Particle filter theory and practice with positioning applications

TLDR

The particle filter, introduced in 1993, provides a numerical solution to nonlinear Bayesian filtering and has a mature theory with many successful applications. The tutorial surveys key theoretical aspects of particle filtering relevant to applications and illustrates these with positioning examples where conventional Kalman filter approaches would perform poorly. It presents the general particle filter algorithm, compares it to EKF and PMF, discusses tuning, design alternatives, computational bottlenecks and remedies, and covers the Rao‑Blackwellized PF framework, while also providing a stand‑alone, code‑rich positioning application guide. The reviewed positioning applications, all based on real data and some from real‑time implementations, demonstrate the particle filter’s superior performance over classical Kalman filter methods.

Abstract

The particle filter (PF) was introduced in 1993 as a numerical approximation to the nonlinear Bayesian filtering problem, and there is today a rather mature theory as well as a number of successful applications described in literature. This tutorial serves two purposes: to survey the part of the theory that is most important for applications and to survey a number of illustrative positioning applications from which conclusions relevant for the theory can be drawn. The theory part first surveys the nonlinear filtering problem and then describes the general PF algorithm in relation to classical solutions based on the extended Kalman filter (EKF) and the point mass filter (PMF). Tuning options, design alternatives, and user guidelines are described, and potential computational bottlenecks are identified and remedies suggested. Finally, the marginalized (or Rao-Blackwellized) PF is overviewed as a general framework for applying the PF to complex systems. The application part is more or less a stand-alone tutorial without equations that does not require any background knowledge in statistics or nonlinear filtering. It describes a number of related positioning applications where geographical information systems provide a nonlinear measurement and where it should be obvious that classical approaches based on Kalman filters (KFs) would have poor performance. All applications are based on real data and several of them come from real-time implementations. This part also provides complete code examples.