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A state-space model of a system with input vector u, output vector y, and disturbance e takes the following form in continuous time:

d (x(t)) / dt = Ax(t)+Ke(t)
y(t) = Cx(t)+e(t)

In the MATLAB function ssest I am able to extract the A,C and the K parameters, however I am really interested on extracting the e(t) parameter in order to build the covariance of the residues.

  data = iddata(X(:,1:100,10)',[],1);
  opt  = ssestOptions('EstCovar',true);
  sys  = ssest(data,[1:10],opt);

  A = sys.A;                      % state transition matrix
  C = sys.C;                      % observation matrix
  K = sys.K;                      % inovation form

Can someone tell me, if with this function, I am able to do so?

am304
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tTimoteof
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1 Answers1

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e(t) is a disturbance, it's not part of the model (it's an input to the model) so it doesn't make sense to "extract" it, you can't do that. It's whatever you want it to be.

See the documentation page on ssest for more details.

am304
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  • Thank you for the reply! But @am304, regarding the *state-space estimation*, it estimate the parameters that *minimize* the residues, am I right? So if this is true, I should be expecting to obtain the information of the residues in the end, as the outcome result of the iterations of the minimization. – tTimoteof Apr 15 '16 at 10:14
  • Have a look at [`idssdata`](http://uk.mathworks.com/help/ident/ref/idssdata.html) and [Comparison of various model identification methods](http://uk.mathworks.com/help/ident/examples/comparison-of-various-model-identification-methods.html) – am304 Apr 15 '16 at 10:27
  • Regarding the first suggestion it returns the uncertenty of the parameters. However how can I convert that information into the uncertenty of the model? This because, having in mind the equations refered in the introduction to this question, the matrix dimentions must match, and also these equations show clearly a model uncertenty. I was looking here [State-Space Models in Matlab](http://www.mathworks.com/help/ident/state-space-models.html) however no luck yet. – tTimoteof Apr 15 '16 at 11:48
  • can you give me more input, @am304 ? – tTimoteof Apr 15 '16 at 12:17
  • All I can suggest is have a look at [`resid`](http://uk.mathworks.com/help/ident/ref/resid.html), [Examine Model Residuals](http://uk.mathworks.com/help/ident/ug/examine-model-residuals.html) and [What Is Residual Analysis?](http://uk.mathworks.com/help/ident/ug/what-is-residual-analysis.html). It looks like you might to use the System Identification tool. – am304 Apr 15 '16 at 13:42