SIMM Method Based on Acceleration Extraction for Nonlinear Maneuvering Target Tracking

Transcription

1 Journal of Electrical Engineering & Technology Vol. 7, o. 2, pp. 255~263, SIMM Method Baed on Acceleration Extraction for onlinear Maneuvering Target Tracking Hyun Seung Son*, Jin Bae Park and Young Hoon Joo** Abtract Thi paper preent the art interacting ultiple odel (SIMM) uing the concept of predicted point and axiu noie level. Maxiu noie level ean the larget value of the ere noie. We utilize the poitional difference between eaured point and predicted point a acceleration. Coparing thi acceleration with the axiu noie level, we extract the acceleration to recognize the characteritic of the target. To etiate the acceleration, we propoe an optional algorith utilizing the propoed ethod and the Kalan filter (KF) electively. Alo, for increaing the effect of etiation, the weight given at each ub-filter of the interacting ultiple odel (IMM) tructure i varying according to the rate of noie cale. All the procedure of the propoed algorith can be ipleented by an on-line yte. Finally, an exaple i provided to how the effectivene of the propoed algorith. Keyword: Acceleration, Kalan Filter (KF), Interacting Multiple Model (IMM), Maneuvering target tracking. Introduction owaday, the target tracking proble including target dynaic, aneuvering target tracking, and eaureent origin uncertainty ha becoe not only a ilitary interet but alo cloely linked application to our live [-5]. The Kalan filter (KF) ade the tracking proble grow and utain the capability of that until now. The tandard KF i well-known a uccefully applicable with nearly contant velocity but unacceptable in cae of nonlinear aneuver ince the unknown acceleration work a a large proce noie on the dynaic odel. In order to olve thi proble, a variety of technique have been tudied and developed in the field of the tate etiation over decade [6-9]. The firt attept wa ade by Singer, who propoed a target tracking odel in which aneuver wa aued by the firt order Markov proce with tie correlation [0]. Since the Singer ethod, a lot of reearche have been diverely developed. One approach i related to the input etiation (IE) technique [-5] and the other are the interacting ultiple odel (IMM) and the adaptive interacting ultiple odel (AIMM) [6-22]. Later technique provided the better tracking perforance than prior one for a aneuvering target. However, thee ethod have liit and additional requireent to track a aneuvering target. It i difficult to approxiate acceleration adaptively becaue the overall proce noie Correponding Author: Dept. of Electrical and Electronic Engineering, Yonei Univerity, Korea. (jbpark@yonei.ac.kr). * Dept. of Electrical and Electronic Engineering, Yonei Univerity, Korea. (onhyung@yonei.ac.kr). ** Dept. of Control and Robot Engineering, Kunan Univerity, Korea. (yhjoo@kunan.ac.kr) Received: April 6, 20; Accepted: October 26, 20 variance i tie-varying and ay be nonlinear. The IMM algorith require the predefined ub-odel with different conditi-on, and ay not guarantee good perforance in the cae that one of ub-odel doe not exactly atch the target otion. In the cae of the AIMM algorith, the accelera-tion interval for the different acceleration level hould be deterined in advance and the delay involved in etiating target acceleration hould be alo treated appropriately. The ot iportant proble in the previou tudie i to increae the tracking error by conidering the acceleration of a target a the iple yte noie. Motivated by the above obervation, we propoe a novel art interacting ultiple odel (SIMM) for tracking the nonlinear aneuvering target by extracting the noie variance and the acceleration of the target. To do thi, firt of all, we propoe the ethod of calculating the noie variance and acceleration of a target at every apling tie through the ditance difference between the eaured point and the predicted point. Then, we propoe the ethod of tracking the nonlinear aneuvering target by calculating the velocity and poition of the target through adjutent of noie variance and copenation of acceleration. Finally, we deontrate applicability and feaibility of the propoed SIMM through the iulation. Thi paper i organized a follow: Section 2 how the aneuvering target odel and briefly review the AIMM algorith a the repreentative of the conventional aneuvering target tracking ethod. The detail of the odified KF and the SIMM algorith are decribed in Section 3. In Section 4, the effectivene of the propoed intelligent tracking ethod copared with the AIMM algorith i hown. Finally concluion are drawn in Section 5.

