Problem 6.6 We consider the state-space model given by:

Xt+1 = FXt + Vt Yt = GXt +Wt where the covariance matrices of the white noises {Vt}t and {Wt}t are the identity matrices and where the other parameters are given by:
F = 

.2 −.1 3 1 0 0 0 1 0 
 , and G = 
1 1 0 0 1 1 
.
We assume that the values of the one step ahead estimates ˆXt0 of the state vector, and Ωt0 of its covariance matrix are given by:
ˆX t0 = 

1.2 .3 .45 
 , and Ωt0 = 

1.25 1 1 1 1.25 1 1 1 1 
 .
We also assume that the next 5 values of the observation vector Y are given by:
Yt0 = 
−.1 1 
, Yt0+1 = 
.3 .9 
, Yt0+2 = 
.47 −.8 
, Yt0+3 = 
.85 −1.0 
, Yt0+4 = 
.32 .9 
.
For each time t = t0 + 1, t = t0 + 2, t = t0 + 3, t = t0 + 4 and t = t0 + 5, use Kalman filtering to compute the one step ahead estimates ˆXt, its prediction quadratic error Ωt, and of the next observation vector ˆ Yt|t−1, and its prediction quadratic error Δ(1)
t−1.