An AEKF-SLAM Algorithm with Recursive Noise Statistic Based on MLE and EM

Abstract

Extended Kalman Filter (EKF) has been popularly utilized for solving Simultaneous Localization and Mapping (SLAM) problem. Essentially, it requires the accurate system model and known noise statistic. Nevertheless, this condition can be satisfied in simulation case. Hence, EKF has to be enhanced when it is applied in the real-application. Mainly, this improvement is known as adaptive-based approach. In many different cases, it is indicated by some manners of estimating for either part or full noise statistic. This paper present a proposed method based on the adaptive-based solution used for improving classical EKF namely An Adaptive Extended Kalman Filter. Initially, the classical EKF was improved based on Maximum Likelihood Estimation (MLE) and Expectation-Maximization (EM) Creation. It aims to equips the conventional EKF with ability of approximating noise statistic and its covariance matrices recursively. Moreover, EKF was modified and improved to tune the estimated values given by MLE and EM creation. Besides that, the recursive noise statistic estimators were also estimated based on the unbiased estimation. Although it results high quality solution but it is followed with some risks of non-positive definite matrices of the process and measurement noise statistic covariances. Thus, an addition of Innovation Covariance Estimation (ICE) was also utilized to depress this possibilities. The proposed method is applied for solving SLAM problem of autonomous wheeled mobile robot. Henceforth, it is termed as AEKF-SLAM Algorithm. In order to validate the effectiveness of proposed method, some different SLAM-Based algorithm were compared and analyzed. The different simulation has been showing that the proposed method has better stability and accuracy compared to the conventional filter in term of Root Mean Square Error (RMSE) of Estimated Map Coordinate (EMC) and Estimated Path Coordinate (EPC).