To make optimal use of the Kalman filter, it is of great importance to determine the covariance of the measurement noise \(\underline{R}(k)\) and the system noise \(\underline{Q}(k)\) as accurately as possible. Only by precisely determining these two covariances is it possible to achieve optimal state estimation and a correct estimation of the covariance of the estimation error. For many applications, it is not sufficient to estimate these two quantities just once, as they can change significantly over time. The following presents an approach that enables rapid and adaptive determination of the measurement and system noise. This linear Kalman filter with adaptive estimation of the two covariance matrices is hereafter referred to as the ROSE filter (Rapid Ongoing Stochastic covariance Estimation filter).