Optimization of the distribution of the observations of the oscillatory system

Let θ be the m-vector of the unknown parameters, and suppose r_i(i=l,...m) are number of the measurements of the functions H_i^Tθ, where H_i^T are given vectors. Assume, that the errors of the measurements εi are mutually uncorrelated random values with expectations being zero and variances being σ_i. So, if y_i are the mean values of r_i measured values then averaged equations of the measurements can be written as y_i=H_i^T θ+ε_i, where the variances of ε_i equal σ_i/r_i. Suppose, that the overall number of observations is N. We consider the optimal experimental design problem with A-optimum criterion (A-problem). This problem may be formulated as a problem of definition of the set of time moments t_i and numbers p_i=r_i/N to minimize a given function. This method is applied to the problem of optimization of distribution of observations of an artificial satellite of the Earth