mr.t
Aug19-08, 06:34 AM
1. The problem statement, all variables and given/known data
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)
y(k) = Cx(k) + v(k)
By using the state:
x(k) = \bmatrix s(k) \\ w(k-1) \endbmatrix
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
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)
y(k) = Cx(k) + v(k)
By using the state:
x(k) = \bmatrix s(k) \\ w(k-1) \endbmatrix
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