The parallel bayesian toolbox for high-performance bayesian filtering in metrology

Abstract

The Bayesian theorem is the most used instrument for stochastic inferencing in nonlinear dynamic systems and also the fundament of measurement uncertainty evaluation in the GUM. Many powerful algorithms have been derived and applied to numerous problems. The most widely used algorithms are the broad family of Kalman filters (KFs), the grid-based filters and the more recent particle filters (PFs). Over the last 15 years, especially PFs are increasingly the subject of researches and engineering applications such as dynamic coordinate measurements, estimating signals from noisy measurements and measurement uncertainty evaluation. This is rooted in their ability to handle arbitrary nonlinear and/or non-Gaussian systems as well as in their easy coding. They are sampling-based sequential Monte-Carlo methods, which generate a set of samples to compute an approximation of the Bayesian posterior probability density function. Thus, the PF faces the problem of high computational burden, since it converges to the true posterior when number of particles NP?8. In order to solve these computational problems a highly parallelized C++ library, called Parallel Bayesian Toolbox (PBT), for implementing Bayes filters (BFs) was developed and released as open-source software, for the first time. In this paper the PBT is presented, analyzed and verified with respect to efficiency and performance applied to dynamic coordinate measurements of a photogrammetric coordinate measuring machine (CMM) and their online measurement uncertainty evaluation.