TrackingApplications withFuzzy-BasedFusionRulesAlbenaTchamovaJean DezertAbstractThe objective of this paper is to present andevaluatetheperformanceof aparticularfusionrulebasedonfuzzy T-Conorm/T-Norm operators for two tracking applications:(1) TrackingObjectsTypeChanges, supportingtheprocessofidentication, (e.g. friendlyaircraft against hostileones, ghteragainst cargo) andconsequently for improving the quality ofgeneralizeddataassociation; (2) Alarmsidenticationandpri-oritizationinterms of degreeof dangerrelatingtoaset of apriori dened, out of the ordinary dangerous directions. Theaimis topresent anddemonstratetheabilityof TCNruletoassure coherent and stable way for identication and to improvedecision-making process intemporal way. AcomparisonwithperformanceofDSmTbasedPCR5fusionruleandDempstersruleisalsoprovided.KeywordsObjects type identication; Alarmclassication;Datafusion;DSmT, TCNrule, PCR5rule, Dempstersrule.I. INTRODUCTIONAnimportant functionof eachsurveillancesystemis tokeepandimprovetargetstracksmaintenanceperformance,aswell astoprovideasmart operational control, basedontheintelligent analysisandinterpretationofalarmscomingfromavarietyofsensorsinstalledintheobservationarea.Targetstype estimates can be used during different target tracking pro-cess stages for improving data to track association and for thequality evaluation of complicated situations characterized withcloselyspacedor/andcrossingtargets[1],[2].Itsupportstheprocessof identication, e.g. friendlyaircraft against hostileones, ghter against cargo. In such case, although the attributeofeachtarget isinvariant overtime, at theattribute-trackinglevel the type of the target committed to the (unresolved)trackvarieswithtimeandmust betrackedproperlyinordertodiscriminatehowmanydifferent targetsarehiddeninthesame unresolved track. Alarms classication and prioritization[3],[4],[5],[6],[7],[8]is verychallengingtask, becausein caseof multiple suspicious signals (relatingtoa set of a prioridened, out oftheordinarydangerousdirections), generatedfromanumber of sensors intheobservedarea, it requiresthemost dangerousamongthemtobecorrectlyrecognized,in order to decide properly where the video camera should beoriented. There are cases, when some of the alarms generatedcould be incorrectly interpreted as false, increasing the chancetobeignored, incasewhentheyarereallysignicant anddangerous.Thatway the critical delayof the proper responsecould cause signicant damages. In both cases above, theuncertaintyandconictsencounteredinobjectsandsignalsdata, could weaken or even mistake the respective surveillancesystem decision. That is why a strategy for an intelligent, scanbyscan,combination/updatingofdatageneratedisneededinorder toprovidethesurveillancesystemwithameaningfuloutput. Inthis paper we focus our attentiononthe abilityofthesocalledT-Conorm-Norm(TCN)fusionrule, denedwithinDezert-SmarandacheTheory(DSmT)ofplausibleandparadoxical reasoningtoimprovetheprocessof datafusionand to successfully nalize the decision-making procedures inbothdescribedsurveillancecases.Thisworkis basedonpre-liminary research in [9],[10]. In section II we recallbasicsofProportional Conict Redistribution rule no.5 (PCR5), denedwithinDSmT. BasicsofPCR5basedTCNfuzzyfusionruleare outlined in section III. Section IV presents the problem ofalarmsclassicationandexaminetheabilityof TCNfusionruletosolveit. InsectionVtheperformanceof TCNruleisanalyzedrelatedtotheproblemoftarget typetracking. Inboth sections, a comparative analysis of TCN rule solution withthose, obtainedbyPCR5andDempster-Shafers(DS)ruleisprovided.ConcludingremarksaregiveninsectionVI.II. BASICSOF PCR5FUSIONRULEThegeneralprincipleofProportionalConictRedistribu-tion rules is to: 1) calculate the conjunctive consensus betweenthe sources of evidences; 2) calculate the total or partialconictingmasses; 3)redistributetheconictingmass(totalor partial) proportionallyonnon-emptysetsinvolvedinthemodel accordingtoall integrityconstraints. Theideabehindthe Proportional Conict Redistribution rule no. 5 denedwithinDSmT[9] (Vol. 2) is totransfer conictingmasses(totalorpartial)proportionallytonon-emptysetsinvolvedinthe model according to all integrity constraints. Under Shafersmodel assumption of the frame , PCR5 combination rule foronly two sources of information is dened as: 5() = 0and 2 {}

