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State-Space Model Estimation Methods

You can estimate state-space models using one of the following estimation methods:

  • N4SID — Noniterative, subspace method. The method works on both time-domain and frequency-domain data and is typically faster than the SSEST algorithm. You can choose the subspace algorithms such as CVA, SSARX, or MOESP using the n4Weight option. You can also use this method to get an initial model (see n4sid), and then refine the initial estimate using the iterative prediction-error method ssest.

    For more information about this algorithm, see [1].

  • SSEST — Iterative method that uses prediction error minimization algorithm. The method works on both time-domain and frequency-domain data. For black-box estimation, the method initializes the model parameters using n4sid and then updates the parameters using an iterative search to minimize the prediction errors. You can also use this method for structured estimation using an initial model with initial values of one or more parameters fixed in value.

    For more information on this algorithm, see [2].

  • SSREGEST — Noniterative method. The method works on discrete time-domain data and frequency-domain data. It first estimates a high-order regularized ARX or FIR model, converts it to a state-space model and then performs balanced reduction on it. This method provides improved accuracy on short, noisy data sets.

With all the estimation methods, you have the option of specifying how to handle initial state, delays, feedthrough behavior and disturbance component of the model.


[1] van Overschee, P., and B. De Moor. Subspace Identification of Linear Systems: Theory, Implementation, Applications. Springer Publishing: 1996.

[2] Ljung, L. System Identification: Theory For the User, Second Edition, Upper Saddle River, N.J: Prentice Hall, 1999.

[3] T. Chen, H. Ohlsson, and L. Ljung. “On the Estimation of Transfer Functions, Regularizations and Gaussian Processes - Revisited”, Automatica, Volume 48, August 2012.