2 256 SIMM Method Baed on Acceleration Extraction for onlinear Maneuvering Target Tracking 2. Preliinarie The dynaic odel of the aneuvering target are decribed for all axe by x( k+ ) = Fx( k) + G[ a( k) + ω( k)], () zk ( ) = Hxk ( ) + vk ( ) (2) where x( k) = [ x ( ), ( ), ( ), ( ), ( ), ( )] T x k x x k xy k x y k xz k x z k i the tate vector with the poition and the velocity eleent for a aneuvering target. The ter a(k) and ω ( k) are the unknown deterinitic acceleration and the proce noie, z(k) and v(k) are the eaureent vector and the eaureent noie, ω ( k) and v(k) are conidered a zero-ean white Gauian noie equence with variance q and r, repectively. When t i the apling tie, the yte atrix F, the gain atrix G, and the eaureent atrix H are pecified a follow: 2 t t / t t t /2 0 F =, G =, t t t / t H = In the cae of nonlinear aneuver, the deterinitic unknown acceleration input of the aneuvering target i regarded a an additive proce noie. Hence, () can be rewritten a x( k+ ) = Fx( k) + Gω( k) (3) where ω( k) = a( k) + ω( k) i aued to be the overall proc-e noie. Fro thee dynaic, previou reearche dealt with the noie including unknown acceleration. A finite nuber of ub-odel, aigned acceleration level, and parallel tructure are the required condition. The perforance of the previou algorith wa developed to a certain degree with above upport. After all, thee KF-baed conventional technique cannot exceed the liit that the yte appro-xiate the oveent of the target adaptively including the acceleration input. Hence, we propoe a novel approach which can utain the perforance in cae of linear and nonlinear aneuver together in thi paper. 3. SIMM Baed on the Extracting Acceleration In thi ection, we tudy the relation of the eaureent point, etiated point, noie, and acceleration. Further, we invetigate how the acceleration ipact on the aneuvering dynaic. With the application of the acceleration, we introduce the SIMM baed on the copenating the acceleration uing the axiu noie level. Uing thi odel, we can etiate the tate of the linear and nonlinear aneuvering target. The baic idea of the copenating the acceleration arie fro the fact that the priary purpoe of velocity feedback i to aid in the prevention of dynaic overhoot in the tracking yte. To olve thi proble, it i neceary to obtain the adequate velocity with the accurate accelera-tion. In thi apect, we review the iple tracking yte in the apect of the noie and acceleration for better under-tanding [5]. 3. Review of the tracking yte Target tracking i the ean by which target paraeter are eaured with repect to the tracking tation. Thee paraeter uch a aziuth, elevation, range, and relative target velocity are ultiately eployed to predict the colliion between the target and whatever weapon i launched againt it. The line-of-ight (LOS) between the enor and target i ued to track the target. If the tracking eleent wa at all tie pointed directly along thi LOS, tracking reult would be perfect and no error would exit. Unfortunately, the tracking reult of the continuou eaureent i not exact and oe error are alway generated in reality. Therefore a econd line, the tracking line, i defined a the line that for the axi of yetry of the radiated energy, coonly called the antenna bore-ight axi decribed in Fig.. Thi error give rie to the central proble of any tracking yte. Miniizing error between the LOS and the tracking line i the ot coniderable factor in the tracking proble. Further target velocity data i a ajor input for the error of the tracking proce. Since target poition data hould be available to the weapon control yte at all tie, oe ean of detecting target otion i required if the enor i to follow the target. There are two tracking and two copenating ethod for detecting target otion and tracking it. They are following four technique. ) Aziuth tracking: Reverberation forulated by each bea caue aziuth error. Diinihing the error i the ain purpoe of the tracking. The following anner are generally ued for any tracking yte. (a) Sequential lobing: A bea i poitioned in one direction, and in ubequent pule the bea i orientated lightly offet fro the previou direction. There are two reflecting ignal occurred with directivity in here. The tracking yte acquire the optial aziuth value when

