Decision support systems and modern maritime air defence fuzzy identification of targets

Décision support Systems and modem maritime air defence

Fuzzy identification of targets

W.W. Sillevis Smitt, B. Bruggeman

Royal Netherlands Naval College/Delft Unievrsity of Technology

Department of sensor, weapon and command Systems

P.O.Box 10.000, 1780 CA Den Helder, The Netherlands

1. A b s t r a c t

Naval air defence officers nowadays face an air threat that is characterised by increasing complexity, while reaction tintes get shorter. Therefore the devel-opment of air defence Systems is of primary interest in the design of new naval combatants. Besides weapons and sensors, also the improvement of the décision Systems for air defence is subject of study.

Target identification is one of the key processes in maritime air defence ßdAD). In this process infor-mation from different sensors and sources is inte-grated in order to determine the class or type of the target. Dijftculties in this process are caused by un-certainty in information and the real time character of the process. Especially information about the tar-get trajectory is uncertain and, although of great importance, hardly used in automatic identification

Systems.

In this study the specific problems of target identifi-cation are addressed. A multi-level structure for target identification has been developed. Target types and classes are represented as hypotheses. A multi-hypothesis testing technique is used to compare ob-served features and hypotheses. In order to capture the uncertain trajectory data a fuzzy algorithm is proposed. Two methods to determine the similarity between observations and hypotheses for these uncer-tain data will be discussed. Finally an experiment with the proto-type simulation model of the identifi-cation system illustrâtes the possibilities of this fuzzy approach.

2. K e y w o r d s

M a r i t i m e air defence, décision support Systems, target identification, similarity measures, fuzzy décision making, fuzzy Systems.

3. I n t r o d u c t i o n

D u r i n g the last ten years the international situation has changed dramatically. Warships are more a n d more deployed i n maritime blockades a n d peacekeeping operations, where they have to opérate cióse to enemy shores w i t h i n reach o f a l l kinds o f anti-ship missiles ( A S M ' s ) a n d aircrafts.

The development o f new A S M ' s is focused o n short reaction times b y u s i n g higher speeds, lower altitudes and a l l kinds o f evasive manoeuvring [ B O N S I G 9 3 ] P O O T O N 9 5 ] . Therefore the a i r threat is n o w char-acterised b y short reaction times a n d a diversiry o f modern A S M ' s .

Consequently a lot o f effort i s put into the improve-ment o f maritime a i r defence systems [ R I C H A R D 9 2 ] . T h e improvements concéntrate o n the development o f new sensors, n e w weapons, integrating sensors w i t h i n a task forcé and advanced command a n d control sys-tems.

T h i s trend leads to another development: the increase i n information. N e w sensors a n d data l i n k systems overwhelm the a i r defence officer(s) w i t h data that plays a role i n the ship's a i r defence.

In order to cope w i t h the increasing amount o f infor-mation i n shorter reaction times, decision-support systems ( D S S ) are needed. A good description o f a D S S is: lit exploits intellectual and computer-related

technologies in order to improve creativity in deci-sions that really matter'. T h i s means that the coordi-nation between m a n a n d computer i s o f great impor-tance.

For a D S S the distiction can be made i n :

• the kernel: the kernel o f a system consisting o f architecture/structure, communication, command & control, man-computer dialoque, informa-tion/knowledge;

• the application: the applicaüons are (depending on the mission) grafted upon the kernel.

Important questions, w i t h regard to the applications, are ' H o w to structure them?' and ' H o w to cope w i t h a l l types of uncertainty a n d information?', that the interaction between application a n d m a n should be realistic and acceptable for men.

T h e a i m o f this study is to come to a general structure for a key-process o f M A D : the identification process. Incidents w i t h U S S Stark (struck by two Exocet missiles) and U S S Vincennes (shot a n Iranian c i v i l -i a n a-ircraft) are examples of what can go w r o n g w h e n the target is not correctiy identified.

T h e correct identification is not only important for the correct assignment of " f r i e n d " or "foe", but also for i m p r o v i n g the ship's defence tactics. E a r l y identi-fication can support the t u n i n g o f parameters for the ship's sensors and weapons.

I n this article an identification algorithm based o n fuzzy decision m a k i n g and similarities is presented. Sensor observations are the input for the identifica-t i o n process. T h e ouidentifica-tpuidentifica-t is a seidentifica-t o f possible identifica-targeidentifica-t identities w i t h a measurement o f belief. T h i s meas-urement is called a fuzzy identity measure. I n chapter 4 some characteristics o f the problem of target i d e n t i -fication are explained. I n chapter 5 a multi-level structure for target identification is proposed. T h e particularities o f each level are discussed. Special attention is given to the interpretation o f target trajec-tory information, w h i c h is closely related to h u m a n reasoning. I n chapter 6 the results o f a simulation are demonstrated. F i n a l l y the conclusions and recom-mendations for further research are given i n chapter 7.

