With the development of autonomous robotics, the ability of a robot to perform SLAM with the highest accuracy and convey reliable data is becoming an inevitable requirement. A key aspect in this respect is the consistency of the estimator which follows that the state estimations produced by it are centered at zero and have a value of covariance matrix lower than that assessed by the filter. However analytical evaluations prove that the EKF-SLAM is an inconsistent estimator as the linearized error state model produced by it has an unobservable subspace having a dimension lower than that of the real-world non-linear SLAM system. As a solution to this problem the First-Estimates Jacobian SLAM (FEJ-SLAM) algorithm was developed where an error state model with similar dimensions as the SLAM system is being used. However, the FEJ-SLAM fails to perform satisfactorily in certain cases. Hence a window-based moving average algorithm (W-MA-FEJ-SLAM) has been proposed as a modification of FEJ-SLAM which can maintain the beauty of the algorithm in noisy environments. The proposed approach has been tested and evaluated extensively to prove that it outperforms the traditional aristocratic algorithms such as Standard EKF-SLAM and the FEJ-SLAM.