This site contains information related to my Master's thesis project on Robot Localization and Kalman Filters. I did the research involved in the project from July 2002 until August 2003 at the Datalogisk Institut of the Copenhagen University (DIKU), Denmark. My supervisors were Prof. Dr. Phil. Peter Johansen from DIKU, and Dr. Marco Wiering from the Faculty of Mathematics and Computer Science, Utrecht University.
| thesis.pdf | Thesis in PDF with URLs to articles and interactive table of contents |
| thesis.ps | Thesis in PostScript |
| errata.txt | Locations of typos |
| kal_loc.pdf | Presentation in PDF |
| HTML | Presentation online |
| matlab_sim.zip | General Kalman Filter simulator for matlab created during project (update July 2009) |
| readme.txt | Readme for the Kalman Filter simulator (update July 2009) |
| demo_fs_ekf.m | Parameterless demo script to get started with the simulator and the extended Kalman filter |
| demo_fs_iekf.m | Parameterless demo script to get started with the simulator and the iterated extended Kalman Filter |
The robot localization problem is a key problem in making truly autonomous robots. If a robot does not know where it is, it can be difficult to determine what to do next. In order to localize itself, a robot has access to relative and absolute measurements giving the robot feedback about its driving actions and the situation of the environment around the robot. Given this information, the robot has to determine its location as accurately as possible. What makes this difficult is the existence of uncertainty in both the driving and the sensing of the robot. The uncertain information needs to be combined in an optimal way.
The Kalman Filter is a technique from estimation theory that combines the information of different uncertain sources to obtain the values of variables of interest together with the uncertainty in these. The filter has been successfully applied in many applications, like missions to Mars, and automated missile guidance systems. Although the concept of the filter is relatively easy to comprehend, the advantages and shortcomings can only be understood well with knowledge of the pure basics and with experience.
In this work we provide a thorough discussion of the robot localization problem and Kalman Filter techniques. First, we look at current methods to obtain location information, pointing out advantages and disadvantages. We formalize how to combine this information in a probabilistic framework and discuss several currently used methods that implement it. Second, we look at the basic concepts involved in Kalman Filters and derive the equations of the basic filter and commonly used extensions. We create understanding of the workings, while discussing the differences between the extensions. Third, we discuss and experimentally show how Kalman Filters can be applied to the localization problem. We look at system and measurement models that are needed by the filter; that is, we model a driving system, a GPS-like sensor, and a landmark-based sensor. We perform simulations using these models in our own general Kalman Filter simulator showing different behaviors when applying the Kalman Filter to the localization problem. In order to use the landmark-based sensor when it can not uniquely identify landmarks, we extend the Kalman Filter to allow for multiple beliefs.
The material presented in this work forms a basis for further studies in localization literature, application of Kalman Filters in any domain, and in particular practical application of Kalman Filters and localization on physical robots.