1、 Decision-Level Identity FusionTan XinLab 5, System Engineering Dept. 第一頁，共四十五頁。Contents1. Introduction2. Classical inference3. Bayesian inference4. Dempster-Shafers method*5. Generalized Evidence Processing (GEP) Theory6. Heuristic methods for identity fusion7. Implementation and trade-offs第二頁，共四十五

2、頁。IntroductionDecision-level fusionSeeks to process identity declarations from multiple sensors to achieve a joint declaration of identity.(Feature extraction, identity declaration)Data-level fusionFeature-level fusionDecision-level fusion(Data fused)(joint identity declaration)第三頁，共四十五頁。Introductio

3、nSensorASensorBSensorNFeature ExtractionIdentityDeclarationIdentityDeclarationIdentityDeclarationAssociationDecisionLevelFusion IdentityFusion第四頁，共四十五頁。IntroductionDecision-Level Fusion TechniquesClassical inferenceBayesian inferenceDempster-Shafers methodGeneralized evidence processing theoryHeuris

4、tic methods第五頁，共四十五頁。Classical inferenceStatistical inference techniques seek to draw conclusions about an underlying mechanism or distribution, based on an observed sample of data.Classical inference typically assumes an empirical probability model.Empirical probability assumes that the observed fr

5、equency distribution will approximate the probability as the number of trials.heren trials, occurrence of k timesTheoretical base第六頁，共四十五頁。Classical inferenceOne disadvantageStrictly speaking, empirical probabilities are only defined for repeatable events.Classical inference methods utilize empirica

6、l probability and hence are not strictly applicable to nonrepeatable events, unless some model can be developed to compute the requisite probabilities.第七頁，共四十五頁。Classical inferenceMain technique hypothesis testingDefine two hypothesis1. A null hypothesis, H0 (原假設)2. An alternative hypothesis,H1 (備擇假

7、設)Test logic1. Assume that the null hypothesis (H0) is true;2. Examine the consequences of H0 being true in the sampling distribution for statistic;3. Perform a hypothesis test, if the observation have a high probability of being observed if H0 is true, the declare the data do not contradict H0.4. O

8、therwise, declare that the data tend to contradict H0.第八頁，共四十五頁。Classical inferenceMain technique hypothesis testingTwo assumptions are required1. an exhaustive and mutually exclusive set of hypothesis can be defined2.we can compute the probability of an observation, given an assumed hypothesis.第九頁，

9、共四十五頁。Classical inferenceGeneralize to include multidimensional data from multiple sensors.Requires a priori knowledge and computation of multidimensional probability density functions. (a serious disadvantage)第十頁，共四十五頁。Classical inferenceAdditional disadvantages1. Only two hypotheses can be assesse

10、d at a time;2. Complexities arise for multivariate data;3. Do not take advantage of a priori likelihood assessment.Usage: identification of defective parts in manufacturing and analysis of faults in system diagnosis and maintenance.第十一頁，共四十五頁。Bayesian inferenceBayesian inference updates the likeliho

11、od of a hypothesis given a previous likelihood estimate and additional evidence (observations).The technique may be based on either classical probabilities, or subjective probabilities.Subjective probabilities suffer a lack of mathematical rigor or physical interpretation. Nevertheless, if used with

12、 care, it can be useful in a data fusion inference processor.第十二頁，共四十五頁。Bayesian inferenceBayesian formulationSuppose H1,H2,Hi, represent mutually exclusive and exhaustive hypotheses第十三頁，共四十五頁。Bayesian inferenceFvide a determination of the probability of a hypothesis being true, given th

13、e evidence. Classical inference give us the probability that an observation could be ascribed to an object or event, given an assumed hypothesis.2.allow incorporation of a priori knowledge about the likelihood of a hypothesis being true at all.3.use subjective probabilities for a priori probabilitie

14、s for hypothesis, and for the probability of evidence given a hypothesis.第十四頁，共四十五頁。Bayesian inferenceMultisensor fusionFor each sensor, a priori data provide an estimate of the probability that the sensor would declare the object to be type i given that the object to be of type j, noted as P(Di|Oj)

15、. These declarations are then combined via a generalization of Bayesian formulation described before. This provides an updated, joint probability for each possible entity Oj.Input to Bayes formulation: P(Di|Oj). for each sensor and entity or hypothesis Hi;P(Oj) a priori probabilities第十五頁，共四十五頁。Bayes

