Skip to main content
SpringerLink
Log in

Bayesian and Dempster-Shafer fusion

  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

The Kalman Filter is traditionally viewed as a prediction-correction filtering algorithm. In this work we show that it can be viewed as a Bayesian fusion algorithm and derive it using Bayesian arguments. We begin with an outline of Bayes theory, using it to discuss well-known quantities such as priors, likelihood and posteriors, and we provide the basic Bayesian fusion equation. We derive the Kalman Filter from this equation using a novel method to evaluate the Chapman-Kolmogorov prediction integral. We then use the theory to fuse data from multiple sensors. Vying with this approach is the Dempster-Shafer theory, which deals with measures of “belief”, and is based on the nonclassical idea of “mass” as opposed to probability. Although these two measures look very similar, there are some differences. We point them out through outlining the ideas of the Dempster-Shafer theory and presenting the basic Dempster-Shafer fusion equation. Finally we compare the two methods, and discuss the relative merits and demerits using an illustrative example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Blackman S, Popoli R 1999Design and analysis of modern tracking systems (Boston: Artech House)

    MATH  Google Scholar 

  • Blasen E 1998 Decision making in multi-fiscal and multi-monetary policy measurements.Proc. Int. Conf. on Multisource-Multisensor Information Fusion (Fusion ’98) 1: 285–292

    Google Scholar 

  • Braun J 2000 Dempster-Shafer theory and Bayesian reasoning in multisensor data fusion,Sensor Fusion: Architectures, Algorithms and Applications IV; Proc. SPIE 4051: 255–266

    Google Scholar 

  • Cooper M, Miller M 1998 Information gain in object recognition via sensor fusion.Proc. Int. Conf. on Multisource-Multisensor Information Fusion (Fusion ’98) 1: 143–148

    Google Scholar 

  • Cremer F, den Breejen E, Schutte K 1998 Sensor data fusion for anti-personnel land mine detection.Proc. EuroFusion 98 55–60

    Google Scholar 

  • Debon R, Solaiman B, Cauvin J-M, Peyronny L, Roux C 1999 Aorta detection in ultrasound medical image sequences using Hough transform and data fusion.Proc. 2nd Int. Conf. on Information Fusion (Fusion ’99) 1: 59–66

    Google Scholar 

  • Debon R, Solaiman B, Roux C, Cauvin J-M, Robazkiewicz M 2000 Fuzzy fusion and belief updating. Application to esophagus wall detection on ultrasound images.Proc. 3rd Int. Conf. on Information Fusion (Fusion 2000) 1: TuC5_17-TuC5_23

    Google Scholar 

  • Dempster A P 1967 Upper and lower probabilities induced by a multivalued mapping.Ann. Math. Stat. 38: 325–339

    MathSciNet  MATH  Google Scholar 

  • Dempster A P 1968 A generalization of Bayesian inference,J. R. Stat. Soc. B 30: 205–247.

    MathSciNet  Google Scholar 

  • Hall D, Garga A 1999 Pitfalls in data fusion (and how to avoid them).Proc. 2nd Int. Conf. on Information Fusion (Fusion ’99) 1: 429–436

    Google Scholar 

  • Hatch M, Jahn E, Kaina J 1999 Fusion of multi-sensor information from an autonomous undersea distributed field of sensors.Proc. 2nd Int. Conf. on Information Fusion (Fusion ’99) 1: 4–11

    Google Scholar 

  • Haupt G, Kasdin N, Keiser G, Parkinson B 1996 Optimal recursive iterative algorithm for discrete nonlinear least-squares estimation.J. Guidance, Control Dynam. 19: 643–649

    Article  MATH  Google Scholar 

  • Heifetz M, Keiser G 1999 Data analysis in the gravity probe B relativity experiment.Proc. 2nd Int. Conf. on Information Fusion (Fusion ’99) 2: 1121–1125

    Google Scholar 

  • Ho Y C 1964 A Bayesian approach to problems in stochastic estimation and control.IEEE Trans. Autom. Control AC-9: 333

    Article  Google Scholar 

  • Hush D, Horne B 1993 Progress in supervised neural networks: what’s new since Lippman?IEEE Signal Process. Mag. 10(1): 8–39

    Article  Google Scholar 

  • Kewley D J 1992 Notes on the use of Dempster-Shafer and fuzzy reasoning to fuse identity attribute data, Defence Science and Technology Organisation, Adelaide. Technical memorandum SRL-0094-TM

  • Kokar M, Bedworth M, Frankel C 2000 A reference model for data fusion systems.Sensor fusion: Architectures, algorithms and applications IV; Proc. SPIE 4051: 191–202

    Google Scholar 

  • Krieg M L 2002 A Bayesian belief network approach to multi-sensor kinematic and attribute tracking.Proc. Conf. on Information, Decision and Control (IDC2002)

  • Myler H 2000 Characterization of disagreement in multiplatform and multisensor fusion analysis.Signal processing Sensor fusion, and target recognition IX; Proc. SPIE 4052: 240–248

    Google Scholar 

  • Rodríguez F, Portas J, Herrero J, Corredera J 1998 Multisensor and ADS data integration for en-route and terminal area air surveillance.Proc. Int. Conf. on Multisource-Multisensor Information Fusion (Fusion ’98) 2: 827–834

    Google Scholar 

  • Shafer G 1976A mathematical theory of evidence (Princeton, NJ: University Press)

    MATH  Google Scholar 

  • Schwartz S 2000 Algorithm for automatic recognition of formations of moving targets.Sensor fusion: Architectures, algorithms and applications IV; Proc. SPIE 4051: 407–417

    Google Scholar 

  • Simard M-A, Lefebvre E, Helleur C 2000 Multisource information fusion applied to ship identification for the recognised maritime picture.Sensor fusion: Architectures, algorithms and applications IV; Proc. SPIE 4051: 67–78

    Google Scholar 

  • Strömberg D 2000 A multi-level approach to sensor management.Sensor fusion: Architectures, algorithms and applications IV; Proc. SPIE 4051: 456–61

    Google Scholar 

  • Triesch J 2000 Self-organized integration of adaptive visual cues for face tracking.Sensor fusion: Architectures, algorithms and applications IV; Proc. SPIE 4051: 397–406

    Google Scholar 

  • Viola P, Gilles S 1996 at: http://www-rocq.inria.fr/gilles/IMMMI/immmi.html The report is by Gilles who uses Viola’s work, and is entitled “Description and experimentation of image matching using mutual information”

  • Watson G, Rice T, Alouani A 2000 An IMM architecture for track fusion.Signal processing, sensor fusion, and target recognition IX; Proc. SPIE 4052: 2–13

    Google Scholar 

  • Zachary J, Iyengar S 1999 Three dimensional data fusion for biomedical surface reconstruction.Proc. 2nd Int. Conf. on Information Fusion (Fusion ’99) 1: 39–45

    Google Scholar 

  • Zou Y, Ho Y K, Chua C S, Zhou X W 2000 Multi-ultrasonic sensor fusion for autonomous mobile robots.Sensor fusion: Architectures, algorithms and applications IV; Proc. SPIE 4051: 314–321

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information and Communications Group, Faculty of Engineering, The University of Technology, Sydney, Australia

    Subhash Challa

  2. Electronic Warfare and Radar Division, Defence, Science and Technology Organisation (DSTO), Adelaide, Australia

    Don Koks

Authors
  1. Subhash Challa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Don Koks
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Challa, S., Koks, D. Bayesian and Dempster-Shafer fusion. Sadhana 29, 145–174 (2004). https://doi.org/10.1007/BF02703729

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02703729

Keywords

Search

Navigation