FUSE Fusion Utility Sequence Estimato Belu V. Dasaathy Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500 belu.d@dynetics.com Sean D. Townsend Dynetics, Inc. P. O. Box 5500 Huntsville, AL 3584-5500 sean.townsend@dynetics.com Abstact - An expet system GIFTS (a Guide to Intelligent Fusion Technology Selection) developed to aid senso fusion system design, was pesented at Fusion 98 as an on-going poect with additional suppot tools unde development. In this pape, a simulation tool, FUSE, that execises a decisions in - decision out (DEI-DEO) fusion model to estimate the benefits (utility) along a sequence of multiple obsevations, is pesented. This can be employed eithe independently o as one of the tools suppoting GIFTS. FUSE pemits the simulation of diffeent Boolean fusion logic functions in the context of senso suites with two independent sensos. The inputs to FUSE ae the senso pefomance chaacteistics in tems of the pobabilities of coect and incoect decisions fo taget and decoy classes along with paametes that define the fusion logic and duation. The outputs of the system ae the fused system pefomance expessed in tems of pobabilities of coect-, incoect- and non- decisions ove the specified ange of obsevations. Wheneve any of these input paametes ae alteed, FUSE esponds instantaneously by updating the fused system pefomance. In ode to futhe aid the use in the compaison of the diffeent fusion logic altenatives and to assess the benefits of tempoal fusion though multiple independent obsevations, FUSE povides seveal gaphic visualization options. Key Wods: decision fusion, fusion benefits, fusion logic, tempoal fusion. Intoduction A common question that aises, especially fom outside the senso fusion community, is why fuse the sensos at all. An often head comment is: Why should I fuse my two sensos when senso numbe one has supeio pefomance? I will ust be degading its pefomance by mixing in less eliable infomation. Of couse fusing sensos can be beneficial, but it is often had to convey this message without showing had data to the septic. Even assuming that one is convinced of the advantages of pusuing fusion, a second question is often how the fusion should be accomplished. This is the challenge of detemining what to fuse, when to fuse [], and how to fuse. Thee is abundant liteatue offeing diffeent methods of accomplishing fusion [2,3], but few univesal ules to follow. Instead, each scenaio has been individually analyzed and all methods have to be consideed in the appopiate context. FUSE (Fusion Utility Sequence Estimato) is designed to addess both of these questions, albeit in a limited fashion. To help with the fist poblem (addessing the utility of fusion), FUSE can be used as a stand-alone fusion simulato. A use simply inputs appopiate values fo the individual senso chaacteistics though the use inteface and fused decision pobabilities ae immediately updated. Hence, the advantages of fusion can be instantaneously gleaned. To futhe aid in examining the fusion benefits, gaphical epesentations can be displayed. FUSE, when used in conunction with GIFTS (a Guide to Intelligent Fusion Technology Selection) [4], addesses the lage poblem as well. GIFTS guides a use though an inteactive quey session that defines a fusion system achitectue that is appopiate to the poblem envionment unde consideation. Included within the GIFTS achitectue, ae seveal suppot tools that povide assistance to the designe in developing and assessing the detailed fusion system design coesponding to the chosen achitectue. FUSE is an additional assessment tool that can be included in the GIFTS achitectue o can be opeated as a stand-alone simulation. FUSE employs a decisions in -decision out (DEI-DEO) fusion model to estimate the benefits along a sequence of multiple obsevations using a two-senso suite unde AND and OR boolean logic. In this pape, the initial vesion of FUSE will be intoduced. In Section 2, an oveview of the basic