3 Hyun Seung Son, Jin Bae Park and Young Hoon Joo 257 the yte find the equilibriu point diinihing the gap between two bea a Fig. 2. circuit of a ono pule yte in both aziuth and elevation i depicted in Fig. 3. 2) Range tracking: The purpoe of the range tracking i to follow the target in range and provide continuou ditance inforation or lant range to the target. Range tracking i accoplihed in a iilar anner to dual bea angle tracking. Once the range ha been eaured, the tracking yte attept to predict the range on the next pule. Thi etiate becoe the reference to which the next eaureent will be copared. Uing two range window, called the early and late range gate, ake the coparion depicted in Fig. 4. Fig.. Relation of LOS and track line Fig. 2. Sequential lobing Fig. 3. Coparator circuit of ono pule radar ignal (b) Conical can: Mechanical ethod by rotating the feed horn in a all circle around the focal point of a fixed paraboloid. If the feed point i oved tranverely away fro the focu, the bea will be at an angle with the axi. If the feed point i ocillated back and forth, the bea will wing fro ide to ide. If the feed point i rotated in a circle about the axi, a conical can will reult. If the target i not exactly on the antenna axi, an error exit between the LOS and track line. Thi error i iediately detectable becaue a the bea rotate, the return pule are aplitude odulated due to the varying proxiity of the target with the bea center. (c) Mono pule: Mono pule tracking yte deterine aplitude odulation uing only one pule with ultiple proceed bea intead of a train pule. Thi yte ue the ignal coparator circuit copoed of the four feed horn producing four bea. In the circuit, four hybrid can be connected to provide aziuth and elevation error. To deterine aziuth, the u of the C and D horn output are ubtracted fro that of the A an B horn. Elevation error i deterined by ubtracting the u of the output of the B and D horn fro the u of the output of the A and C horn. Siplified icrowave coparator Fig. 4. Range gate 3) Poition feedback: A the yte ove in repone to the original error, the reult i to poition the tracking line in coincidence with the LOS. Thi action by the yte reduce the poition error ignal until near zero, thu providing an indication that the yte ha reponded correctly to the error initially eaured by the radar. The equilibriu tate of the tracking yte then i a null copoite error ignal, reulting in zero output to the drive

4 258 SIMM Method Baed on Acceleration Extraction for onlinear Maneuvering Target Tracking yte. The true equilibriu tate i never achieved while the yte i actually tracking, but that operating properly, the yte will alway tend toward thi tate. 4) Velocity feedback: The feedback voltage i ubtracted fro the output drive ignal of the gyro. The priary purpoe of velocity feedback i to aid in the prevention of dynaic overhoot. The following algorith for olving the tracking proble i baed on the auption that the radar provide target poition inforation once each can. Thi chee to be ipleented i the eential proce for any tracking yte. ) Target detection: After everal can, the tracking yte proceor contain what aount to a three dienional binary atrix repreenting the entire earch volue of the radar. The bea plitting hould eet the angular reolution le than the bea-width of the radar. 2) Generation of tracking gate: A gate can be defined a a all volue of pace copoed of any cell eaning the three-dienional binary atrix repreenting the entire earch volue of the radar. If the target i within the acquiition gate on the next can, the aller tracking gate i generated. That gate ove to the new expected target poition on ubequent can decribed in Fig. 5. A coon ean of dealing with a turn or linear acceleration of the aneuvering target i the turning gate. Fig. 5. Gate proceing for track file or decreaed in aplitude a copared to the next pule in the train. Such a fluctuation could eaily occur if there i a udden change on the target radar cro ection (RCS). 