Kalman filter tuning is based on the process and measurement noise covariances that are often obtained by ad hoc methods. After the filter is tuned, it is necessary to evaluate the quality of the state estimation. In this article, several methods are described for the quality evaluation of the Kalman filter performance. The article includes simulation results evaluating the reliability of the described optimality tests. The sequential test is then used for an adaptive algorithm for a Kalman filter. Further, properties of an autocorrelation function are discussed and several methods for its estimation are compared..