4. T h e p r o b l e m of t a r g e t i d e n t i f i c a t i o n

T h e process o f target identification i n maritime air defence can be defined as the determination o f the identity o f an enemy f l y i n g object.

There are different levels o f identification. Targets can be classified according to sort, class and type (figure 1).

Target identities in maritime air defence

1

I Air targets |

I

Sort _{1 Aircraft ]} I Missiles I

1 I

1 I I 1

Class

1

L-F14 L-LynxSH14 -Exocet L-HARM

L-SSN-19 Shipwreck

Figure 1: Identity levels i n maritime air defence Identification to the level o f target class gives the general identity o f the aircraft or missile. T h e charac-teristics and capabilities are s i m i l a r w i t h i n a class, so the identity k n o w n at class level permits general

conclusions o n defence tactics a n d defence system settings. E a c h class contains one or more target types. A target type is the most detailed identity level i n maritime air defence. A l l k i n d o f information o n characteristics of A S M ' s and aircraft is k n o w n at the type level. A target identified b y type permits a suit-able defence tactic and parameter setting o f the ship's defence systems.

T h e process o f target identification is one o f the proc-esses i n the air defence model. T h e process is fed by sensor information and provides the c o m m a n d and control process w i t h information that is used to eliminate the threat. It is important to realise that not only sensor information is used, but also historic knowledge and situational information. F i g u r e 2 shows the identification process i n relation to other processes a n d information/knowledge i n the a i r de-fence model.

Three m a i n characteristics have to be taken into ac-cotait w h e n designing a n identification System. 1. Multi-type information.

T h e identification problem is a multi-type informa-tion problem. T h e informainforma-tion cornes f r o m various sensors and sources, o n différent time-scales, formats a n d dimensions. F o r instance, a threat situation c a n be characterised by the f o l l o w i n g information:

Radar contact: Inconung target i n position 045 de-grees, 20 miles, speed around 300 knots, course 225 degrees, height

1000 ft;

ESM-intercept: Interception o f radar signal 10 G h z , puise w i d t h 2,5 \iS, P R F 0,7 sec; Intelligence: A hostile ship o f type A m i g h t be

about 50 miles north-east. T h i s ship is fitted w i t h A S M ' s o f type B . i i Crisis situation U Sensors Intelligent Other

processes Sensors Intelligence

Other processes i V|w«»«r.cationU- Situational i_ I . I information Ä \ \ 1 -T • ^ " *s* Command • 1 _

» HZ

W

A l l this information is important for the identificatíon of the target, but the structure and scale are not u n i -form, so integration and fusión i s not 'just l i k e that' possible.

T h i s leads to the f o l l o w i n g important requirement for an identification process: a l l information has to be transformed to comparable units of the same dimen-sions. O n l y then integration and fusión o f information w i l l be possible.

2. Uncertainty.

A problem i n a i r defence rises because the informa-tion may be incomplete, imprecise, fragmentary, contradictionary or deficient i n one way or another. Some information is observed by the unit's o w n sen-sors, other information through data-link, telex or voice reports. T h e information is subject to atmospheric losses, interference f r o m other sources, m a -nipulation or deceptioa Uncertainty i n information can be divided into three different kinds o f informa-tion uncertainty [ K L I R 9 5 ] :

• fuzziness (lack o f definite or sharp distinctions), also k n o w n as vagueness, unclearness a n d h a z i -ness;

• discord (disagreement i n several alternatives), also k n o w n as conflict and discrepancy;

• nonspecificity (two or more alternatives not distinguishable), also k n o w n as variety, diversity and imprecisión.

The uncertainty is increased, because a target i n a n air defence scenario w i l l be not co-operative. Instead, the enemy tries to remain undetected and conceal its identiry a n d intentions. I n maritime a i r defence these "countermeasures" can be divided into different classes:

• concealment: Methods to prevent the enemy f r o m observing deployments, capabilities intentions and movements;

• j a m m i n g : Interfering the enemy sensors b y send-i n g out h send-i g h power ssend-ignásend-is;

• deception: Injection o f false or misleading infor-mation.

3. Real-time process.

Another characteristic is the real-time character o f the identification process. T h e development o f there being less time for reaction means that the time factor i n maritime a i r defence is becoming increasingly important. T h e time factor has three aspects.

Firstly, there is often no time for collecting a l l the necessary information. T h e identification process starts immediatly after detecting a n air contact a n d conclusions as to the identiry have to be made, even i f only limited and uncertain data is available.