5() = 12()+22{}2=[

1()2

2(2)

1() + 2(2)+

2()2

1(2)

2() + 1(2)] (1)All sets involvedintheformula(1) areincanonical form.

12()correspondstotheconjunctiveconsensus,i.e:

12() =1,2212=

1(1)2(2).Originally published as Tchamova A., Dezert J., Tracking applications with fuzzy-based fusion rules, Proc. of 2013 IEEE International Symposium on INnovations in Intelligent SysTems and Application (INISTA 2013), Albena, Bulgaria, June 19-21, 2013, and reprinted with permission.Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4403All denominators aredifferent fromzero. If adenominatoris zero, that fraction is discarded. No matter howbig orsmall is the conictingmass, PCR5mathematicallydoes abetter redistributionof the conictingmass thanDempster-Shafers rule since PCR5 goes backwards on the tracks of theconjunctive rule and redistributes the partial conicting massesonlytothesetsinvolvedintheconictandproportionallytotheir massesput intheconict, consideringtheconjunctivenormalformofthepartialconict.PCR5isquasi-associativeandalsopreserves theneutral impact of thevacuous beliefassignment.III. BASICSOF TCNFUSIONRULETheT-Conorm-Normruleofcombination[11]representsaclassoffusionrulesbasedonspeciedfuzzyt-Conorm, t-Norm operators [16]. Triangular norms (t-norms) and Triangu-lar conorms (t-conorms) are the most general families of binaryfunctions that satisfy the requirements of the conjunctionanddisjunctionoperators, respectively. TCNruleis denedwithinDSmTbasedPCR5fusionrule.UnderShafersmodelassumptionof the frame , the TCNfusionrule for onlytwosourcesofinformationisdenedas:

()=0and 2 {}

() = 12()+22{}2=[

1().{1(), 2(2)}{1(), 2(2)}+

2().{2(), 1(2)}{2(), 1(2)}] (2)where 12() corresponds to the conjunctive consensus,obtainedby: 12() =1,2212={1(1), 2(2)}.TCNfusionrulerequiresanormalizationprocedure:

() =

()2=

()TheattractivefeaturesofTCNrulecouldbedenedas:veryeasytoimplement, satisfyingtheimpact of neutral VacuousBeliefAssignment;commutative, convergenttoidempotence,reects majority opinion, assures adequate data processingincaseof partial andtotal conict betweentheinformationgranules. Thegeneral drawbackofthisruleisrelatedtothelackof associativity, whichisnot amainissueintemporaldatafusion.IV. ALARMS CLASSIFICATION APPROACHTheapproachassumesall thelocalizedsoundsourcestobesubjectsofattentionandinvestigationforbeingindicationofdangeroussituations.Thespecicinputsoundsattributes,emitted by each source, are sensors level processed andevaluated in timely manner for their contribution towardscorrect alarms classication(intermof degreeof danger).Theappliedalgorithmconsidersthefollowingsteps: Dening the frame of expected hypotheses asfollows: = {1= (E)mergency, 2=(A)larm, 3=(W)arning}. Here Shafers modelholds and we work on the power-set: 2={, E, A, W, E A, E W, A W, E A W}.ThehypothesiswithahighestpriorityisEmergency,followingbyAlarmandthenWarning. Deninganinput rulebasetomapthesounds at-tributes (so called observations) obtained fromalllocalizedsources intonon-Bayesianbasicbelief as-signments