3) Target track correlation and aociation: Target ober- vation on each radar can that urvive hit-pattern recognition and clutter rejection function initially treated a new inforation prior to coparion with previouly held data. We call it correlation with track. 4) Track initiation and track file generation: Concurrent with generation of the acquiition gate, a track file i generated in order to tore the poition and gate data for each track. If the poition data are obtained on ubequent can of the radar, the file i updated with the coordinate, the velocitie and acceleration are then coputed and tored, and the acquiition gate code i canceled. The acquiition gate i then decreaed in ize relative to that of the tracking gate, and the track code i tored, which indicate an active track file. 5) Track gate prediction, oothing, and poitioning: The yte repone otion wa oothed by eploying rate and poition feedback. The ean of oothing track data are α-β tracker, α-β filter, and the Kalan filter. 6) Diplay and future target poition calculation: We hereby how the equence of tracking algorith a nuerical expreion. Pk = Pk + α( Zk Pk) (4) β Vk = Vk + Ak t+ ( Zk Pk) t (5) γ Ak = Ak + ( Zk Pk) t (6) 2 P k P k Vkt + Akt 2 (7) where Z k i target poition eaured by the radar during can k, P k i oothed poition after can k, V k i oothed velocity after can k, P k i oothed acceleration after can k, P k i predicted target poition for can k, t i can tie, and α, β, γ are yte contant that deterine the yte repone, daping, and gain, repectively. 3.2 Application of the acceleration Fig. 6. Ue of a turning gate The turning gate i larger than the tracking gate and i co-located with it initially, eploying eparate logic and algorith that are different fro the tracking routine. The ize of the turning gate i deterined by the axiu acceleration and turn characteritic of valid track. It i decribed in Fig. 6. Seriou tracking error can be generated in uch a yte if the return of any one pule i arkedly increaed The ot iportant calculation of the tracking yte i to diinih the error between the predicted point and the eaureent point decribed in (4). Exiting anner yield velocity by differentiating the error of Z k and P k and obtain the acceleration by differentiating the velocity like (4)-(7). In thi cae the differentiating i executed with the noie factor, o the etiated value i alway accopanied noie. Thee anner depend on only how the yte contant i et up. A target deviate the tracking gate due to the dratic acceleration input a een in Fig. 6. At thi oent,

5 Hyun Seung Son, Jin Bae Park and Young Hoon Joo 259 tracking could lat uing the turning gate but a pretty high aount of error i inevitable for the reult. If thi tate i repeated, the tracking eleent would i the target. Many ethod treating only the overhaul noie could reduce the error to oe degree but it could not be a fundaental olution. The reaon i like that the acceleration in the noie ter play a role of the noie with big agnitude. The baic idea of the propoed ethod arie fro the fact that it i difficult to directly eparate acceleration fro other noie becaue it i given with other coponent. So, we approxiate acceleration of the aneuvering target and utilize thi one to etiate the poition and velocity of the target. Concerning thi proble, the propoed ethod et up the noie level. The error between the predicted point and the eaureent point i divided by thi noie level. The exceedance are regarded a approxiated acceleration and the ret i regarded the ere noie. Only ere noie i on going filtering proce and the filtered output i added correponding the acceleration. Propoed ethod iprove the yte perforance by taking proper action, filtering or copenation, fitting to the each factor. The filtering proce can be proceeded with the le noie. A derivation of uch acceleration i the ubject of thi ection. ) Extracting acceleration and copenation: We ake the axiu noie level a the periive noie value