Secondly, the process is dynamic. D u r i n g the process, sensor data w i l l vary, so the conclusions o n target identiry might differ. I n order to take these variations into account a n d to support the decisión process it is désirable to visualise the belief i n the target identities. Figure 3 shows a n example o f the output o f the iden-tification process versus time.

M M

W

H—I—I—I—i

It is obvious from this figure that at different times target 1, 3 a n d 4 are the most l i k e l y target identity. T h e aspect that only limited time is available c a n have a b i g impact o n the decisión. Whenever possible this should be taken into account i n the design o f a n identification system.

Thirdly, some sensors w i l l need more time for data collection and interpretation then others. T h i s means that various time scales are used.

5. Process of target identification

A s a result o f the three mentioned characteristics o f the identification process the requirements for the fusion techniques are h i g h . T h e process should be able to handle different kinds o f information a n d uncertainties, w i t h i n a real-time environment.

T h e last two decades a variety o f représentations a n d calculi for data fusion have been developed. Methods for handling uncertainty range from the classical Bayesian probability model [ P E A R L 8 7 ] , Shafer-Dempster évidence theory [ S H A F E R 7 6 ] , Zadeh's fuzzy set theory [ Y A G E R 7 7 ] to the linear a n d loga-rithnüc o p i n i o n pool [ G E N E S T 8 6 ] .

A l l methods have their advantages a n d shortcomings, but so far no single algorithm has been developed, that deals w i t h a l l problems P I L L A R D 9 2 ] .

In order to fuse different kinds o f information w i t h their uncertainties a n d incompleteness a multilevel structure for the fusion and integration o f data, i n -formation and knowledge is required. E a c h level has its o w n degree o f abstraction and type o f uncertainty. T h e integration or fusion technique at each level depends on the nature of these characteristics.

In order to distinguish the levels o f abstraction some terminology is introduced. Firstly the sensor

observa-tions. These are the detections of target information (e.g. the interception o f an enemy radar signal). Sec-ondly the target feature. A feature is a quantifiable signal characteristic, that can be extracted f r o m ob-servations and that permits the discrimination among target classes (e.g. the feature "frequency" and "pulse w i d t h ( P W ) " f r o m the radar signal). T h i r d l y , the

signature, that is described by one or more specific features (e.g. the electromagnetic ( E M ) "signature", described by the "features" frequency and P W ) . T h e f o l l o w i n g variables are introduced:

• the possible target identities (type and class) f o r m k hypotheses {h1,h2,..,hk>, p hypotheses for target

classes { C i , C2, . . , Cp} and q hypotheses for target

types { T , , T2, . . , Tq} , w i t h k = p + q ;

• the hypotheses are characterised by m features {fi,f2,..,fm}, not a l l features apply for each

hy-pothesis (e.g. passive h o m i n g missiles do not have radar related features);

• the knowledge about possible values o f fi for class Cj can be represented by a fuzzy set A y ;

• a set o f features f; f o r m a signature { s i g n i , s i g n2,

.., signn}, w i t h n<m;

• f r o m the sensor observations {Si,s2,..,Sr} the

fea-ture vector (f*j, f*2,.., f*m) is determined;

T h e a i m of this study is to come to a general architec-ture for an identification system that can handle a l l kinds of uncertainties. Therefore the approach is based o n central decision m a k i n g and passing uncer-tainties to higher levels o f decision.

T o continue w i t h the structure o f the identification process: figure 4 illustrates the four levels. First a general description o f the four level process w i l l be given. T h e n every process is described i n more detail. Special attention is given to level 2.

other friendly units Level 1 Level 2 Level 3 Level 4 J| THREAT INFO

35 „,

sign,

m sign g sign„,

FUSION OF SIMILARITIES EVALUATION

MOST UKELYTARGET ID'S

Figure 4: The four4evel identification process

T h e process of target identification starts w i t h the detection o f threat information by one or more sen-sors. The observations are put into the identification process.

A t level 1 the observations are processed i n order to determine certain features. F o r some features fusion of data f r o m various sensors or successive observa-tions may be necessary (e.g. fusion of position obser-vations and D o p p l e r i n order to determine the feature "target speed").

A t level 2 similar features f o r m signatures a n d are compared w i t h k n o w n characteristics o f possible target identities. These target identities are the hy-potheses. F o r each hypothesis the similarity o f a k n o w n signature to observed features is determined. T h i s process is called "signature sirnilarity". The "signature sinularity" for each hypothesis a n d signa-ture is passed to level 3.

