Automatic Updates of Transition Potential Matrices in Dempster-Shafer Networks Based on Evidence Inputs

Abstract

<jats:p>Sensor fusion is a topic central to aerospace engineering and is particularly applicable to unmanned aerial systems (UAS). Evidential Reasoning, also known as Dempster-Shafer theory, is used heavily in sensor fusion for detection classification. High computing requirements typically limit use on small UAS platforms. Valuation networks, the general name given to evidential reasoning networks by Shenoy, provides a means to reduce computing requirements through knowledge structure. However, these networks use conditional probabilities or transition potential matrices to describe the relationships between nodes, which typically require expert information to define and update. This paper proposes and tests a novel method to learn these transition potential matrices based on evidence injected at nodes. Novel refinements to the method are also introduced, demonstrating improvements in capturing the relationships between the node belief distributions. Finally, novel rules are introduced and tested for evidence weighting at nodes during simultaneous evidence injections, correctly balancing the injected evidenced used to learn the transition potential matrices. Together, these methods enable updating a Dempster-Shafer network with significantly less user input, thereby making these networks more useful for scenarios in which sufficient information concerning relationships between nodes is not known a priori.</jats:p>

Application of Dempster–Shafer Networks to a Real-Time Unmanned Systems Risk Analysis Framework

“…Primarily used in sensor fusion and risk analysis [66] and typically requiring higher computational resources, Dempster-Shafer Theory provides useful properties that overcome some of the issues facing the risk calculation technologies underpinning quantitative, general risk analysis frameworks discussed in Section III.A.1. Extensions to DS networks were developed as a prerequisite to this work [67], enabling the UAS risk analysis performed in Section IV.…”

“…This section focuses on applying Dempster-Shafer networks with auto-updating joint conditional probability matrices [67] to a UAS scenario -a hovering multirotor making real-time decisions on whether to land, and, if so, in which area to land. The scenario is shown in Figure 2.…”

“…Training for the DS network was performed offline via simulation. While online training is feasible through this system, current methodology [67] uses the results of each operation to learn the transition potentials -the relationships -of the network. Specifically, this method connects the long-term and real-time in-operation timelines through the transition potentials.…”

“…the "Flight Systems Risk" node had no effect on the change in risk of the "Internal Risk" node), the two transitions are still trained together. This is a direct result of the simplification in the transition updated methodology [67], in which the result of the parent nodes multiplied by the transition potentials are assumed to be the same when provided as evidence to the combination method in the child node. This third method still uses that simplification, but then only trains the transition to which the episode applies.…”

“…Previous data retention methods discussed for training in Section IV.C uses Murphy's rule [71] and weighting rules previously developed [67] to capture episodic data, maintaining information across extended periods. This method Fig.…”