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In this paper, we examine the H∞ Filter-based SLAM especially about its convergence properties. In contrast to Kalman Filter approach that considers zero mean gaussian noise, H∞ Filter is more robust and may provide sufficient solutions for SLAM in an environment with unknown statistical behavior. Due to this advantage, H∞ Filter is proposed in this paper, to efficiently estimate the robot and landmarks location under worst case situations. H∞ Filter requires the designer to appropriately choose the noise's covariance with respect to γ to obtain a desired outcome. We show some of the conditions to be satisfy in order to achieve better estimation results than Kalman Filter. From the experimental results, H∞ Filter performs better than Kalman Filter for a case of bigger robot initial uncertainties. Subsequently, this proved that ∞ Filter can provide another available estimation method for especially in SLAM.