Toward Efficient Computation of the Dempster-Shafer Belief Theoretic Conditionals

Dempster-Shafer (DS) belief theory provides a convenient framework for the development of powerful data fusion engines by allowing for a convenient representation of a wide variety of data imperfections. The recent work on the DS theoretic (DST) conditional approach, which is based on the Fagin-Halpern (FH) DST conditionals, appears to demonstrate the suitability of DS theory for incorporating both soft (generated by human-based sensors) and hard (generated by physics-based sources) evidence into the fusion process. However, the computation of the FH conditionals imposes a significant computational burden. One reason for this is the difficulty in identifying the FH conditional core, i.e., the set of propositions receiving nonzero support after conditioning. The conditional core theorem (CCT) in this paper redresses this shortcoming by explicitly identifying the conditional focal elements with no recourse to numerical computations, thereby providing a complete characterization of the conditional core. In addition, we derive explicit results to identify those conditioning propositions that may have generated a given conditional core. This "converse" to the CCT is of significant practical value for studying the sensitivity of the updated knowledge base with respect to the evidence received. Based on the CCT, we also develop an algorithm to efficiently compute the conditional masses (generated by FH conditionals), provide bounds on its computational complexity, and employ extensive simulations to analyze its behavior

Convergence analysis of consensus belief functions within asynchronous ad-hoc fusion networks

In a multi-agent data fusion scenario, agents may iteratively exchange their states to arrive at a consensus state which signifies `general agreement' among the agents. Agent states that are being exchanged may have been generated from hard (i.e., physics based) or soft (i.e., human based evidence. such as opinions or beliefs regarding an event) sensors. Convergence analysis becomes an extremely challenging problem in such complex fusion environments, which may involve communication delays, ad-hoc paths, etc. In this paper, we analyze consensus of a Dempster-Shafer theoretic (DST) fusion operator by formulating the consensus problem as finding common fixed points of a pool of paracontracting operators. Due to its DST basis, this consensus protocol can deal with a wider variety of data imperfections characteristic of hard+soft data fusion environments. It also easily adapts itself to networks where agent states are captured with probability mass functions because they can be considered a special case of DST models

Consensus-Based Credibility Estimation of Soft Evidence for Robust Data Fusion

Due to its subjective naturewhich can otherwise compromise the integrity of the fusion process, it is critical that soft evidence (generated by human sources) be validated prior to its incorporation into the fusion engine. The strategy of discounting evidence based on source reliability may not be applicable when dealing with soft sources because their reliability (e.g., an eye witnesses account) is often unknown beforehand. In this paper, we propose a methodology based on the notion of consensus to estimate the credibility of (soft) evidence in the absence of a ‘ground truth.’ This estimated credibility can then be used for source reliability estimation, discounting or appropriately ‘weighting’ evidence for fusion. The consensus procedure is set up via Dempster-Shafer belief theoretic notions. Further, the proposed procedure allows one to constrain the consensus by an estimate of the ground truth if/when it is available. We illustrate several interesting and intuitively appealing properties of the consensus procedure via a numerical example

Convergence Analysis of Iterated Belief Revision in Complex Fusion Environments

We study convergence of iterated belief revision in complex fusion environments, which may consist of a network of soft (i.e., human or human-based) and hard (i.e., conventional physics-based) sensors and where agent communications may be asynchronous and the link structure may be dynamic. In particular, we study the problem in which network agents exchange and revise belief functions (which generalize probability mass functions) and are more geared towards handling the uncertainty pervasive in soft/hard fusion environments. We focus on belief revision in which agents utilize a generalized fusion rule that is capable of generating a rational consensus. It includes the widely used weighted average consensus as a special case. By establishing this fusion scheme as a pool of paracontracting operators, we derive general convergence criteria that are relevant for a wide range of applications. Furthermore, we analyze the conditions for consensus for various social networks by simulating several network topologies and communication patterns that are characteristic of such networks

Achieving Consensus Under Bounded Confidence in Multi-Agent Distributed Decision-Making

Understanding the conditions under which a multi agent system reaches a consensus has wide applicability in distributed decision-making environments. The iterative exchange of local states (or opinions) between agents must usually adhere to various constraints. For example, an agent may update its state only from neighboring agents whose state does not differ by more than the agent's bound of confidence (BoC). In this paper, a novel method for generating an Erdols-Renyi random network that guarantees a consensus in a multi-agent system subject to agents' BoC constraints is presented. For the case when agents maintain binary uniformly distributed states, we provide theoretical results on the sensitivity of the network structure generated with respect to changes in the agent BoCs. To allow for more general types of uncertainty to be captured in agent states and the state update scheme, a Dempster-Shafer (DS) belief theoretic opinion model along with a non-parametric kernel density estimation method is utilized and the results are illustrated via a simulation. The method presented has numerous applications in social networks, autonomous mobile robots, distributed sensor systems, and viral marketing, to name a few. Furthermore, the model can be utilized to generate fault-tolerant multi-agent systems where the random network generation makes it difficult to fragment the agents via pre-planned attacks. A case study on autonomous robot soldiers is used for an illustration of these ideas

A belief theoretic approach for characterization of underwater munitions

Characterization, management and remediation of military munitions, especially in underwater environments, is a challenging task given all the technical and physical barriers. Optical cameras are better suited for identifying the physical shape of objects. But in underwater, low visibility almost prohibits the use of these cameras. Acoustic imaging is a good alternative to this, but the characteristics of imaging along with numerous artifacts of physical systems which are not easy to model, makes the object recognition task non-trivial. We explore here the possibility of exploiting the geometry of the object shadows for identification of objects itself. The inherited imperfections of the data and the numerous artifacts of sonar systems are counteracted via the use of a fusion algorithm which incorporates evidence from multiple perspectives. A Dempster-Shafer belief theoretic evidence updating scheme which is capable of modeling a wider variety of data imperfections is used for the fusion task. We illustrate the method via the use of real data obtained at a test site located in the Florida Atlantic University premises