(.). At theveryrst timemoment =0westart withapriori basicbeliefassignment (history)set tobeavacuousbeliefassignment ( )=1,sincethereisnoinformationabout therst detecteddegreeofdangeraccordingtosoundsources. Combination of currently received measurements bba

(.) (for each of located sound sources), based ontheinput interfacemapping, withahistorysbba, inorder toobtainestimatedbbarelatingtothecurrentdegree of danger (.) = [

](.). TCN ruleisappliedintheprocessof temporal datafusiontoupdatebbasassociatedwitheachsoundemitter. Flagfor anespeciallyhighdegreeof danger hastobetaken, whenduringtheapriori denedscanningperiod, themaximumPignisticProbability[9]isas-sociated with the hypothesis Emergency. In this work,weassumeShafersmodel andweusetheclassicalPignisticTransformation[9], [15] totakeadecisionaboutthemodeofdanger. Itisdenedfor 2by() = () (3)where denotesthecardinalityof.A. SimulationScenarioAset ofthreesensorslocatedat different distancesfromthe microphone arrayare installedinanobservedarea forprotectionpurposes,togetherwithavideocamera[13].Theyare assembledwithalarmdevices: Sensor 1withSonitron,Sensor 2 with E2S, and Sensor 3 with SystemSensor. Incaseofalarmevents(smoke,ame,intrusion,etc.)theyemitpowerful sound signals with various duration and frequency ofintermittence (Table 1), depending on the nature of the event.Table1Soundsignalparameters.Continuous Intermittent-I Intermittent-II(Warning) (Alarm) (Emergency)

= 0Hz

= 5Hz

= 1Hz

= 10s

= 30s

= 60sThefrequencyofintermittencies

,associatedwiththelo-calized sound sources is utilized in the specic input interface(therulebase)below.Rule1: if

1then

()=0.9and

( ) = 0.1.Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 44040 5 10 15 20 25 3000.51Scan numberPignistic ProbabilityEMERGENCY Source: Estimation of Degrees of Danger via TCN Rule Ground TruthEmergencyAlarmWarning5 10 15 20 25 30 3500.51Scan numberPignistic ProbabilityALARM Source: Estimation of Degrees of Danger via TCN Rule Ground TruthEmergencyAlarmWarning10 15 20 25 30 35 4000.51Scan numberPignistic ProbabilityWARNING Source: Estimation of Degrees of Danger via TCN Rule Ground TruthEmergencyAlarmWarningFig.1. TCNrulePerformancefordangerlevelestimation.Rule2:if

5then

() = 0.7,

( ) =0.2and

( ) = 0.1.Rule3:if

0then

() = 0.6and

( ) = 0.4.Three main cases are estimated: the probabilities of modes,evaluated for Sensor 1 (associated with Emergency mode),Sensor2(associatedwithAlarmmode), andSensor3(asso-ciated with Warming mode. The decisions should be governedat the video camera level, taken periodically, depending on: 1)specicities of the video camera (time needed to steer the videocamera toward a localized direction); 2) time duration neededto analyze correctly and reliably the sequentially gatheredinformation. Wechooseasareasonablesamplingperiodforcameradecisions

= 20,i.e.atevery10thscan.B. TCNruleperformancefordangerlevelestimation.Fig.1showsthevaluesof PignisticProbabilitiesof eachmode (E, A, W) associated with three sound emitters (1stsource in E mode, (subplot on the top), 2nd source in A mode(subplot inthemiddle), and3rdsourceinWmode, (subplotin the bottom)) during the all 30 scans. Each source hasbeenperturbedwithnoisesinaccordancewiththesimulatedGroundTruth,associatedwithparticularsoundsource.Theseprobabilities are obtainedfor eachsource independentlyasaresult of sequential datafusionof

