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In the robotic field of study, localization is one of the important methods for autonomous mobile robot navigation. Probabilistic approaches have received significant attention in the robotics community. The discrete Bayes and Kalman filters are the fundamental algorithms in probabilistic approach which have to be clearly understood in order to develop more advanced filtering algorithms. This paper discusses discrete Bayes and Kalman filtering algorithms. The mathematical representation of each filter algorithm, in the 1-dimensional case, presented in detail. The algorithms were implemented using python to simulate the probability of the robot position. The algorithms complexity was analyzed with respect to the computational cost and size of memory used. From this study, it has been observed that the Kalman filter is computationally more efficient, and less memory is required.