Sensors2020,20,38 1;doi:10.3390/s20020381 www.mdpi.com/journal/sensors
Article
ANovelEvidenceConflictMeasurementforMulti‐
SensorDataFusionBasedontheEvidenceDistance
andEvidenceAngle
ZhanDeng*andJianyuWang
SchoolofAutomation,NanjingUniversityofScienceandTechnology,Nanjing210094,China,
wangjyu@njust.edu.cn
* Correspondence:ZhanDeng@njust.edu.cn
Received:9December2019;Accepted:8January2020;Published:9January2020
Abstract:Asanimportantmethodforuncertaintymodeling,Dempster–Shafer(DS)evidencetheory
has been widely used in practical applications. However, the results turned out to be almost
counter‐intuitivewhenfusingthedifferentsourcesofhighlyconflictingevidencewithDempster’s
combination rule. In previous researches, most of them were mainly dependent
on the conflict
measurementmethodbetweentheevidencerepresentedbytheevidencedistance.However,itis
inaccuratetocharacterizetheevidenceconflictonlythroughtheevidencedistance.Toaddressthis
issue, we comprehensively consider the impacts of the evidence distance and evidence angle on
conflictsinthispaper,andpropose
anewmethodbasedonthemutualsupportdegreebetweenthe
evidencetocharacterizetheevidence conflict.First,theHellingerdistancemeasurementmethodis
proposedtomeasurethedistancebetweentheevidence,andthesinevalueofthePignisticvector
angleisusedto characterizethe anglebetween the evidence.The
evidencedistanceindicatesthe
dissimilaritybetween the evidence,andtheevidence anglerepresentsthe inconsistency between
the evidence. Next, two methods are combined to get a new method for measuring the mutual
support degree between the evidence. Afterward, the weight of each evidence is determined by
using the mutual support
degree between the evidence. Then, the weights of each evidence are
utilized to modify the original evidence to achieve the weighted average evidence. Finally,
Dempster’scombinationruleisusedforfusion.Somenumericalexamplesaregiventoillustratethe
effectivenessandreasonabilityfortheproposedmethod.
Keywords: Dempster–Shafer evidence theory; conflict measurement; mutual support degree;
Hellingerdistance;Pignisticvectorangle
1.Introduction
Inpracticalapplications,mostinformationacquisitionisdonebysensors.Duetothecomplexity
ofthetarget,thedataprovidedbyasinglesensormaynotbesufficienttoobtainalloftheinformation
desiredfordatafusion,providingalltheinformationoftargetestimationwithmultiplesensorsis,
therefore, often required. However, the data derived from multiple sensors could be uncertain or
evenconflicting.Howtodealwithuncertaininformationeffectivelyhasbeenpaidmuchattention.
Dempster–Shafer (DS) evidence theory is a powerful tool to represent and deal with uncertain
information. It has been widely used in practical
problems related to uncertainty modeling and
reasoning, such as information fusion [1–4], fault diagnosis [5–11], decision‐making [12–16], risk
assessment[17–21],multi‐criteriadecision‐making[22,23],andpatternrecognition[24–27].
DSevidencetheory,alsocalledtheoriesofbelieffunctions,wasfirstlyproposedbyDempsterin
1967[28]andfurtherdevelopedby
Shaferin1976[29].DSevidencetheorycannotonlyeffectively
express stochastic uncertainty information, but can also express incomplete and subjective