(.)sequenceusingTCN combinational rule. For a completeness of study and forcomparisonpurposes, the respective performances of PCR5andDSrulearepresenteding.2andg.3.TCN rule shows a stable, quite proper and effective behav-ior, following the performance of PCR5 rule. A special featureof TCN rule performance are the smoothed estimates and morecautiousdecisionstakenattheparticulardecisivescans.The results obtained show the strong ability of PCR5 ruleto take care in a coherent and stable way for the evolution of allpossible degrees of danger, related to all the localized sources.It is especially signicant in case of sound sources data0 5 10 15 20 25 3000.51Scan numberPignistic ProbabilityEMERGENCY Source: Estimation of Degrees of Danger via PCR5 Rule Ground TruthEmergencyAlarmWarning5 10 15 20 25 30 3500.51Scan numberPignistic ProbabilityALARM Source: Estimation of Degrees of Danger via PCR5 Rule Ground TruthEmergencyAlarmWarning10 15 20 25 30 35 4000.51Scan numberPignistic ProbabilityWARNING Source: Estimation of Degrees of Danger via PCR5 Rule Ground TruthEmergencyAlarmWarningFig.2. PCR5rulePerformancefordangerlevelestimation.0 5 10 15 20 25 3000.51Scan numberPignistic ProbabilityEMERGENCY Source: Estimation of Degrees of Danger via Dempster Rule Ground TruthEmergencyAlarmWarning0 5 10 15 20 25 3000.51Scan numberPignistic ProbabilityALARM Source: Estimation of Degrees of Danger via Dempster Rule Ground TruthEmergencyAlarmWarning0 5 10 15 20 25 3000.51Scan numberPignistic ProbabilityWARNING Source: Estimation of Degrees of Danger via Dempster Rule Ground TruthEmergencyAlarmWarningFig.3. DempstersrulePerformancefordangerlevelestimation.discrepancies andconicts, whenthehighest prioritymodeEmergency occurs. PCR5 rule prevents to produce a mistakendecision,thatwaypreventstoavoidthemostdangerouscasewithout immediateattention. Asimilaradequatebehavior ofperformanceisestablishedincasesoflowerdangerpriority.DS rule shows weakness in resolving the cases examined.In Emergency case, DS rule does not reect at all new obtainedinformativeobservationssupportingtheWarningmode. Thispathological behavior reects the dictatorial power of DSrulerealizedbyagivensource[12], whichis fundamentalin Dempster-Shafer reasoning [14]. In our particular casehowever, DS rule leads to a right nal decision by coincidence,but this decision could not be accepted as coherent and reliable,because it is not built on a consistent logical ground. In cases oflowerdangerspriority(perturbedWarningandAlarmmode),DS rule could cause a false alarm and can deect the attentionAdvances and Applications of DSmT for Information Fusion. Collected Works. Volume 4405from the existing real dangerous source by assigning a wrongsteeringdirectiontothesurveillancecamera.V. TARGET TYPE TRACKING APPROACHTheproblemcanbesimplystatedasfollows: Let = 1, 2, ...,

be the time index and considerpossibletarget types

= {1, . . . ,

}inthe environment; for example = {, }and 1 , 2 ; or ={, , },etc. at eachinstant , a target of true type ()(not necessarilythesametarget) is observedbyanattribute-sensor(weassumeaperfecttargetdetectionprobabilityhere). the attribute measurement of the sensor (saynoisyRadar CrossSectionfor example) isthenprocessedthroughaclassierwhichprovidesadecision

()onthetypeoftheobservedtargetateachinstant. The sensor is ingeneral not totallyreliable andischaracterizedbya confusionmatrixC = [

= (

=

=

)]Thegoalistoestimate()fromthesequenceofdecla-rations done by the unreliable classier up to time, i.e. howtobuildanestimator() =(

(1),

(2), . . . ,

())of(). The principle of the estimator is based on the sequentialcombination of the current basic belief assignment (drawnfrom classier decision, i.e. our measurements) with the priorbba estimated up to current time fromall past classierdeclarations.Thealgorithmfollowsthenextmainsteps: Initializationstep(i.e. =0). Select thetarget typeframe = {1, . . . ,

} and set the prior bba(.)as vacuous belief assignment, i.e (1. . .

