4. Nonlinear propagation of the confidence region

As time goes by, the confidence region is deformed by the integral flow. If the linear approximation of the flow, represented by the state transition matrix, were applicable, then the confidence ellipsoid at time t₀ (defined by the matrix C₀) would be deformed into a confidence region not very different from the confidence ellipsoid at time t, defined by the matrix C_t. However, this is not the case when the time span $\Delta t=t-t_0$ is long enough to generate an uncertainty in $\lambda$ which is large, say a significant fraction of one radiant.