A t level 3 a l l signature similarities are fused i n the "fiision of similarities" process. T h e relative i m p o r -tance o f a signature for the f i n a l decision is expressed by weight factors. There are many datafusion tech-niques at this level, w h i c h have been examined ex-tensively [ G O O D M A N 8 7 ] [ W A L T Z 9 0 ] . T h e fused similarities for a l l hypotheses are propagated to level 4.

L e v e l 4 of the identification process is the correlation of the outcome of level 3 w i t h the "situational infor-mation". T h i s extra knowledge about the tactical situation is i n practice very important for evaluating the outcome o f automatic target recogmtion ( A T R ) systems. T h i s is the highest level o f abstraction. T h i s process evaluates and f i n a l l y presents the most prob-able target identities.

In the next paragraph the different levels and their characteristics w i l l be discussed.

5.1 L e v e l 1: F e a t u r e détermination

The first process i n the identification algorithm maps observations Si o n the features f*j and is called "feature détermination". T h e sensor observations m a y come f r o m different sensors. Sensors i n maritime a i r de-fence are radar (search a n d track), electronic support measures ( E S M ) , infrared sensors, electro-optical sensors. T h e features are quantifiable signal charac-teristics, w h i c h permit the discrimination o f a target class or type. T h e mapping is not always a one-to-one relation.

There are many different ways to obtain target fea-tures f r o m sensor observations. T h e appropriate technique dépends o n the feature a n d type o f sensor. In the literature the f o l l o w i n g methods are m e n -tioned:

• State estimation is the process o f determining a n estimate o f the state o f a target, based o n obser-vations related to its state. State estimation techniques are especially used for estimating the target's position, velocity, accélérations a n d f u -ture track. A large a n d diverse set o f estimating techniques have been developed, resulting i n several overview a n d survey articles [ T A Y L O R 8 8 ] . E x a m p l e s o f estimating techniques are a ß a n d aßyfilters, K a l m a n f i l -ters, fiizzy target trackers. [ S I C K I N G 9 3 ]

• I n ESM-sensors various kinds o f waveform

classiflers are used to obtain features like

quency, pulse-width a n d puise répétition fre-quency f r o m a n intercepted radar signal.

• Pattern récognition techniques are used for i m a g i n g sensors such as infrared a n d electro-optical sensors.

5.2 L e v e l 2: S i g n a t u r e s i m i l a r i t y

T h e "signature similarity" is a m a p p i n g f r o m a set o f features f*i to a value between 0 a n d 1. T h i s value is a degree o f belief that the signature originates f r o m a certain target class or type (hypothesis).

In gênerai: the signature similarity S between a set o f features F* a n d their possible values A for the h y -potheses H can then be defined as follows:

S ( F * , A ) : H - [ 0 , 1 ]

In maritime a i r defence several signatures can be distinguished. E a c h signatures has its o w n character-istics. T h e fusion technique should dépend o n the characteristics o f the signature's data and knowledge.

In practice however, trajectory information is impor-tant for a i r defence ofBcers, when identifying targets. Features like target speed, height and manoeuvres are easily recognised o n the tactical displays a n d intui-tively interpreted b y the members o f the a i r defence team.

In order to incorporate this valuable information i n the target identification process, a method to déter-mine the signature similarity for this uncertain trajec-tory information is proposed. T h e fact that humans perform relatively w e l l (as l o n g as there is enough time) i n this uncertain environment brings the fuzzy methods into scope. T h e use o f fuzzy logic i n k n o w l -edge base Systems is usually referred to as approxi-mate reasoning. T h e identification o f trajectory signa-tures is therefore based o n the principles o f approxi-mate reasoning.

In the next part o f this chapter the implementation procédure w i l l be discussed. First, the structure for representing the uncertain knowledge about signature features is presented. Second, the fuzzy i m p l i c a t i o n i n this case is discussed. T h i r d , two methods o f inferring the observed feature values f*; w i t h the knowledge are discussed. B o t h methods resuit i n a fiizzy similarity measure for each hypothesis. F i n a l l y the uncertainty and lack o f information are discussed.

1. Représentation of knowledge

T h e knowledge about characteristic values o r features f i , f2,.., fm for target class C i c a n be represented i n the

following r u l e R i :

Iffi isAjj and... f„ is A„i then ident is C}

S i m i l a r mies are formulated for each target class and type.

In these rules the premise (or antécédent) is a c o m b i -nation o f fiizzy propositions, the conséquence i s a singleton, representing the target class o r type. W h e n the fuzzy sets A y are identified b y the membership functions UAij(fi) then the f o l l o w i n g n-dimensional fuzzy relation R i representing the combined fuzzy features of class j , can be constructed:

R1= I ( T ( A ,J, A2,j, . . . , Anj ) , Cj) .

