This paper presents an analysis of H _∞ Filter(HF) for Robotics Mapping and Localization with unknown noise statistics. HF which is also known as the minimax filter is proposed in this paper to estimate the robot and landmarks location while robot moves through an unknown environment. Some of the conditions are proposed to ensure that the state covariance in HF is converging to a steady state value. Furthermore, the analysis of HF convergence for a robot observing landmarks are presented to examine its behavior through the observations. From the experimental results, HF gives a sufficient estimation about the environment. Subsequently, such a result can provide other available estimation methods with the capability to ensure and improved estimation in robotic mapping and localization problem.