The particle filter provides a solution to the state inference problem in nonlinear dynamical systems. This problem is indeed interesting in its own right, but it also shows up as a sub-problem in many relevant areas, such as for example sensor fusion and nonlinear system identification. The aim of this tutorial is to provide you with sufficient knowledge about the particle filter to allow you to start implementing particle filters on your own.
We will start out by providing a brief introduction to probabilistic modeling of dynamical systems in order to be able to clearly define the nonlinear state inference problem under consideration. The next step is to briefly introduce two basic sampling methods, rejection sampling and importance sampling. The latter is then exploited to derive a first working particle filter. The particle filter can be interpreted as a particular member of a general class of algorithms referred to as sequential Monte Carlo (SMC). This relationship is explored in some detail in order to provide additional understanding.
The particle filtering theory has developed at an increasing rate over the last two decades and it is used more and more in solving various applied problems. During this tutorial I focus on the method and to some extent on the underlying theory. Hence, I will not show any real world examples, I save them for my seminar on Thursday, where I will show how the particle filter has been instrumental in solving various nontrivial localization problems.
Thomas B. Schön is an Associate Professor with the Division of Automatic Control at Linköping University (Linköping, Sweden). He received the BSc degree in Business Administration and Economics in Jan. 2001, the MSc degree in Applied Physics and Electrical Engineering in Sep. 2001 and the PhD degree in Automatic Control in Feb. 2006, all from Linköping University. He has held visiting positions with the University of Cambridge (UK) and the University of Newcastle (Australia). He is a Senior member of the IEEE. He received the best teacher award at the Institute of Technology, Linköping University in 2009. Schön's main research interest is nonlinear inference problems, especially within the context of dynamical systems, solved using probabilistic methods. He is active within the fields of machine learning, signal processing and automatic control. He pursue both basic research and applied research, where the latter is typically carried out in collaboration with industry.