The Parallel Bayesian Toolbox for High-performance Bayesian Filtering in Metrology

Open access

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→∞. 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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Schwenke H. Neuschaefer-Rube U. Pfeifer T. Kunzmann H. (2002). Optical methods for dimensional metrology in production engineering. CIRP Annals - Manufacturing Technology 51 (2) 685-699.

  • [2] Estler W.T. Edmundson K.L. Peggs G.N. Parker D.H. (2002). Large-scale metrology - an update. CIRP Annals - Manufacturing Technology 51 (2) 587-609.

  • [3] BIPM IEC IFCC ILAC ISO IUPAC IUPAP and OIML. (2008). Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM 1995 with minor corrections). JCGM 100:2008.

  • [4] BIPM IEC IFCC ILAC ISO IUPAC IUPAP and OIML. (2008). Evaluation of measurement data - Supplement 1 to the ‘Guide to the expression of uncertainty in measurement’ - Propagation of distributions using a Monte Carlo method. JCGM 101:2008.

  • [5] BIPM IEC IFCC ILAC ISO IUPAC IUPAP and OIML. (2008). International vocabulary of metrology - Basic and general concepts and associated terms (VIM). JCGM 200:2008.

  • [6] Cappé O. Moulines E. Ryden T. (2005). Inference in Hidden Markov Models. Springer.

  • [7] Fraser A.M. (2008). Hidden Markov Models and Dynamical Systems (1st ed.). Society for Industrial and Applied Mathematics.

  • [8] Doucet A. de Freitas N. Gordon N. (2001).Sequential Monte Carlo Methods in Practice.Springer.

  • [9] Douc R. Cappé O. Moulines E. (2005). Comparison of resampling schemes for particle filtering. In Image and Signal Processing and Analysis : 4th International Symposium (ISPA 2005) 15-17 September 2005.IEEE 64-69.

  • [10] Daum F. Huang J. (2003). Curse of dimensionality and particle filters. In Aerospace Conference 8-15March 2003. IEEE Vol. 4 4-1979-4-1993.

  • [11] Google Project Hosting. Parallel Bayesian Toolbox. http://code.google.com/p/parallel-bayesian-toolbox/.

  • [12] Sanderson C. (2010). Armadillo: An open source C++ linear algebra library for fast prototyping and computationally intensive experiments. Technical Report. NICTA.

  • [13] CMake home page. http://www.cmake.org/.

  • [14] Bar-Shalom Y. Li X.-R. Kirubarajan T. (2001).Estimation with Applications to Tracking and Navigation : Theory Algorithms and Software. Wiley - Blackwell.

  • [15] Rosenband D.L. Rosenband T. (2009). A design case study: CPU vs. GPGPU vs. FPGA. In Formal Methods and Models for Co-Design : 7th IEEE/ACM International Conference (MEMOCODE’09) 13-15July 2009. IEEE 69-72.

  • [16] Garcia E. Hausotte T. Amthor A. (2013). Bayes filter for dynamic coordinate measurements - Accuracy improvment data fusion and measurement uncertainty evaluation. Measurement 46 (9) 3737-3744.

  • [17] Garcia E. Zschiegner N. Hausotte T. (2013).Parallel high-performance computing of Bayes estimation for signal processing and metrology. In Computing Management and Telecommunications (ComManTel) 21-24 January 2013. IEEE 212-218.

  • [18] Welch G. Bishop G. The Kalman Filter homepage. http://www.cs.unc.edu/~welch/kalman.

  • [19] Identification and Decision Making Research Group University of West Bohemia. Nonlinear Estimation Framework homepage. http://nft.kky.zcu.cz/nef.

  • [20] Cambridge University. Sequential Monte Carlo methods (Particle filtering) homepage. http://wwwsigproc.eng.cam.ac.uk/smc/software.html.

  • [21] The Orocos Project. The Bayesian Filtering Library. http://www.orocos.org/bfl.

  • [22] BiiPS Project. BiiPS (Bayesian inference with interacting Particle Systems) homepage. http://alea.bordeaux.inria.fr/biips.

  • [23] Michael Stevens. Bayes++. Open source Bayesian Filtering classes. http://bayesclasses.sourceforge.net.

Search
Journal information
Impact Factor

IMPACT FACTOR 2018: 1.122
5-year IMPACT FACTOR: 1.157

CiteScore 2018: 1.39

SCImago Journal Rank (SJR) 2018: 0.325
Source Normalized Impact per Paper (SNIP) 2018: 0.881

Cited By
Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 200 98 5
PDF Downloads 76 42 3