On the application of Kalman filter for the estimation problem with weakly coloured noises

The anisotropy-based estimation problem for linear discrete time invariant system is considered in the paper. The asymptotic formulas for estimator matrices, estimation error covariance matrice and anisotropic norm of estimation error system under the condition of small values of mean anisotropy of input disturbance are demonstrated. Also the maximum edge of external disturbance anisotropy, providing the prescribed accuracy of anisotropy-based estimator approximation by Kalman filter, is determined in the article. The stated problems solution is demonstrated in the graphical results of numerical modelling for linear discrete time invariant stable system.