Dempster-Shafer Evidential Theory

Lawrence A. Klein

doi:10.1117/3.563340.ch6

Chapter 6:
Dempster-Shafer Evidential Theory

Book: Sensor and Data Fusion: A Tool for Information Assessment and Decision Making

Author(s): Lawrence A. Klein

Published: 2004
https://doi.org/10.1117/3.563340.ch6

Abstract

Dempster-Shafer evidential theory, a probability-based data fusion classification algorithm, is useful when the sensors (or more generally, the information sources) contributing information cannot associate a 100 percent probability of certainty to their output decisions. The algorithm captures and combines whatever certainty exists in the object discrimination capability of the sensors. Knowledge from multiple sensors about events (called propositions) is combined using Dempster's rule to find the intersection or conjunction of the propositions and their associated probabilities. When the intersection of the propositions reported by the sensors is an empty set, Dempster's rule redistributes the conflicting probability to the nonempty set elements. When the conflicting probability becomes large, application of Dempster's rule can lead to counterintuitive conclusions. Several modifications to the original Dempster-Shafer theory have been proposed to accommodate these situations. 6.1 Overview of the process An overview of the Dempster-Shafer data fusion process as might be configured to identify targets or objects is shown in Figure 6.1. Each sensor has a set of observables corresponding to the phenomena that generate information received about objects and their surroundings. In this illustration, a sensor operates on the observables with its particular set of classification algorithms (sensor-level fusion). The knowledge gathered by each Sensor k, where k = 1, â¦, N, associates a declaration of object type (referred to in the figure by object oi where i = 1, â¦, n) with a probability mass or basic probability assignment mk(oi) between 0 and 1. The probability mass expresses the certainty of the declaration or hypothesis, i.e., the amount of support or belief attributed directly to the declaration. Probability masses closer to unity characterize decisions made with more definite knowledge or less uncertainty about the nature of the object. The probability masses for the decisions made by each sensor are then combined using Dempster's rules of combination. The hypothesis favored by the largest accumulation of evidence from all contributing sensors is selected as the most probable outcome of the fusion process. A computer stores the relevant information from each sensor. The converse is also true, that is, targets not supported by evidence from any sensor are not stored.

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CHAPTER 6

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