決策層特征融合decision level identity fusionppt課件

1、 Decision-Level Identity FusionTan XinLab 5, System Engineering Dept. Contents1. Introduction2. Classical inference3. Bayesian inference4. Dempster-Shafers method*5. Generalized Evidence Processing (GEP) Theory6. Heuristic methods for identity fusion7. Implementation and trade-offsIntroductionDecisi

2、on-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)IntroductionSensorASensorBSensorNFeature

3、ExtractionIdentityDeclarationIdentityDeclarationIdentityDeclarationAssociationDecisionLevelFusion IdentityFusionIntroductionDecision-Level Fusion TechniquesClassical inferenceBayesian inferenceDempster-Shafers methodGeneralized evidence processing theoryHeuristic methodsClassical inferenceStatistica

4、l 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 frequency distribution will approximate the probabil

5、ity as the number of trials.heren trials, occurrence of k timesTheoretical baseClassical inferenceOne disadvantageStrictly speaking, empirical probabilities are only defined for repeatable events.Classical inference methods utilize empirical probability and hence are not strictly applicable to nonre

6、peatable events, unless some model can be developed to compute the requisite probabilities.Classical inferenceMain technique hypothesis testingDefine two hypothesis1. A null hypothesis, H0 (原假設(shè))2. An alternative hypothesis,H1 (備擇假設(shè))Test logic1. Assume that the null hypothesis (H0) is true;2. Examine

7、 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. Otherwise, declare that the data tend to contradict H0.Classical infere

8、nceMain 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.Classical inferenceGeneralize to include multidimensional data from multiple sensors

9、.Requires a priori knowledge and computation of multidimensional probability density functions. (a serious disadvantage)Classical inferenceAdditional disadvantages1. Only two hypotheses can be assessed at a time;2. Complexities arise for multivariate data;3. Do not take advantage of a priori likelih

10、ood assessment.Usage: identification of defective parts in manufacturing and analysis of faults in system diagnosis and maintenance.Bayesian inferenceBayesian inference updates the likelihood of a hypothesis given a previous likelihood estimate and additional evidence (observations).The technique ma

11、y be based on either classical probabilities, or subjective probabilities.Subjective probabilities suffer a lack of mathematical rigor or physical interpretation. Nevertheless, if used with care, it can be useful in a data fusion inference processor.Bayesian inferenceBayesian formulationSuppose H1,H

12、2,Hi, represent mutually exclusive and exhaustive hypothesesBayesian inferenceFvide a determination of the probability of a hypothesis being true, given the evidence. Classical inference give us the probability that an observation could be ascribed to an object or event, given an assumed

13、 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 probabilities for hypothesis, and for the probability of evidence given a hypothesis.Bayesian inferenceMultisensor fusionFor each sensor, a prior

14、i 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). These declarations are then combined via a generalization of Bayesian formulation described before. This provides an updated, joint probabilit

15、y for each possible entity Oj.Input to Bayes formulation: P(Di|Oj). for each sensor and entity or hypothesis Hi;P(Oj) a priori probabilitiesBayesian inferenceSensor #1ObservablesClassifierDeclarationSensor #2ETCSensor #nETCP(D1|Oj)P(D2|Oj)P(Dn|Oj)BayesianCombinationFormulaDecision Logic:MAPThreshold

16、 MAPetcD1D2DnFused Indentity DeclarationBayesian inferenceDisadvantages1.Difficulty in defining priori functions: P(Oj)2plexity when there are multiple potential hypothesis and multiple conditionally dependent events3.Requirements that competing hypothesis be mutually exclusive: cannot assign eviden

17、ce to object Oi and Oj.4.Lack of an ability to assign general uncertainty.Bayesian inferenceAn IFFN ExampleIdentification-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 ident

18、ity to determine whether observed aircraft are friendly, potential enemies, or neutral.Dempster-Shafers methodThe 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 e

19、vidence to hypothetical propositions. It argue that humans assign measures of belief to combinations of hypothesis (i.e. to propositions).Dempster-Shafers methodHypothesis & PropositionsA hypothesis is a fundamental statement about nature.A proposition may be either a hypothesis or a combination of

20、hypotheses. Propositions may contain overlapping or conflicting hypothesisDempster-Shafers 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,

21、, An Dempster-Shafers method2n general propositions may be developed by Boolean combinations.One important general propositionIf evidence is assigned to it is equivalent to a general level of uncertainty.Dempster-Shafers methodThe D-S method assigns evidence to both single and general propositions i

22、nstead of assigning probability to hypotheses (Bayesian).Probability 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 D

23、empster-Shafers methodThe probability of a proposition 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.Dempster-Shafe

24、rs methodE1E2.EkH1H2.HNBayes Assignment of EvidenceEvidenceHypothesesE1E2.EkH1H2.HND-S Assignment of EvidenceEvidenceHypothesesDempster-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 probab

25、ility of Ai;If Bi is a general 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(shù)Dempster-Shafers methodEvidential interval, spt(Bi), Pls(Bi)The plausibility of a proposition Ai isWhich means lack of evidence that refute

26、s the proposition似真度函數(shù)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.Dempster-Shafers methodSensor #1ObservablesClassifierDeclarationSensor #2ETCSenso

27、r #nETCCompute orEnumerateMassDistribution forGivendeclarationETCETCCombine/FuseDistributionsViaDempstersRules ofCombinationM(Oj)=F(mi(Oj)DecisionLogicMi(Oj)Fused Indentity DeclarationDempster-Shafers methodDempsters Rule of CombinationProposition 1=u0=hypothesis A is trueProposition 2=u1=hypothesis

28、 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)Dempster-Shafers methodDempsters rule of combinat

29、ion for two independent sources isDempster-Shafers methodDempsters rule of combination for multi sources isDempster-Shafers methodDillard describes an algorithm for combing probability masses in a more complex situation.Dempsters rules of combination are both commutative and associative. Hence data

30、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, and Computers,1983, Naval Post Graduate School, S

31、anta 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.Generalized Evidence Processing (GEP) TheoryCriticisms of D-S infereneLack of rigor in defining evidence through independent ob

32、servationSeveral issues frequently cited about D-S method.Thomopoulos proposed another generalization of Bayesian theory termed the generalized evidence processing (GEP) approach.Generalized Evidence Processing (GEP) TheoryAn exampleGEP assigns probability masses and combines those mass data based o

33、n a priori conditional probability of hypotheses H0 and H1.d0=hypothesis H0 is trued1=hypothesis H1 is trued2=hypothesis H0 or H1 is trueGeneralized Evidence Processing (GEP) TheoryIn D-S, the evidence is combined in accordance with the intersection of propositionsIn GEP, the combination is based on

34、 quantified impact of the resulting decisions.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 of a sensor. (group decision-making)Voting methodsScoring modelsOrdinal ranking techniquesQ-so

35、rt methodsPair-wise rankingHeuristic methods for identity fusionVoting methods: address the identity fusion problem by a democratic process.Suppose M sensors observe a phenomenon, and each sensor makes an identity declaration from n alternative hypotheses.Sum the number of sensors (votes) that decla

36、re 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 sensor performance.Heuristic methods for identity fusionScoring Models: use a weighted sum to specify the merit

37、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 computes the sumM is the total number of sensors, wi is an priori weight assigned to the ith hypothesis, and c is a normali

38、zation constant.Implementations and trade-offsTrade-offs?Inference performanceRequired computer resourcesRequirement for a priori informationGeneral utilityImplementations 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 tec