An Analytical Framework for Soft and Hard Data Fusion: A Dempster-Shafer Belief Theoretic Approach

The recent experiences of asymmetric urban military operations have highlighted the pressing need for incorporation of soft data, such as informant statements, into the fusion process. Soft data are fundamentally different from hard data (generated by physics-based sensors), in the sense that the information they provide tends to be qualitative and subject to interpretation. These characteristics pose a major obstacle to using existing multi-sensor data fusion frameworks, which are quite well established for hard data. Given the critical and sensitive nature of intended applications, soft/hard data fusion requires a framework that allows for convenient representation of various data uncertainties common in soft/hard data, and provides fusion techniques that are robust, mathematically justifiable, and yet effective. This would allow an analyst to make decisions with a better understanding of the associated uncertainties as well as the fusion mechanism itself. We present here a detailed account of an analytical solution to the task of soft/hard data fusion. The developed analytical framework consists of several main components: (i) a Dempster-Shafer (DS) belief theory based fusion strategy; (ii) a complete characterization of the Fagin-Halpern DS theoretic (DST) conditional notion which forms the basis of the data fusion framework; (iii) an evidence updating strategy for the purpose of consensus generation; (iv) a credibility estimation technique for validation of evidence; and (v) techniques for reducing computational burden associated with the proposed fusion framework. The proposed fusion strategy possesses several intuitively appealing features, and satisfies certain algebraic and fusion properties making it particularly useful in a soft/hard fusion environment. This strategy is based on DS belief theory which allows for convenient representation of uncertainties that are typical of soft/hard domains. The Fagin-Halpern (FH) notion is perhaps the most appropriate DST conditional notion for soft/hard data fusion scenarios. It also forms the basis for our fusion framework. We provide a complete characterization of the FH conditional notion. This constitutes a strong result, that sets the foundation for understanding the FH conditional notions and also establishes the theoretical grounds for development of algorithms for efficient computation of FH conditionals. We also address the converse problem of determining the evidence that may have generated a given change of belief. This converse result can be of significant practical value in certain applications. A consensus control strategy developed based on our fusion technique allows consensus analysis to be carried out in a multitude of applications that call for extended flexibility in uncertainty modeling. We provide a complete theoretical development of the proposed consensus strategy with rigorous proofs. We make use of these consensus notions to establish a data validation technique to assess credibility of evidence in the absence of ground truth. Credibility estimates can be used in fusion equations and also be used to estimate reliability of sources for subsequent fusion operations. Computational overhead is one of the major obstacles associated with data fusion operations, especially in DS theoretic methods. We propose a graphical procedure and its associated message passing scheme for efficient computation of the conditionals, along with the theoretical bounds for computational costs. In addition, we propose a method based on statistical sampling techniques to approximate DST data models. This allows for efficient computational representations as well as further reductions in computational costs associated with DS theoretic fusion operations. We have used several example scenarios throughout the presentation to clarify and validate the proposed notions and techniques. We conclude the dissertation by providing several guidelines for future research and summary of the work that is being presented