me in the right direction?

EDIT: I'm mostly interested in state estimation and model calibration, however also more generic references may be of help, because I'm relatively new to the field.

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  • $\begingroup$ @RichardHardy, thanks for the edit, I didn't know there was a reference tag, and it's pretty popular too! Nice $\endgroup$ – DeltaIV Nov 29 '16 at 12:56
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I do not have extensive experience in this area, but for an entry into the field I found the introductory materials by Sebastian Thrun to be accessible.

An overview of state-space modeling approaches is given in the earlier parts of the textbook

Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic robotics. MIT press.

which also has a website with supplementary materials. An applied overview of this material is also contained in his Udacity course Artificial Intelligence for Robotics: Programming a Robotic Car, which includes Python code, and is free (at the time of this writing).

For the classical linear-Gaussian case (Kalman filtering), I have mostly learned from online sources as needed. After you have some familiarity with the basics you might try a Google scholar search for papers in your particular application area, and then backtrack their "methods" references.

(Note also that the Signal Processing and/or Robotics StackExchange sites might have more users with relevant experience, compared to here.)

Hope this helps!

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