In this relation, T is a conjunction based o n a gênerai tnorm and I (will be discussed later) is a fuzzy i m p l i -cation. T represents the and connective. I represents the if-then connective. M a n y t-norms have been de-veloped. A discussion about the best choice i n this case is beyond the scope o f this study. T h e " m i n i m u m operator" (Zadeh's t-norm) will be used because o f its simplicity and widespread use.

Figure 5: Two-dimensional fuzzy knowledge space T h e multi-dimensional fuzzy relations can represent a corrélation between éléments o f a product space. I n this case this product space c a n be called a "fuzzy feature space". F i g u r e 5 shows the features for two target classes i n a two dimensional fuzzy feature space.

In this way a n-dimensional fuzzy feature space, w i t h membershipfunctions for a i l features a n d each h y -pothesis can be established. T h i s fuzzy feature space is the knowledge représentation o f the fuzzy trajectory signature information.

2. The fuzzy implication

The implication i s a mapping f r o m the antécédent and conséquence space to [0,1] (fi x f2 .. f„ x c

-[0,1]). I n the literature many implication functions have been proposed. T w o basic types o f implications can be distinguished [ J A G E R 9 5 ] :

a. fuzzy implications c o m p l y i n g w i t h the classical implication; thèse I-operators are a généralisation o f the classical implication (S-implications, (e.g. Kleene-Dienes implication I(a,b)=max(l-a,b)); b. fuzzy implications c o m p l y i n g w i t h the classical

conjunction (T-norms) f o r instance the M a m d a n i implication I(a,b)=min(a,b) and L a r s e n I(a,b)=ab. Based o n this distinction a number o f combinations can be defined.

I n this case a n appropriate implication is type b , M a m d a n i - i m p l i c a t i o n . T h i s implication i s easy to implement and very popular i n fuzzy control.

S. Tnference of the rule-base

T h e question is now, how to infer the class f r o m the observed feature values f*i w i t h the characteristic values Ay o f the hypothèses. T h e answer i s a two step process. Step 1 i s the establishment o f a fuzzy

sub-space. Step 2 is the actual inference w h i c h results i n the similarities for a i l classes Q .

Step 1. E s t a b l i s h a subspace that contains only the features that have been observed, extracted o r (intuitively) determined. T h i s détermines the struc-ture o f the antécédent space. It i s important to realise that the discrimination between certain target types and classes i n a subspace might be impossible. I n that case the similarities f o r thèse classes are equal a n d the discrimination has to be done at another level. Figure 6 illustrâtes i n a two dimensional feature space that the différence between C i a n d C3 c a n not be

distinguished, w h e n f2 i s u n k n o w n .

î

î

•un

î

Figure 6: Indistinguishable classes i n subspaces Step 2. T h e inference o f determining the class f r o m the observed feature values w i t h raies can be done i n various ways. A s the conséquences are crisp sets, the inference i s reduced to the détermination o f the s i m i -larity between observed features a n d the premises. I n the literature différent methods are described, f r o m the généralisation o f the reasoning schemes f r o m classical logic (generalised modus ponens), distance functions a n d similarity measures to various fuzzy truth values. I n this application a method that ftts the représentation o f knowledge and features i s required. I n order to cope w i t h différent situations two methods for inferring the rule-base are proposed. T h e first method (a.) i s based on distance- and similarity

measures, the second method (b.) i s based on t-norm implications. First o f a i l both methods are introduced,

then some considérations as to u s i n g method a. o r b . are given.

T h e properties o f both methods are discussed below. a. Inference based on distance- and similarity

meas-ures. I n this method the similarity between features

and knowledge i s obtained b y some k i n d o f similarity measure o r distance function. The feature values are represented b y a multi-dimensional fuzzy set F*, the possible values f o r class j b y the multi-dimensional fuzzy set Aj. T h e similarity for class Cj i s then given by the f o l l o w i n g expression:

For the calculation o f the similarity or distance be-tween F* and Aj many methods have been reported i n literature. W h e n u s i n g a distance function d(F*,Aj) the similarity equals [TTJRKSEN90]:

S(F*. A.) =

-V—

J 1 + d(F A,)

M a n y methods for measuring the similarity (or dis-tance) between fuzzy sets have been reported i n the literature. I n [ S E T N E S 9 5 ] an overview o f thèse measures and their properties is given. M o s t o f the similarity measures that are proposed are Symmetrie similarities. In this application however F* and Aj are not Symmetrie (illustrated i n I V ) . I n [ T V E R S K Y 7 7 ] it has already been mentioned that similarity meas-ures may not be a Symmetrie relation. T h e require-ments for a similarity measure i n this application are:

R - 1. If (F R - 2. If (F* R - 3. If (F* Ai> Sc (F , Aj) = i ; n Aj) = 0 => Sr( F Ap

= o;

Based o n the similarity measures proposed i n P U B O I S 8 0 ] an asymmetric measure for this a p p l i -cation is developed. T h e measure is based o n fuzzy intersection and fuzzy cardinality and meets the above mentioned requirements:

IF* O A J

SC( F A j ) - , w i t h

xeX

The fuzzy intersection F n A^ can be determined using a minimum-operator and is called the cardinality, also k n o w n as the power of a fuzzy set. T h i s similarity measure can be interpreted as the "relative fit o f F* i n A j " . It meets the intuitional judgement of a set o f data against background k n o w l

-edge about the possible values of the features.

b. Inference based on a T-implication. The inference of a fuzzy rule by a T-implication was proposed i n [ D U B O I S 8 4 ] and is n o w extensively used i n fuzzy control. T h e similarity can be obtained by a s u p - T composition. It can be shown [ J A G E R 9 5 ] that for the m i n i m u m and the product operator the similarity between F* and Aj is given by the f o l l o w i n g expres-sions:

m i n i m u m operator:

s ^ ( F *f = h g t ^ F * n A j ) ;

product operator:

S ( F * , A . ) = h g t | ( F * * A . ) .

T h i s similarity measure gives a "degree o f fulfilment" between observed features and premises.

4. Discussion about uncertainty in knowledge and feature values

In the choice between methods a. and b. the uncer-tainty i n the feature values is crucial. Three différent situations are distinguished (figure 7):

1. Numerical feature value 3.a. Feature value fuzzy set

•î

A '

t — •

f — •

2. Feature value fuzzy number3.b. Feature value roughly known Figure 7:Three situation i n inference

1. W h e n no uncertainty is taken into account features can be represented by crisp values. M e t h o d b. seems to be an appropriate similarity measure. The similar-ity for one feature i can be obtained b y evaluating the membership value: a ^ . = / ^ ( f ^ ) • The similarity for F* can be determined by u s i n g some k i n d o f T -norm. F o r numerical feature values o f f . the follow-i n g applfollow-ies:

= 1 and f . n A . j = h g t ( f £ n hL.) I n this case method a. and b. are similar.

Other distance measures can be developed to measure the distance between fuzzy sets a n d numerical values, but that is beyond the scope of this research.

2. W h e n uncertainty originating f r o m measurement uncertainty is taken into account, feature values can be represented b y fuzzy numbers. T h e shape o f the membership function that represents the fuzzy n u m -ber can depend o n the Performance o f sensors, envi-ronmental conditions, etc. and m a y v a r y w i t h time. B o t h methods a. and b. can be used i n this case. M e t h o d a. is preferred, because R - l to R - 4 are met. 3. W h e n the feature values are more uncertain, quali-fied by linguistic terms and represented by fuzzy sets, they can be represented by fuzzy sets. M e t h o d a. is now preferred, because R - l to R - 4 are met (Situation 3 a i n f i g . 7).

A specific situation arises when the uncertainty i n the features is more than the fuzziness i n the antecedent. Features are only roughly k n o w n T h i s is another k i n d o f uncertainty. T h e more uncertain about the feature values, relatively to the required accuracy, the smaller the similarity. T h i s k i n d o f similarity is, i n fact, a measure o f nonspecificity (situation 3b i n fig.7). F r o m the three situations o f uncertainty i n features can be concluded that method a. always applies. Methods a. a n d b . are equal i n the case o f crisp fea-ture values. A major (practical) disadvantage o f method a. is the considerably higher processing re-quirement.

I n the next table the v a l i d i t y o f method a. and b. i s summarised.

f c r i s p f* fuzzy number f* fuzzy set

M e t h o d A

+

+

+

M e t h o d B

+

+/-

-T h e negative results for method b. is influenced b y the choice for a M a m d a n i - i m p l i c a t i o n . Further re-search is needed into the validation o f method b . f o r other implication functions.

5.3 L e v e l 3: F u s i o n of s i m i l a r i t i e s

T h e next level i n the identification process is the combination o f the signature similarities for each signature and hypothesis i n order to determine the combined belief i n a hypothesis. T h i s process c a n be seen as a m u l t i attribute decision m a k i n g problem ( M A D M ) .

There are many algorithms to fuse data f r o m different sensors, for example .two popular algorithms are Dempster-Shafer rules o f combination [ B O G L E R 8 7 ] and the Bayesian method. I n [ W A L T Z 9 0 ] a n over-v i e w is giover-ven.

