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Mathematical Problems in Engineering
Volume 2015, Article ID 238131, 14 pages
Research Article

Sufficient Condition for Estimation in Designing Filter-Based SLAM

1Faculty of Electrical and Electronics Engineering, Universiti Malaysia Pahang, Pekan Campus, 26600 Pekan, Pahang, Malaysia
2Department of System Design Engineering, School of Integrated Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

Received 29 April 2014; Accepted 29 July 2014

Academic Editor: Tofigh Allahviranloo

Copyright © 2015 Nur Aqilah Othman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Extended Kalman filter (EKF) is often employed in determining the position of mobile robot and landmarks in simultaneous localization and mapping (SLAM). Nonetheless, there are some disadvantages of using EKF, namely, the requirement of Gaussian distribution for the state and noises, as well as the fact that it requires the smallest possible initial state covariance. This has led researchers to find alternative ways to mitigate the aforementioned shortcomings. Therefore, this study is conducted to propose an alternative technique by implementing filter in SLAM instead of EKF. In implementing filter in SLAM, the parameters of the filter especially γ need to be properly defined to prevent finite escape time problem. Hence, this study proposes a sufficient condition for the estimation purposes. Two distinct cases of initial state covariance are analysed considering an indoor environment to ensure the best solution for SLAM problem exists along with considerations of process and measurement noises statistical behaviour. If the prescribed conditions are not satisfied, then the estimation would exhibit unbounded uncertainties and consequently results in erroneous inference about the robot and landmarks estimation. The simulation results have shown the reliability and consistency as suggested by the theoretical analysis and our previous findings.