(untitled) (Journal of Academic Research, 2025)
In this paper, in order to simplify the understanding of the Kalman filter and its applications in practice, the optimization of Kalman filter is done empirically, and compared with the Luenberger observer. Therefore, a series of experiments are done for the range of current and delayed Kalman filter innovation gains with specific process dynamic and stochastic parameters. Also, for the sake of comparison, the same is applied on the observer as well. Where, the stochastic process parameters are the stochastic disturbance or the modeling error covariance (Q), and the measurement error covariance (R). Consequently, the tests of the current Kalman filter showed that the empirically measured optimal Kalman innovation gains are identical to the computations of the Kalman filter algorithms. On the other hand, the tests for the delayed version showed that empirical optimal innovation gains slightly diverge from computations of the algorithms.