16、ian inferenceSensor #1ObservablesClassifierDeclarationSensor #2ETCSensor #nETCP(D1|Oj)P(D2|Oj)P(Dn|Oj)BayesianCombinationFormulaDecision Logic:MAPThreshold MAPetcD1D2DnFused Indentity Declaration第十六頁，共四十五頁。Bayesian inferenceDisadvantages1.Difficulty in defining priori functions: P(Oj)2.Complexity wh

17、en there are multiple potential hypothesis and multiple conditionally dependent events3.Requirements that competing hypothesis be mutually exclusive: cannot assign evidence to object Oi and Oj.4.Lack of an ability to assign general uncertainty.第十七頁，共四十五頁。Bayesian inferenceAn IFFN ExampleIdentificati

18、on-friend-foe-neutral system developed by Ferrante, Inc. of the U.K. This system uses multiple sensors designed to operate onboard an aircraft to perform joint declarations of identity to determine whether observed aircraft are friendly, potential enemies, or neutral.第十八頁，共四十五頁。Dempster-Shafers meth

19、odThe D-S method utilizes probability intervals and uncertainty intervals to determine the likelihood of hypotheses based on multiple evidence.D-S method seeks to model the way humans assign evidence to hypothetical propositions. It argue that humans assign measures of belief to combinations of hypo

20、thesis (i.e. to propositions).第十九頁，共四十五頁。Dempster-Shafers methodHypothesis & PropositionsA hypothesis is a fundamental statement about nature.A proposition may be either a hypothesis or a combination of hypotheses. Propositions may contain overlapping or conflicting hypothesis第二十頁，共四十五頁。Dempster-Sha

21、fers methodFrame of discernmentThis is a set of mutually exclusive and exhaustive sets of propositions. In essence, the frame of discernment is the miniature “world” we are trying to observe and understand.=A1, A2, , An 第二十一頁，共四十五頁。Dempster-Shafers method2n general propositions may be developed by B

22、oolean combinations.One important general propositionIf evidence is assigned to it is equivalent to a general level of uncertainty.第二十二頁，共四十五頁。Dempster-Shafers methodThe D-S method assigns evidence to both single and general propositions instead of assigning probability to hypotheses (Bayesian).Prob

23、ability mass, m( ), to represent assigned evidence.m( ), denotes a probability mass assigned either to an elementary proposition or to a general proposition. The sum of all mass function assigned to elementary and general propositions is 第二十三頁，共四十五頁。Dempster-Shafers methodThe probability of a propos

24、ition Ai is given by summing the probability masses for the pertinent elements in and 2.We sum m() for the element of that contains Ai exactly and in addition, sum the m() for those general proposition in 2 that contain Ai as an element.第二十四頁，共四十五頁。Dempster-Shafers methodE1E2.EkH1H2.HNBayes Assignme

25、nt of EvidenceEvidenceHypothesesE1E2.EkH1H2.HND-S Assignment of EvidenceEvidenceHypotheses第二十五頁，共四十五頁。Dempster-Shafers methodEvidential interval, spt(Bi), Pls(Bi)The support for a proposition Bi isIf Bi is a simple proposition (Bi = Ai), then the spt(Bi) is simply the probability of Ai;If Bi is a ge

26、neral proposition, (e.g., Bi = A1A2 A3)then the support for Bi is the sum of probability masses contributing to all elements of Bi.眾信度函數第二十六頁，共四十五頁。Dempster-Shafers methodEvidential interval, spt(Bi), Pls(Bi)The plausibility of a proposition Ai isWhich means lack of evidence that refutes the proposi

27、tion似真度函數A useful feature of D-S approach is the ability to establish a general level of uncertainty. The D-S method provides a means to explicitly account for unknown possible causes of observational data.第二十七頁，共四十五頁。Dempster-Shafers methodSensor #1ObservablesClassifierDeclarationSensor #2ETCSensor

28、 #nETCCompute orEnumerateMassDistribution forGivendeclarationETCETCCombine/FuseDistributionsViaDempstersRules ofCombinationM(Oj)=F(mi(Oj)DecisionLogicMi(Oj)Fused Indentity Declaration第二十八頁，共四十五頁。Dempster-Shafers methodDempsters Rule of CombinationProposition 1=u0=hypothesis A is trueProposition 2=u1