I n this chapter two methods that are used i n connec-tion w i t h M A D M a n d fuzzy logic, the averaging a n d distance functions w i l l be discussed. Subsequently some considerations about weight- a n d confidence factors are given.

a. Average value. T h e average value o f the signature similarities for a certain alternative. M a n y different averaging operators are used i n the decision theory. M o s t o f them are a special f o r m o f the generalised function:

Hi

F o r s-°° the general goal function becomes the " m a x i m u m " operator a n d for s—<*> the " m i n i m u m " operator. F o r s = 1 the function is the arithmetic mean and f o r s = 0 the geometric mean.

I n many articles the fuzzy approach i n decision m a k i n g is associated w i t h the " m a x - m i n " criterion (s—°°). However, the right value o f s depends o n the decision problem a n d the person w h o takes the deci-sion. Further study is needed to examine the value o f s that represents the decisions o f a i r defence officers.

b. Distance function. A target feature vector is a vec-tor w i t h a value between 0 a n d 1 for each feature. T h e best solution is represented b y a reference alternative " X " . T h e "distance" between the reference alternative and the actual values is a measurement o f the s i m i -larity. T h e target closest to this reference is the best alternative. A general distance function to calculate the distance o f alternative C, and X is:

m D(C,, X) =

2

,r >

1

z

j=l

c. Weight factors. T o account for the relative impor-tance o f certain features weight factors w}- between 0 and 1 c a n be added. These factors do not represent the confidence i n a feature, but give the relative weight o f a certain (group of) signature i n the fused similarity. A discriminating signature could result i n a h i g h weight factor. T h e weight factors should c o m -ply w i t h the f o l l o w i n g condition:

n

Sw. =

1

i=

1

d. Confidence factor. T o account f o r the confidence i n features (and sensor observations) a n extra

confi-dence factor (CF) c a n be introduced. T h i s factor, from 0 (no confidence) to 1 (high confidence) is ac-counted for, p r i o r to the fusion o f similarities. T h e confidence factor depends o n the performance o f the sensors a n d the likeliness o f spoofing, j a m m i n g and deception b y the enemy.

The operator that combines the C F w i t h the feature similarity can be a T - n o r m or some other operator.

5.4 L e v e l 4: E v a l u a t i n g t h e result

The process o f calculating the support for each hy-pothesis is repeated for every sample. T h i s i s one o f the inputs o f level 4. Another input is information about the tactical situation. T h e output o f this process is a n evaluated fuzzy identity measure f o r the most likely hypotheses.

In the literature several studies o n this h i g h level o f decision support can be reported. I n [ H E U S D E N 9 5 ] an overview is given o f the possible use o f artificial intelligence i n C o m m a n d and Control. I n [ B O A S S O N 9 5 ] some requirements for new tech-nologies are mentioned. I n practice this level o f deci-sion m a k i n g is not yet supported. Based o n the practi-cal situation some factors can be mentioned that play a role i n the evaluation of A T R data:

a. The dynamic behaviour of the "identity measures" are a direct consequence o f the real-time aspect of the identification process. Some reasons that cause this dynamic behaviour are:

• N e w sensor observations, for instance new E M -emissions;

• Significant changes i n trend data, for instance change of target's height or detection o f m a -noeuvres;

• F u z z y data becomes clearer, for instance radar image recognition at a closer range;

• Change of weight factors, due to variation i n sensor performance;

• Noise.

Figure 3 showed how dynamic behaviour influences the decision process. T h i s can be taken into account by considering the change i n belief values. The easi-est way o f doing this is to display the fuzzy identity measures versus time (as i n figure 3). Automatic methods for taking this into account can range f r o m approximate reasoning to various filtering techniques. b. The situational information (tactical environment) gives important information about the possibility that a hypothesis may occur. Some factors that play a role i n the tactical situation are:

• Knowledge about the presence of a weapon carrier (position [relative], capabilities and i n -tentions);

• E n e m y behaviour (surveillance activities, j a m -m i n g , spoofing etc.)

• Knowledge about the environment, the p r o x i m -ity o f land, airfields, etc.

T h i s information plays a n important role i n the h u -m a n interpretation o f threat infor-mation. Based o n this information some hypotheses can be excluded, w h i l e others have a h i g h possibility o f taking place. Several systems for t a k i n g this information into ac-count have been proposed. I n [ W A L T Z 9 0 ] an over-v i e w is giover-ven. A n early study into the possibilities of fuzzy logic for these kinds of decision m a k i n g is done i n [ D O C K E R Y 7 7 ] .

Approximate reasoning techniques and fuzzy expert systems might provide sound basis for this k i n d of decision support.

c. Equal support for different alternatives is another factor that has to be taken into account w h e n evaluat-i n g the results o f level 3. T h evaluat-i s unspecevaluat-ifevaluat-icevaluat-ity between several hypotheses is caused by similar target types, uncertainty i n information a n d lack o f special infor-mation. The level 4 evaluation process should be able to deal w i t h this k i n d o f uncertainty.