) =1sinceonehasnoinformationabout therst targettypethatwillbeobserved. Generationofthecurrent bba

(.)fromthecur-rent classier declaration

() based on attributemeasurement. Atthisstep, onetakes

(

())=

()

()and all the unassigned mass 1

(

()) is then committed to total ignorance

1 . . .

. Combinationof current bba

(.) withprior bba

(.)togettheestimationofthecurrentbba(.).Symbolically we will write the generic fusion operatoras , so that (.) =[

](.) =[

](.). The combination is done according eitherDemspters rule(i.e. (.) =

(.)) or PCR5rule(i.e. (.) = 5(.)). Estimation of True Target Type is obtained from (.)by taking the singleton of , i.e. a Target Type, havingthemaximumof belief (or eventuallythemaximumPignisticProbability). set(.) = (.);do = + 1 and go back to stepb).0 10 20 30 40 50 60 70 80 90 10000.10.20.30.40.50.60.70.80.91Scan numberprobability mass assigned to Cargo typeEstimation of belief assignment for Cargo Type GroundtruthDemspters rulePCR5 ruleTCN rule (summin) TCN rule (maxmin)TCN rule (maxbounded product)Fig.4. EstimationofbeliefassignmentforCargotype.A. SimulationsresultsIn order to evaluate the performances of TCN-basedestimator, a set of Monte-Carlo simulations on a verysimple scenario for a 2DTarget Type frame, i.e. ={(), ()} is realized for classier with a follow-ingconfusionmatrix:C =[0.9 0.10.1 0.9]Weassumetherearetwocloselyspacedtargets: CargoandFighter. Due to circumstances, attribute measurements receivedarepredominatelyfromoneoranotherandbothtargetsgen-erates actuallyonesingle(unresolvedkinematics) track. Tosimulate suchscenario, a GroundTruthsequence over 100scans was generated. The sequence starts with the observationof aCargotypeandthentheobservationof thetarget typeswitches twotimes ontoFighter type duringdifferent timeduration.Ateachtimestepthedecision