29、=hypothesis B is trueProposition 3=u2=hypothesis A or B is trueS1 S2m2(u0)m2(u1)m2(u2)m1(u0)m(u0)=m1(u0)m2(u0)k10=m1(u0)m2(u1)m(u0)=m1(u0)m2(u2)m1(u1)k01=m1(u1)m2(u0)m(u0)=m1(u1)m2(u1)m(u0)=m1(u1)m2(u2)m1(u2)m(u0)=m1(u2)m2(u0)m(u0)=m1(u2)m2(u1)m(u0)=m1(u2)m2(u2)第二十九頁，共四十五頁。Dempster-Shafers methodDem

30、psters rule of combination for two independent sources is第三十頁，共四十五頁。Dempster-Shafers methodDempsters rule of combination for multi sources is第三十一頁，共四十五頁。Dempster-Shafers methodDillard describes an algorithm for combing probability masses in a more complex situation.Dempsters rules of combination are

31、 both commutative and associative. Hence data from sensors may be combined in a hierarchical manner. As a result a variety of parallel implementation might be developed.Dillard, R. A., “Tactical Inferencing with the Dempster-Shafer Theory of Evidence” The Asilomar Conference of Circuits, Systems, an

32、d Computers,1983, Naval Post Graduate School, Santa Clara, CA, pp. 321-316For 2 or 3 sensors in a nonparallel implementation, the D-S technique requires approximately twice the computational effort of Bayesian inference.第三十二頁，共四十五頁。Generalized Evidence Processing (GEP) TheoryCriticisms of D-S infere

33、neLack of rigor in defining evidence through independent observationSeveral issues frequently cited about D-S method.Thomopoulos proposed another generalization of Bayesian theory termed the generalized evidence processing (GEP) approach.第三十三頁，共四十五頁。Generalized Evidence Processing (GEP) TheoryAn exa

34、mpleGEP assigns probability masses and combines those mass data based on a priori conditional probability of hypotheses H0 and H1.d0=hypothesis H0 is trued1=hypothesis H1 is trued2=hypothesis H0 or H1 is true第三十四頁，共四十五頁。Generalized Evidence Processing (GEP) TheoryIn D-S, the evidence is combined in

35、accordance with the intersection of propositionsIn GEP, the combination is based on quantified impact of the resulting decisions.第三十五頁，共四十五頁。Heuristic methods for identity fusionTreat the identity fusion problem as if a group of humans were faced with a decision problem. Each human performs the task

36、 of a sensor. (group decision-making)Voting methodsScoring modelsOrdinal ranking techniquesQ-sort methodsPair-wise ranking第三十六頁，共四十五頁。Heuristic methods for identity fusionVoting methods: address the identity fusion problem by a democratic process.Suppose M sensors observe a phenomenon, and each sens

37、or makes an identity declaration from n alternative hypotheses.Sum the number of sensors (votes) that declare that hypothesis to be true. The joint declaration of identity is simply the hypothesis that the count is a maximum.Weighted voting schemes may be employed to account for differences in senso

38、r performance.第三十七頁，共四十五頁。Heuristic methods for identity fusionScoring Models: use a weighted sum to specify the merit of each candidate hypothesis based on a ranking or scoring by each sensor.Each sensor, k, assigns a rank or value , rik, for all n possible hypothesis,Hi.A scoring model simply comp

39、utes the sumM is the total number of sensors, wi is an priori weight assigned to the ith hypothesis, and c is a normalization constant.第三十八頁，共四十五頁。Implementations and trade-offsTrade-offs?Inference performanceRequired computer resourcesRequirement for a priori informationGeneral utility第三十九頁，共四十五頁。I

40、mplementations and trade-offsInference accuracy and performanceHas not been studied in a systematic way. Several authors have performed comparisons under limited circumstances.Much more research needs to be performed in this area.Buede and Martin compare the performance of D-S method and Bayesian fusion.=Bayesian fusion process achieves a greater accuracy than the D-S technique第四十頁，共四十五頁。Implementations and trade-offsInference accuracy and performanceHas not been studied in a systematic way. Several authors have performed comparisons