STATE SPACE MODEL NOTATION  QUICK GUIDE
We write the state space model for exponential family observations
{Y_{t}} and
Gaussian latent process {q_{t}} for t=1,2,¼,n as

  
exp{y_{t}^{T}h_{t}  b(h_{t}) + c(y_{t})}, 
   
      
      
      
      



for known values of the prior mean m_{0} and the prior variance C_{0}.
In the definition we have introduced the system matrices which are
needed for specifying an object of class state space model
 F_{t}:
 The p × d design matrix usually consisting
of known functions of covariates at time t. It links the state
vector to the observation vector by means of a dynamic linear
regression, whose coefficient vector is determined by the first
order vector autoregression in the system equation.
 G_{t}:
 The p × p evolution transfer matrix
at time t. It is the design matrix for the latent process, and
usually consists of known functions of covariates and possible
previous observations. Often the evolution transfer matrices are
blockdiagonal; each block representing a certain aspect of the
model e.g. trend or seasonal effects.
 W_{t}:
 The evolution variance at time time. It can depend on
covariates and an unknown parameter vector. When applying
the iterated extended Kalman filter and smoother
W_{t} is allowed to be singular. However, when
simulating from a state space model it
must be a proper variance matrix.
