Mathematical Aspects of the Implementation of Particle Filters on FPGA

Abstract

AbstractParticle filters are a type of Bayesian filters commonly used for system state estimation such as tracking and localization applications. Tracking and localization are important tasks for autonomous robots, and particle filters are particularly well suited to deal with such tasks, as demonstrated by many RoboCup-Teams. However the computational complexity of particle filters lead to a high load of the Central Processing Unit (CPU) resulting in a high clock and a high energy usage. This limits the use of particle filters in small autonomous robots or intelligent embedded sensor for traffic surveillance. The algorithm is well suited for parallel execution, on customized hardware architectures. Such architectures can be realized using Field Programmable Gate Arrays (FPGA). The parallel execution leads to a significant reduction of clock and therefore of energy, making embedded high performance particle filters possible, relieving the CPU from a computational expensive task while providing high performance tracking capabilities. For reasons of logical cell usage the use of fixed point representations of the numbers involved in the computation of the algorithm is used. This poses a bigger problem than one might expect, as the original theory of the particle filter is based on continuous representations, and the algorithm won't work without modifications to counter the effects resulting from the limited precision of the fixed point number representation. A fixed point based particle filter for tracking of an object in six dimensions, 2D-translation, rotation, and translation and rotation speed has been implemented on a FPGA and the feasibility of some treatment approaches has been shown.