- #1
mr.t
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Homework Statement
A time discrete stocastic signal is described by
s(k) = w(k-1) + aw(k-2), |a|<1
and w(n) is white gaussian noise with m_w = 0, \sigma_w^2 = 1. It is observed under influence of white noise:
y(k) = s(k) + v(k)
where v(n) is white gaussian noise with m_v = 0, \sigma_v^2=1. v(n) and w(n) are independant.
Problem: Find the space-state model:
x(k+1) = Ax(k) + Bw(k)<br /> y(k) = Cx(k) + v(k)
By using the state:
x(k) = \bmatrix s(k) \\ w(k-1) \endbmatrix
Homework Equations
(given above)
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 I am suppose to use the specified states? How does that affect the state-space model?
Im confused, please help me!
Thanks!
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