Accurate Localization Given Uncertain Sensors

The necessity of accurate localization in mobile robotics is obvious - if a robot does not know where it is, it cannot navigate accurately to reach goal locations. Robots learn about their environment via sensors. Small robots require small, efficient, and, if they are to be deployed in large numbers, inexpensive sensors. The sensors used by robots to perceive the world are inherently inaccurate, providing noisy, erroneous data or even no data at all. Combined with estimation error due to imperfect modeling of the robot, there are many obstacles to successfully localizing in the world. Sensor fusion is used to overcome these difficulties - combining the available sensor data in order to derive a more accurate pose estimation for the robot. In this thesis, we dissect and analyze a wide variety of sensor fusion algorithms, with the goal of using a set of inexpensive sensors in a suite to provide real-time localization for a robot given unknown sensor errors and malfunctions. The sensor fusion algorithms will fuse GPS, INS, compass and control inputs into a more accurate position. The filters discussed include a SPKF-PF (Sigma-Point Kalman Filter - Particle Filter), a MHSPKF (Multi-hypothesis Sigma-Point Kalman Filter), a FSPKF (Fuzzy Sigma-Point Kalman Filter), a DFSPKF (Double Fuzzy Sigma-Point Kalman Filter), an EKF (Extended Kalman Filter), a MHEKF (Multi-hypothesis Extended Kalman Filter), a FEKF (Fuzzy Extended Kalman Filter), and a standard SIS PF (Sequential Importance Sampling Particle Filter). Our goal in this thesis is to provide a toolbox of algorithms for a researcher, presented in a concise manner. I will also simultaneously provide a solution to a difficult sensor fusion problem - an algorithm that is of low computational complexity (\u3c O(n³)), real-time, accurate (equal in or more accurate than a DGPS (differential GPS) given lower quality sensors), and robust - able to provide a useful localization solution even when sensors are faulty or inaccurate. The goal is to find a locus between power requirements, computational complexity and chip requirements and accuracy/robustness that provides the best of breed for small robots with inaccurate sensors. While other fusion algorithms work well, the Sigma Point Kalman filter solves this problem best, providing accurate localization and fast response, while the Fuzzy EKF is a close second in the shorter sample with less error, and the Sigma-Point Kalman Particle Filter does very well in a longer example with more error. Fuzzy control is also discussed, especially the reason for its applicability and its use in sensor fusion