How Do You Model a Discrete Stochastic Signal Using State-Space Representation?

[mr.t]

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 independent.

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!

 

[mr.t]

Just want to let you guys know that I've solved it. (pretty sure at least )