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Kalman, state-space model

  1. Aug 19, 2008 #1
    1. The problem statement, all variables and given/known data
    A time discrete stocastic signal is described by
    [tex]s(k) = w(k-1) + aw(k-2)[/tex], |a|<1
    and w(n) is white gaussian noise with [tex]m_w = 0, \sigma_w^2 = 1[/tex]. It is observed under influence of white noise:
    [tex]y(k) = s(k) + v(k)[/tex]
    where v(n) is white gaussian noise with [tex]m_v = 0, \sigma_v^2=1[/tex]. v(n) and w(n) are independant.

    Problem: Find the space-state model:
    [tex]x(k+1) = Ax(k) + Bw(k)
    y(k) = Cx(k) + v(k)[/tex]

    By using the state:
    [tex]x(k) = \bmatrix s(k) \\ w(k-1) \endbmatrix[/tex]

    2. Relevant equations
    (given above)

    3. The attempt at a solution
    I have only solved these problems when there is a AR-part. As this is an ARMA(0,2) I have no clue and need help. If its just an MA-part, then the whole A-matrix is zero? And how should I use the fact that Im suppose to use the specified states? How does that affect the state-space model?

    Im confused, please help me!
    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 20, 2008 #2
    Just want to let you guys know that i've solved it. (pretty sure at least :tongue2:)
     
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