Some considerations concerning this problem and possible approaches:

• I f several target types are indistinguishable, a distinction between target classes might be pos-sible;

• A lack o f information m i g h t result i n informa-t i o n requesinforma-ts informa-to cerinforma-tain sensors (e.g. special ainforma-t- at-tention is given to determine a distinguishing feature value);

• I f the unspecified target types result i n similar defence actions, no further identification is re-quired;

• E l i m i n a t e the impossible hypotheses a n d con-centrate o n the possible;

• Take the situational information into account (pt. b.) and modify the belief values.

6. Simulations

A Simulation model o f the target identifier has been b u i l d u s i n g M A T L A B w i t h the " F u z z y Toolbox". Inputs for the model are:

• Knowledge about the threat: height/distance pro-file, speed- and E M - i n f o r m a t i o n about three target types. T h e height pattern is defined for three fuzzy distances: far, m e d i u m and close.

• The target parameters o f the missile that is to be identified.

• Noise can be added.

• Selection o f identification method a. or b .

After defining the model, a missile r u n has to be made i n Order to generate a set o f 'observations'. Outputs are:

• the fuzzy feature space a n d the missile's flight pattern;

• the fuzzy similarity versus time.

Figure 8 shows a n example o f similarity versus time.

0.8 0.6 0.4 0.2 1' 1 " I I 10 20J Radar o nJ 30 40 A 50 60 Time T- Radar off Figure 8: Ouput o f the simulation model

F r o m this example the f o l l o w i n g conclusions can be drawn:

• the E M (radar) signature is supporting target 2 and decreasing the similarity o f target 1 and 3; • based o n the height/distance and speed

informa-tion target 1 is the most l i k e l y target.

M o r e simulations are needed i n order to investigate the possibilities and limitations o f the target identifi-cation system.

7. Conclusions a n d recommendations

In this article the problem o f target identification i n maritime air defence has been addressed. A general structure to deal w i t h its specific problems has been proposed. The four-level system w i t h the particulari-ties o f each level are described. Special attention is given to the incorporation o f uncertain target trajec-tory data. A similarity measure for this type o f infor-mation is suggested.

7.1 Conclusions

• T h e proposed representation o f uncertain k n o w l -edge i n a fuzzy feature space offers the possibility to account for uncertaity i n knowledge. It has been shown that the proposed similarity measure (method a.) is a flexible and p r o m i s i n g measure that handles both crisp and fuzzy data. E v e n data that is only roughly k n o w n can be incoorperated i n the identification process.

• A t the highest level, important factors o f the identification system are the situational i n f o r m a -tion and dynamic behaviour. A s this informa-tion is i n practice o f major importance for air defence officers a decision support system should be able to deal w i t h this k i n d o f information as w e l l . 7.2 R e c o m m e n d a t i o n s

Suggestions for further study.

• Further research is needed into methods a. a n d b. for representing uncertainty and integrating dif-ferent kinds o f data. I n this studies special atten-tion should be given to: h o w to handle " l a c k of information" and the use o f specific fuzzy opera-tors and membership functions. E s p e c i a l l y the use o f other fuzzy implications i n combination w i t h method b. needs further research.

• F o r level 2 (signature similarity) the determina-tion o f the similarity for other signatures needs further research. M e t h o d a. m i g h t be useful for orther kinds o f data.

• T h e use o f fuzzy numbers to express the meas-urement uncertainty needs further research. T h e adjustment o f membership functions, depending o n the uncertainty at a certain moment, might be a n interesting possibility to account f o r this k i n d o f uncertainty.

• F o r level 4 further study is needed into the use of situational knowledge a n d d y n a m i c behaviour. D e c i s i o n m a k i n g at this level is characterised by a h i g h level o f abstraction.

• A n overall simulation model has to be b u i l t to test the proposed structure w i t h (classified) data o f real targets.

F r o m this study the f o l l o w i n g conclusions can be drawn.

• The proposed four level identification system seems to be a flexible structure that offers the possibility to account for different levels o f ab-straction;

• T h e similarity measures i n this study only account for "positive evidence". It might be interesting to study the use o f certainty factors defined o n the interval f r o m -1 to 1 [ S H O R T L I F F E 9 2 ] .

The fuzzy similarity as output o f the identification system is a number between 0 a n d 1. Further re-search can be done into a fuzzy (linguistic) output (e.g. "similarity class i = "very similar"). T h i s k i n d o f output is probably easier to comprehend for the user.

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