fusion concepts undelying the estimation techniques is pesented along with a summay of the GIFTS achitectue. Section 3 is a desciption of the FUSE simulation and section 4 pesents how FUSE can be used as a ealistic analysis tool. Section 5 offes some closing comments and outlines the scope fo futhe development. 2. Bacgound This section contains the basics of the methods by which FUSE estimates fusion benefits and the GIFTS achitectue. Fo moe details on the estimation techniques see [5]. Those inteested in GIFTS should loo up [4]. 2. Fused Pobability Estimation Thee ae two basic fusion stategies that ae used in FUSE. The two stategies ae OR and AND boolean logic. Both stategies opeate in an envionment whee two sensos ae opeating in paallel, have a povision fo multiple loos, and have a non-decision option as well as the nomal binay decisions. OR logic fuses decisions by maing a binay decision if the two sensos ae not contadictoy and a nondecision othewise. AND logic, on the othe hand, equies that the two sensos mae concuing decisions to obtain a binay decision and a non-decision othewise. Let c i, w i, and u i coespondingly epesent the pobabilities of coect, incoect, and non-decision of obects ={Taget (T), Decoy (D)} by the sensos i = {,2}, whee both sensos ae deemed independent. Similaly, p, q, and epesent the fused pobabilities of coect, incoect, and non-decision of obect afte the th fusion attempt unde logic f = {OR (o), AND (a)}. Using these definitions we note that c w + u =. () i + i i It can then be shown fo OR logic that = c c + c u + u c (2) po 2 2 2 qo w w2 + w u2 + u w2 = (3) o u u2 + c w2 + w c2 =. (4) Similaly, the following equations can be developed fo AND logic. = (5) pa c c2 = (6) qa w w2 a c P Q u = u 2 u + u 2 c + c 2 w + w 2 u + w 2 c + u 2 w + 2 The th pobabilities can thus be witten as [ i p = p i= = i q = q i= = [ ] ] (7) (8) (9) = P Q (0) p q =. () These eleven equations fom the basis of the fusion benefit analysis in FUSE. Thee types of fusion benefits will be defined. These ae with espect to the pobability of coect decision, pobability of incoect decision, and both. A fusion benefit exists with espect to the pobability of a coect decision when P > max( c, c2 ). (2) Similaly, the fusion benefit with espect to the pobability of an incoect decision would be Q < min( w, w2 ). (3) A oint fusion benefit is thus when both (2) and (3) simultaneously hold tue. 2.2 GIFTS GIFTS is cuently composed of fou modules. The pimay component is the achitectue selection pocess that detemines the elevant achitectue. The second piece is a efeence database that can be used to help answe poblem specific questions. The thid pat is an FEI-DEO fusion selecto. It povides a means of choosing an implementation of FEI-DEO fusion. The final component is FUSE that is discussed in this pape to simulate DEI-DEO fusion. Though the use of all the modules, GIFTS can povide aid to the fusion system achitectue designe duing the diffeent phases of development. The use, who nows the specifics of a fusion poblem, uses GIFTS to detemine a poposed achitectue. This is accomplished by esponding to poblem spe-
cific questions posed by the pimay component of GIFTS. Once the poposed achitectue has been ceated, the use will begin a poblem specific efining pocess that will poduce a fusion solution. Duing this time, the goal is to detemine the optimal means of implementing the diffeent fusion modes in the poposed achitectue. (Of couse the option of not utilizing a fusion mode in the poposed achitectue is always available. It may be that even though fusion is pactical in this mode, thee is no easonable means of implementing it in the use s application, o a estaint outside the ealm of GIFTS could be a limiting facto.) It is at this point in the development pocess that the emaining modules of GIFTS will be useful. The efeence tool can be used to povide souces of infomation on diffeent fusion levels. The efeence tool will povide a list of efeences that ae elated to the fusion modes in the poposed achitectue. Thus, the efeence tool maes use of the nowledge gained by the pimay component. Similaly, if the use has not peviously detemined methods fo pefoming FEI-DEO fusion o maing local decisions, then the FEI-DEO fusion selecto will be helpful. In this tool, the use is ased application specific questions to detemine the most appopiate implementation method. The FUSE tool would be used to investigate DEI-DEO fusion as discussed in this pape. 3. The FUSE Tool FUSE is cuently implemented on a PC using Visual C++ [6]. It will thus un with no alteations on Windows 95, Windows 98, o Windows NT. The use can alte the senso chaacteistics by choosing "Fusion Inputs" fom the Fusion menu, o by clicing on the fusion chaacteistics button on the toolba. Figue shows the use inteface with the Fusion menu activated. Afte "Fusion Inputs" has been chosen, the Data Definition Dialog Box (DDDB) will appea. It is though this dialog box that the fusion chaacteistics can be alteed. Figue 2 is the default setting of the