correpond with the capability of the equipent. It ean the degree of preciion. Thi noie include only the noiy factor like proce noie and eaured one. oie only ake the error to the dynaic odel. In thi paper, we utilize the axiu noie level a criteria to approxiate acceleration. After chooing the adequate value of a axiu noie level, we deterine whether acceleration i included or not by coparing thi one with the poitional error between the predicted point and eaured point at each apling tie. Let u uppoe a linear oving target. There i no acceleration input in thi cae and the target ove at regular interval. Thi oveent depend on only the tie and velocity. When we take a look at the relation between neighboring two point, later one depend on the prior one velocity and elaped tie like a x ( k) Δt and the noie ω i added to thi. If we retrict the noie to a certain value, we can conjecture about the poitional difference between the two point a a certain range. We can aue the axiu noie level even though we cannot get the exact proce noie. It explain that the axiu noie i the value of the preciion a the characteritic of the equipent. ext, let u think of the nonlinear aneuvering cae. In thi cae, the ditance gap will be uch variable by the acceleration input incurring the aneuvering. What the oveent of the aneuvering target i largely varied ean that the ditance gap of x(k) and x(k+) get out of the range ±axiu noie. We introduce the following auption to ditinguih acceleration input fro ere noie. Auption : Firt, there i no correlation between eaureent noie and proce noie. Second, acceleration input ha bigger value or aller one than other. The reaon i like that the accuracy get higher and the error get lower by the advance in technology. The procedure which i approxiating acceleration and copenating to the tracking dynaic i like follow. Firt, we get the predicted point at t = k by uing only the poition data of the target at t = k a follow: uk ˆ( k ) = xk ˆ( k ) + xk ( k ) Δt. (8) Then, we get the error between the predicted point and eaureent point a follow: ek ˆ( k ) = zk ( k) uk ˆ( k ). (9) We approxiate the axiu noie level ax according to the diperion of the error fro t = 0 to t = k. The axiu noie level i calculated with weight at every apling tie like ( ) ˆ ax = p k e( k). (0) n k = The weight becoe bigger when the ae value i repeated. If the error becoe bigger harply, we kip the procedure becaue the acceleration i added. Coparing (9) with (0), we et the error a acceleration when it i bigger than ax and copenate the velocity coponent of the by adding acceleration a follow: xˆ( k k ) = xˆ( k k ) + aˆ( k k ) Δ t. () When the error i aller than the ax, we regard thi one a ere noie for linear aneuvering and ove on to the filtering tep. We repeat thi procedure at every apling tie. To ake the tracking accuracy higher, we et thi procedure a a ub-odel of the IMM and et the ax differently at each ub-odel. 3.3 Propoed tracking ethod: SIMM Let xˆ ( k ) be the etiation of x(k) at k baed on the th ub-odel and xˆ( k ) be the cobined etiate fro ub-filter. One cycle of the propoed algorith i uarized a follow: ) Interaction of the etiate (ixing): The expected ixed tate etiate xˆ 0 ( k )( k ) and it error covariance P0 ( k k ) are coputed fro the tate etiate and their error covariance of ub-filter, repectively, a foll-ow: xˆ ( k k ) = μ ( k k ) xˆ ( k k ), (2) 0 n n n=

6 260 SIMM Method Baed on Acceleration Extraction for onlinear Maneuvering Target Tracking Pˆ ˆ 0 ( k k ) = μn ( k k ) Pn( k k ) n= + ( xˆ ( ) ˆ n k k x0( k k ) ) T xˆ ( k k ) xˆ ( k k ) [ ( ) ] n 0 (3) where the ixing probability μ n and the noralization contant α are repreented by μ ( k k ) = φ μ ( k ), (4) n n n α α = φnμn( k ) n= (5) where φ n i the odel tranition probability fro the n th ub-odel to the th one, and μ n ( k ) i the odel probability of the n th ub-odel at tie k-. 