Optimization of the distribution of the observations of the oscillatory system

Abstract

Let /spl theta/ be the m-vector of the unknown parameters, and suppose r/sub i/(i=l,...m) are number of the measurements of the functions H/sub i//sup T//spl theta/, where H/sub i//sup T/ are given vectors. Assume, that the errors of the measurements /spl epsi/i are mutually uncorrelated random values with expectations being zero and variances being /spl sigma//sub i/. So, if y/sub i/ are the mean values of r/sub i/ measured values then averaged equations of the measurements can be written as y/sub i/=H/sub i//sup T//spl theta/+/spl epsi//sub i/, where the variances of /spl epsi//sub i/ equal /spl sigma//sub i//r/sub 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/sub i/ and numbers p/sub i/=r/sub 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.