Covariance and correlation matrices of an optimal stochastic system

The orthogonal projection lemma is applied to derive differential equations for the correlation and covariance matrices of filter estimators, whose solution is essentially simplified in the stationary state. The matrix similarity transformation and pseudocommutativity are used to construct an exact algebraic expression for the estimate covariance and correlation matrices.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 72, pp. 88–94, 1990.