2) Filtering algorith: Each ub-odel provide a odel tate etiate update by the tie-varying error between predicted point and eaureent one a follow: xˆ ( ) ˆ k k = Fx( k k ), (6) uˆ ( ) ˆ k k = Hx( k k ), (7) eˆ ( ) ( ) ˆ k k = zx k u( k k ), (8) aˆ ( ) ˆ k k = e( k k )/ t ax w( k), (9) vˆ ( ) ˆ ( ) ˆ k k = v k k + t a( k k ), (20) xˆ ( k) = xˆ ( k k ) + M ( k k ) (2) Λ( k) α μ ( k) =. Λn( k) αn n= (23) 5) Cobination of etiate: The cobined tate etiate and it error covariance are obtained fro the probabilitic u of the tate etiate and their error covariance of ub-filter a follow: xˆ( k k) = μ ( k) xˆ ( k k), (24) = Pk ( k) = μ ( ) ( ) ˆ ( ) ˆ k P k k + x k k xk ( k) = T ( xˆ ( k k) xˆ( k k) ) ]. [ ( ) (25) The propoed algorith i illutrated in Fig. 7. Reark : The propoed SIMM algorith hould be ditinguihed fro conventional algorith in that it ha the following advantage over the. Firt, unlike the IMM algorith, the propoed algorith doe not require ubodel to be predefined in ter of target aneuver propertie, and can guarantee better tracking perforance of the aneuvering target ince the added proceing error can well approxiate proce noie variance. Second, unlike the AIMM algorith, the propoed algorith could be applied to linear and nonlinear aneuver input data adaptively and utain the capability of KF. Third, although the propertie of the aneuver are unknown, the propoed algorith can be utilized if the aneuver i within the axiu acceleration liit. where uˆ ( k ) and e ( k ) are the predicted point and the poi-tion error between eaured point and predicted point at tie k, repectively. aˆ ( k ) and vˆ ( k ) are the etiated acceleration and the etiated velocity to be ued in calcul-ating etiate of xˆ ( k ) at tie k, repectively. Related atrix M ( k ) at tie k i pecified a follow: vˆ ( k k ) M ( k k ) = t. aˆ ( k k ) Alo, we ue KF electively. 3) Coputation of odel likelihood: Model likelihood Λ ( k ) i coputed by the following Gauian function: Λ k = exp( v k S k v k ) (22) T ( ) ( ) ( ) ( ). 2 π S ( ) 2 k 4) Update odel probability: Model probability μ ( k ) i updated according to the odel likelihood and odel tranition probability governed by the finite-tate Markov chain: Fig. 7. Propoed SIMM algorith 4. Siulation Reult To how the effectivene of the propoed intelligent tracking ethod, we introduce a tracking cenario for an incoing cruie iile. The iulated exaple reult of the

7 Hyun Seung Son, Jin Bae Park and Young Hoon Joo 26 propoed ethod are copared with thoe of the AIMM algorith. The target i aued a an incoing cruie iile on the 3-dienional plane. The initial poition of the target i at (00k, 40k) away on the ditant horizon fro the oberver, and it ove with a contant velocity of k/ec along a 58 degree line to x-axi. For each axi, the tandard deviation of the zero ean white Gauian eaureent noie i 0.00k and that of a proce noie i 0.0. The apling tie t i ec and the nuber of iteration i 200. Maxiu noie level for the propoed algorith i 0., 0.0, and 0.00, repectively. The target ha the lateral acceleration a hown in Fig. 8 and the correponding target otion i deterined fro () and (2) and illutrated in Fig. 9. Acceleration [/ 2 ] x-axi y-axi z-axi Tie [Sec] Fig. 8. Acceleration input The propoed algorith and AIMM have 3 ub-filter for the equal condition, repectively. The odel tranition probability atrix, φ n i aued to be 0.97, if n = ; φn = 0.97, otherwie. We further aue that the initial otion of the target i iilar to that fro the firt ub-odel, o the initial odel probability for each ub-odel i choen a V ( k) = e [( v ( ) ˆ ( ) ( ) ˆ ( ) ( ) ˆ x k vx k ) + ( vy k vy k ) + ( vz k vz( k) ) ] = [( vx( k) vx ( k) ) + ( vy( k) vy( k) ) + ( vz( k) vz ( k) ) ] = (27) where Pxyz,,( k ) and ˆ P ( ) xyz,, k are the true point and the etia-ted point, repectively. Z xyz,,( k ) i the eaured point of the target and i the total nuber of iteration, repectively. The vxyz,, ( k ) and vˆ xyz,,( k ) are the true velocitie and the eti-ated velocitie for each axi, repectively. vxyz,,( k ) i the velocity correponding to the eaured point of the target for each axi, repectively. For the quantitative coparion between the perforance of two algorith, we utilize the average of Pe ( k ) and Ve ( k ) expreed in (26) and (27) over the total nuber of