Optimal linear extrapolation of realizations of a stochastic process with error filtering in correlated measurements (Q1907777)

The authors consider the following model of a stochastic process with discrete time: \(Z(i)= X(i)+ Y(i)\), \(i= 1,\dots, I\), where \(Y(i)\) is a random error of observations. They propose the algorithm of linear extrapolation that is based on the method of canonical decomposition of a stochastic process with given correlation matrix. The linear filtering is used to improve the error of prediction. The results of simulation are presented for the case when \(X(i)\) and \(Y(i)\) are Gaussian processes.