49

Figure 3.21-

Unobserved state problem. Two unperturbed RV
trajectories beginning with identical values for Q
but different initial states.ⁱ

Because of the variation of Q^nomand Jfrom one step to the next, it is (unfortunately) necessary to

construct a new discrete system model for each step. This is done by sampling h(K_i) to determine

the model parameters for the current step, Q_i^nomand J_i.

The inverse of this linear model, J^-1, is

then used to choose the perturbation scalings necessary to reach Q_i^d
+1^.

process for a one-dimensional system.

Figure 3.22 illustrates this

Q^d

sample point

extrapolated perturbation value

Figure 3.22-

Model construction and extrapolation.k¹and k²are
two sample points used to construct the forward
model. The inverse model and Q^dyield the
necessary applied perturbation scaling, k^*