Mobile Robot Localization and Mapping using a Gaussian Sum Filter

A Gaussian sum filter (GSF) is proposed in this paper on simultaneous localization and mapping (SLAM) for mobile robot navigation. In particular, the SLAM problem is tackled here for cases when only bearing measurements are available. Within the stochastic mapping framework using an extended Kalman filter (EKF), a Gaussian probability density function (pdf) is assumed to describe the range-and-bearing sensor noise. In the case of a bearing-only sensor, a sum of weighted Gaussians is used to represent the non-Gaussian robot-landmark range uncertainty, resulting in a bank of EKFs for estimation of the robot and landmark locations. In our approach, the Gaussian parameters are designed on the basis of minimizing the representation error. The computational complexity of the GSF is reduced by applying the sequential probability ratio test (SPRT) to remove under-performing EKFs. Extensive experimental results are included to demonstrate the effectiveness and efficiency of the proposed techniques.

[1]  John J. Leonard,et al.  Stochastic mapping frameworks , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[2]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[3]  Yaakov Bar-Shalom,et al.  Design of an interacting multiple model algorithm for air traffic control tracking , 1993, IEEE Trans. Control. Syst. Technol..

[4]  Kwon Soon Lee,et al.  Lyapunov-based Fuzzy Queue Scheduling for Internet Routers , 2007 .

[5]  Ngai Ming Kwok,et al.  Evolutionary particle filter: re-sampling from the genetic algorithm perspective , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[6]  Ali Reza Mehrabian,et al.  Fuzzy Linear Parameter Varying Modeling and Control of an Anti-Air Missile , 2007 .

[7]  Howie Choset,et al.  Bearing-only landmark initialization with unknown data association , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[8]  Joydeep Ghosh,et al.  A mixture-of-experts framework for adaptive Kalman filtering , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Dimitrios Hatzinakos,et al.  An adaptive Gaussian sum algorithm for radar tracking , 1999, Signal Process..

[10]  Hugh F. Durrant-Whyte,et al.  A solution to the simultaneous localization and map building (SLAM) problem , 2001, IEEE Trans. Robotics Autom..

[11]  Fredrik Gustafsson,et al.  Range estimation using angle-only target tracking with particle filters , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[12]  Nikos A. Vlassis,et al.  A Greedy EM Algorithm for Gaussian Mixture Learning , 2002, Neural Processing Letters.

[13]  T. R. Kronhamn,et al.  Bearings-only target motion analysis based on a multihypothesis Kalman filter and adaptive ownship motion control , 1998 .

[14]  Gamini Dissanayake,et al.  Bearing-only SLAM Using a SPRT Based Gaussian Sum Filter , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[15]  Michel Devy,et al.  Undelayed initialization in bearing only SLAM , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[16]  Keum-Shik Hong,et al.  An IMM Algorithm for Tracking Maneuvering Vehicles in an Adaptive Cruise Control Environment , 2004 .

[17]  Peter C. Cheeseman,et al.  Estimating uncertain spatial relationships in robotics , 1986, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[18]  P. S. Maybeck,et al.  Cost-function-based gaussian mixture reduction for target tracking , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

[19]  Jun S. Liu,et al.  Mixture Kalman filters , 2000 .

[20]  Ngai Ming Kwok,et al.  A Modified Particle Filter for Simultaneous Localization and Mapping , 2006, J. Intell. Robotic Syst..

[21]  D. Alspach.  A gaussian sum approach to the multi-target identification-tracking problem , 1975, Autom..

[22]  Sebastian Thrun,et al.  Robotic mapping: a survey , 2003 .

[23]  I. King,et al.  Gaussian mixture distance for information retrieval , 1999, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339).