DDDB. The DDDB consists of two goup boxes labeled "Inputs" and "Fused Decision Pobabilities", espectively along with a button label "OK." The "Inputs" goup is whee the fusion chaacteistics ae contolled. The inputs that can be alteed ae: decision pobabilities fo senso, decision pobabilities fo senso 2, the type of fusion logic, and the numbe of loos pemitted fo each senso. Note that the use can have contol ove the coect and incoect decision pobabilities fo both of the possible binay decisions (T and D). This allows fo the maximum flexibility in the definition of a senso. These pobabilities can be enteed by diectly typing in the desied numbe of by using the adacent slides. It should also be pointed out that fom equation (), the fou non-decision pobabilities ae uniquely defined by the inputs. The fusion logic is selected by a simple chec box (checed fo AND logic and uncheced fo OR logic). The numbe of loos ae enteed by typing the appopiate intege in the box labeled "Numbe of Loos." The "Fused Decision Pobabilities" goup is whee the fused esults, based on the above inputs, ae displayed. The fused coect, incoect, and nondecision pobabilities ae displayed fo both the T and D binay decision. The calculation of fused pobabilities is only one aspect of FUSE. FUSE also povides a collection of visualization tools to help analyze the esults. Each of these options ae accessed though the Fusion menu. (Note that to activate the Fusion menu the input dialog cannot be open. Hence, if the dialog box is open then the OK button needs to be selected to exit the dialog box.) The gaphical options ae: Plot Taget - plots the fused coect, incoect, and non-decision pobabilities, fo the T obect, against the numbe of loos, Plot Decoy - plots the fused coect, incoect, and non-decision pobabilities, fo the D obect, against the numbe of loos, Plot Taget And/OR - plots the fused coect pobability, fo the T obect, unde both AND and OR logic against the numbe of loos, Plot Decoy And/OR - plots the fused coect pobability, fo the D obect, unde both AND and OR logic against the numbe of loos, Plot Taget Fusion Benefits - plots the fused coect and incoect pobabilities, fo the T obect, against the numbe of loos while shading the domain of fusion benefit fo each and maing the domain of oint benefit, and Plot Decoy Fusion Benefits - plots the fused coect and incoect pobabilities, fo the D obect, against the numbe of loos while shading the domain of fusion benefit fo each and maing the domain of oint benefit. The definition of a domain of oint fusion benefit is the intesection of the domains of coect and incoect fusion benefit. The domain of coect (incoect) fusion benefit is the domain whee the coect (incoect) fusion benefit exists. The coect and incoect fusion benefit domain can be thought of as the domain bounded by a fused pobability cuve (with espect to the numbe of loos) and the best pefomance of a single senso. As an example, if the pobability of coect, incoect, and non-decision fo sen-
so ae 7%, 6%, and 3% espectively and 45%, 5%, and 40% fo senso 2, then the best pefomance fo a single senso would be a coect-decision pobability of 7%. Thus the fused coect pobability cuve and a hoizontal line would bound the domain of fusion benefit fo the pobability of a coect decision at 7%. 4. FUSE Usage Illustation Fo FUSE to be of pactical value, one needs to be able to execise it in a ealistic scenaio. It is meant to be a utility to assist a fusion system designe. To demonstate its utility, conside the following scenaio. A fusion system is being designed that employs two souces of decisions (o sensos) that ae independent and capable of multiple loos. (An example of such a system would be a taget acquisition system that employs an active X-band ada and a passive IR senso.) The goal is to balance the pefomance equiements of the system against the costs. Often this balance is obtained while using individual sensos that mae decisions below system specifications and obtain decision pobabilities that meet specifications though fusion. Fo example, the system in this scenaio equies that the pobability of coect and incoect decisions fo the taget obect ae 95% and % espectively, while these pobabilities ae 90% and 5% fo the decoy obect. Fom a cost-benefit analysis, it was detemined that each senso will be manufactued to poduce at best a 65% - 70% pobability of a coect decision and 7% - 0% pobability of incoect decision. Also, the maximum numbe of loos desied should be between 5 