()israndomlygenerated according to the corresponding row of the confusionmatrixof theclassier giventhetruetarget type(knowninsimulations). Thenthealgorithmfromaboveisapplied. Thesimulation consists of 10000 Monte-Carlo runs. The computedaveraged performances (on the base of estimated belief massesobtainedbythetracker) areshownonthegures 4and5.TheyarebasedonTCNfusionrulerealizedwithdifferentt-conormandt-normfunctions. Onthe same gures, for acomparisonpurposes, the respective performances of PCR5and DS rule are presented. It is evident, that PCR5 fusion ruleoutperforms the results based on TCN rule, because PCR5 al-lows a very efcient Target Type Tracking, reducing drasticallythe latency delay for correct Target Type decision. TCN fusionrule shows a stable and adequate behavior, characterized withmoresmoothedprocessofre-estimatingthebeliefmassesincomparison to PCR5. TCN fusion rule with t-conorm=max andt-norm=boundedproduct reactsandadoptsbetter thanTCNwitht-conorm=sumandt-norm=min, followedbyTCNwitht-conorm=maxandt-norm=min.Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 44060 20 40 60 80 10000.10.20.30.40.50.60.70.80.91Scan numberprobability mass assigned to Fighter typeEstimation of belief assignment for Fighter TypeGroundtruthDemspters rulePCR5 ruleTCN rule (summin)TCN rule (maxmin)TCN rule (maxbounded product)Fig.5. EstimationofbeliefassignmentforFightertype.presented: (1) Tracking Objects Type Changes, supportingthe process of identication; (2) Alarms identication andprioritizationinterms of degreeof danger relatingtoasetofapriori dened, out oftheordinarydangerousdirections.Theabilityof TCNruletoassurecoherent andstablewayof identicationandtoimprovedecision-makingprocess intemporal wayaredemonstrated. Different typesof t-conormand t-norms, available in fuzzy set/logic theory provide us withrichnessofpossiblechoicestobeusedapplyingTCNfusionrule. Theattractivefeaturesof TCNruleisitseasyimple-mentationandadequatedataprocessingincaseof conictsbetweentheinformationgranules.VII. ACKNOWLEDGMENTThe research work reported in the paper is partly supportedby the project AComIn Advanced Computing for Innovation,grant 316087, fundedbytheFP7CapacityProgramme(Re-searchPotentialofConvergenceRegions).REFERENCES[1] Bar-ShalomY., Multitarget-Multisensor Tracking: Advanced Applica-tions,ArtechHouse,1990.[2] Blackman S., Popoli R., Design and Analysis of Modern TrackingSystems,ArtechHouse,1999.[3] Khosla R., Dillon T. Learning knowledge and strategy of a neuro expertsystemarchitectureinalarmprocessing, IEEETrans. Power Systems,Vol.12(4),pp.16101618, 1997.[4] Vale Z., Machado A. An expert system with temporal reasoning for alarmprocessing in power system control centers, IEEE Trans. Power Systems,Vol.8(3),pp.13071314, 1993.[5] LinW., LinC., SunZ. Adaptive multiple fault detectionandalarmprocessing for loop systemwith probabilistic network, IEEETrans.PowerDelivery,Vol.19(1),pp.6469,2004.[6] SouzaJ., etal. . Alarmprocessinginelectricalpowersystemsthroughaneurofuzzyapproach, IEEETrans. PowerDelivery, Vol. 19(2), pp.537544, 2004.[7] McArthur S., et al. Theapplicationof model basedreasoningwithinadecisionsupportsystemforprotectionengineers, IEEETrans. PowerDelivery,Vol.11(4),pp.17481754, 1996.[8] FoongO., SulaimanS., Rambli D., AbdullahN. ALAP: AlarmPri-oritizationSystemFor Oil Renery, Proc. of theWorldCongress onEngineeringandComputer ScienceVol II, SanFrancisco, CA, USA,2009.[9] Smarandache F., Dezert J. (Editors) Advances and Applications of DSmTforInformationFusion,ARP,Rehoboth, Vol.1-3,2004-2009.[10] Tchamova A., Dezert, J., Intelligent alarmclassication based onDSmT, 6thIEEEInternational ConferenceIntelligent SystemsSoa,Bulgaria,pp.120-125, 2012.[11] Tchamova A., Dezert J., Smarandache F.,A New Class of Fusion Rulesbased on T-Conormand T-NormFuzzy Operators, Information andSecurity,AnInternationalJournal,Vol.20,pp.77-93, 2006.[12] Tchamova A., Dezert J., On the behavior of Dempsters rule ofcombinationandthefoundationsofDempster-ShaferTheory,6thIEEEInternational ConferenceIntelligent SystemsSoa, Bulgaria, pp.108-113,2012.[13] Behar V., et al. STAP Approach for DOA Estimation using MicrophoneArrays,SignalProc.Workshop,Vilnius,SPIEProc.,Vol.7745,2010.[14] Shafer, G. A Mathematical Theory of Evidence, Princeton Univ., 1976.[15] Smets P., Kennes R. The transferable belief model, Artif. Intel., 66 (2),pp.191-234, 1994.[16] MendelJ.,FuzzyLogicSystemsforEngineering:ATutorial,Proc.oftheIEEE,pp.345377, 1995.Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4407