An Introduction to Bayesian and Dempster-Shafer Data Fusion

The Kalman Filter is traditionally viewed as a Prediction-Correction Filtering Algorithm. In this report 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 pr...

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Bibliographic Details
Main Authors: Koks, Don, Challa, Subhash
Format: Report
Language:English
Subjects:
Active & Passive Radar Detection & Equipment
ALGORITHMS
AQ F04-01-0102
AUSTRALIA
BAYES THEOREM
DATA FUSION
DEMPSTER-SHAFER TECHNIQUE
Electricity and Magnetism
EQUATIONS
FOREIGN REPORTS
KALMAN FILTERING
MULTISENSORS
Statistics and Probability
THEOREM PROVING
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Summary:The Kalman Filter is traditionally viewed as a Prediction-Correction Filtering Algorithm. In this report 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 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 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.