Kalman-filter models for the optimal estimation of the post-fault currents and voltages for computer relaying purposes of power systems are presented. As a prerequisite for the Kalman-filtering implementation, the random description of the fault-induced noise signals was quantitatively studied. Empirical formulas that describe the random nature of the noise based on the probability of fault location and the frequency of occurrence of the different types of faults are given. These empirical formulas offer the possibility of developing other new techniques in computer relaying of power systems;Sensitivity of the Kalman filters to incorrect model parameters was studied through extensive simulation. A Kalman-filtering-based digital distance relay was designed to detect, classify, and locate faults in a high voltage transmission line in the shortest period of time;Comparison of the developed technique with four other algorithms demonstrated that the Kalman-filtering-based algorithm is superior to other techniques in the rate of convergence to the exact values, accuracy, and computer burden. Thus the Kalman-filtering approach appears to be especially well-suited to the power system protection problem.