Parameter estimation for high dimensional ordinary differential equation
In reality, X(t) cannot be measured exactly and d rectly; instead, its surrogate Y can be measured. For simplicity, here we assume an additive measurement
error model to describe the relationship between X(ti) and the surrogate Yi,
= +∈( ) ,Y X ti i i (2)
at random or fixed design time points , ,1t tn , where the measurement errors ( , , )1 nε ε are independent with mean zero and a diagonal variancecovariance matrix Σ. Moreover, in the case of random design, assume that the measurement errors are independent of X(t).