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The unknown noise statistic might degrade the Filter performance or even lead to filter divergence. Accordingly, to enhance the classical EKF to approximate the recursive process and measurement noise statistic, based on Maximum A Posteriori creation and Weighted Exponent (WE) as the divergence suppression method, abbreviated as MAPWE, an adaptive EKF is proposed through this paper. Moreover, the existence of simplification during estimating noise statistics under MAP creation might also degrade its quality. Thus, the suboptimal MAP solution was also estimated based on Weighted Exponent. Indeed, the time-varying noise statistic under this process seems strongly accurate. But the complexity of the measurement covariance might also diverge from its positive definite characteristic. Thus, aiming to prevent this condition, the additional divergence suppression method was also involved in correcting the error state covariance in the smoothing step. This improvement is then used as SLAM algorithm for a mobile robot. Comparing to the conventional methods, it is better in term of RMSE for the estimated path and estimated map.