Prashant Kumar answered . 2024-05-18 14:06:38

x(k+1) = A x(k) + B u(k) + K e(k)
  y(k) = C x(k) + D u(k) + e(k)

H in this case is:

x(k+1) = A x(k) + K e(k)
  yh(k) = C x(k) + e(k)

When you estimate a state space model using PEM, you estimate the values of one or more of A, B, C, D and K. In order to have a nontrivial noise component in your model, make sure that K is not fixed at zero. You do this by using "DisturbanceModel"/'estimate' PV pair in the estimation command or by setting the DisturbanceModel property of an existing IDSS model to 'estimate':

model = pem(data, NX, 'dist', 'estimate')
model2 = idss(drss(NX)) % or some other template you created using IDSS command
model2.DisturbanceMOdel = 'estimate'
model2 = pem(data, model2, 'focus', 'prediction')

   System Identification — Theory For the User, Lennart Ljung, Section 13.4-13.5, 2nd ed, PTR Prentice Hall, Upper Saddle River, N.J., 1999.

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