and 8. Initial values ae fist chosen in the analysis. In this case, senso one has pobabilities of coect (T), coect (D), incoect (T) and incoect (D) of 0.650, 0.549, 0.070, and 0.098 espectively. Similaly, senso two has values of 0.700, 0.647, 0.075, and 0.37. OR logic will be examined with the numbe of loos at five. The DDDB with these values is displayed in Figue 3. Immediately, it can be seen that the esults will not be satisfactoy because the fused pobabilities ae ust shy of the specifications and the non-decision pobability has been diven down to 0 at five loos leaving no oom fo futhe gains. Hence, additional loos will not help. Liewise, fewe loos will degade pefomance. Both of these conclusions can be seen by examining the "Plot Taget" and "Plot Decoy" gaphs. (See figues 4 and 5.) One possibility, yet to be consideed fo these senso inputs is the use of AND as opposed to OR logic. By examining the "Plot Taget And/OR" and "Plot Decoy And/OR", it can be seen that AND logic shows inceased fused coect pobabilities fo geate than five loos. The Plot Decoy And/OR gaph is displayed in figue 6. By checing the AND logic on the DDDB, AND logic esults can be moe investigated futhe. An examination of the "Plot Decoy" gaph, which can be found in figue 7, shows that a minimum of 6 loos will be needed, but unfotunately fo 6 o moe loos the fused pobabilities fo the taget obect do not meet the specifications. Hence, the basic senso chaacteistics need to be tweaed. The pobability of coect (T) decision will be inceased to 0.6600. With this new value, the "Plot Taget And/OR" and "Plot Decoy And/OR" show that fo five loos, OR logic is pefeable but fo 6 o moe loos AND logic will povide bette fused esults. The Plot Taget And/OR is shown in figue 8. Unfotunately, an inspection of eithe the "Plot Taget" o "Plot Decoy" (which is shown in figue 9) chats show that five loos will poduce a pobability of incoect decision that is lage than acceptable. Hence, AND logic will be consideed with six to eight loos. With six loos, the system equiements can be met. Of couse because this analysis is being done in the design phase, anothe useful fact is to now how many loos ae equied fo fusion to be beneficial. An examination of the "Plot Taget Fusion Benefits" and "Plot Decoy Fusion Benefits" shows that fusion benefits can be obtained in the ange of thee to eight loos. These plots ae displayed in figues 0 and espectively. 5. Concluding Comments This wo epesents a continuing effot to futhe the application of fusion technologies by developing tools to aid in fusion system development. As a continuation of this effot, the same logic that was used to develop the theoetical foundations fo detemining fusion benefits fo two sensos should be expanded to include thee o moe sensos and incopoated into FUSE. Futhemoe, additional modules (simila to FUSE) coveing othe fusion modes should be added to incease the utility of the GIFTS achitectue. 6. Refeences [] Rao, N.S.V., To fuse o not to fuse: fuse vesus best classifie, Poceedings of SPIE - Senso Fusion: Achitectues, Algoithms, and Applications II, 3376: 25-34, Apil 998.
[2] Dasaathy, B.V. Decision Fusion. IEEE Compute Society Pess. 994. [3] Vashney, P.K. Distibuted Detection and Data Fusion. Spinge Velag. New Yo. 997. [4] Dasaathy, B.V. and Townsend S.D., GIFTS A Guide to Intelligent Fusion Technology Selection, Poceedings of the Fist Intenational Confeence of Multisouce-Multisenso Infomation Fusion, 65-72, July 998. [5] Dasaathy, B.V., Fusion stategies fo enhancing decision eliability in multisenso envionments, Optical Engineeing, 35 (3): 603-66, Mach 996. [6] Kuglinsi, Shephed, and Wingo. Pogamming Micosoft Visual C++ Fifth Edition. Micosoft Pess. 998. Figue : FUSE menu options Figue 2: Data Definition Dialog Box with default values.
Figue 3: Initial analysis inputs Figue 4: Plot of fused pobabilities fo the taget obect using initial inputs Figue 5: Plot of fused pobabilities fo the decoy obect using initial inputs
Figue 6: Compaison of pobability of coect decision fo decoy obect using initial inputs unde AND and OR logic Figue 7: Plot of fused pobabilities fo decoy obect using AND logic Figue 8: Compaison of pobability of coect decision fo taget obect using evised inputs unde AND and OR logic
Figue 9: Plot of fused pobabilities fo decoy obect using OR logic and evised inputs Figue 0: Fusion benefits fo taget obect using evised inputs and AND logic Figue : Fusion benefits fo decoy obect using evised inputs and AND logic