Initialization

In this chapter we discuss the initializing state vector x(0) in more detail. We have assumed that x(0) is a random vector with mean zero and variance-covariance matrix S(0|0). As might be expected, the specific choice for S(0|0) can have a profound effect on predictions since it affects all the subsequent variances and covariances as they are built up from the values of

Var(x(1)) = F (0)S(0|0)FT (0) + Q(0),

Cov(x(1), ε(1)) = Var(x(1))HT (1)

and

R(1) = Var(ε(1)) = H(1)Var(x(1))HT (1) + W (1).