iteration S a follow: Pe ( k), (28) S Pv ( k) k. = S (29) k = ζ p = = ζ v In thi ection, we how the iulation reult for the SIMM algorith of which perforance are copared with thoe of the AIMM algorith. The iulation of the propoed ethod are conducted by dividing into two cae, poition and velocity. The iulation reult over 00 run copared with thoe of the AIMM ethod are hown by root ean quare error (RMSE) in Fig. 0-2, repectively. Finally, the average reult for all axe i hown in Fig. 3. The nuerical reult in two cae are hown in Table. We can ee that the propoed SIMM algorith produce aller poition error and velocity error than thoe of the AIMM algorith at each apling tie. Table how that it i reported that the tracking error in poition and velocity with our ethod are reduced by 4.6%, 28.5% copared with AIMM, in an average ene, repectively. 0.6, if = ; μ (0) = 0.6, otherwie. Thi iulation i carried out by each axi independently, and the noralized poition error Pe ( k ) and velocity one Ve ( k ) are defined a follow: [( p ( ) ˆ ( )) ( ( ) ˆ ( )) ( ( ) ˆ x k px k + py k py k + pz k pz( k) ) ] = P( k) =, e [( px( k) zx( k) ) + ( py( k) zy( k) ) + ( pz( k) zz( k) ) ] = (26) (a) Poition RMSE (b) Velocity RMSE Fig. 0. Coparion of the poition and the velocity RMSE for propoed ethod veru AIMM at x- axi

8 262 SIMM Method Baed on Acceleration Extraction for onlinear Maneuvering Target Tracking acceleration level in accordance with target aneuver, which are prerequiite of the AIMM algorith, it ha trong potential in practical application. 5. Concluion (a) Poition RMSE (b) Velocity RMSE Fig.. Coparion of the poition and the velocity RMSE for propoed ethod veru AIMM at y-axi (a) Poition RMSE (b) Velocity RMSE Fig. 2. Coparion of the poition and the velocity RMSE for propoed ethod veru AIMM at z-axi In thi paper, the SIMM algorith for tracking the aneuvering target ha been propoed. In the propoed algorith, we have calculated the poitional difference between eaureent point and the predicted point. Then, coparing thi value with the axiu noie level, we have extracted acceleration to etiate the otion of the target. To etiate ore effectively, we have contructed an optional algorith uing the propoed ethod and the KF electively. The ethod extracting acceleration directly in the overall proce noie ha guaranteed better tracking perforance of a aneuvering target. Alo, thi ethod ha been applied effectively to linear and nonlinear aneuver while aintaining the capability of the KF. In the iulation reult, one could ee that the propoed intelligent tracking ethod how the better perforance copared with the AIMM algorith. Acknowledgeent Thi work wa upported by the Huan Reource Developent of the Korea Intitute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea governent Minitry of Knowledge Econoy. (o ) (a) Poition RMSE (b) Velocity RMSE Fig. 3. Coparion of the poition and the velocity RMSE for propoed ethod veru AIMM at all plane Table. Coparion of the poition RMSE and the velocity one for each axi Configuration AIMM ζ p ζ v Propoed ζ p ζ v x-axi y-axi z-axi average Thi i becaue, although aneuvering propertie are unknown, acceleration extracted by the propoed algorith can be well approxiated the tie varying proce noie variance and it variation at every apling intant. On the other hand, we can ee that the poor tracking perforance of the AIMM algorith arie fro the uncertain etiation of coplex target acceleration. Since the propoed algorith doe not require the deignation of Reference [] Y. Bar-halo and X. R. Li, Etiation and tracking principle, technique, and oftware, Artech Houe, 993. [2] M. S. Grewal and A. P. Andrew, Kalan filtering theory and practice, Prentice Hall, 993. [3] Y. Bar-halo and T. E. Fortan, Tracking and data aociation, Acadeic Pre, 988. [4] S. Blackan and R. Popoli, Deign and analyi of odern tracking yte, Artech Houe, 999. [5] Craig M. Payne, Principle of aval Weapon Syte, aval Intitute Pre, [6] B. J. Lee, J. B. Park, and Y. H. Joo, Fuzzy-logicbaed IMM algorith for tracking a aneuvering target, IEE Proceeding Radar, Sonar and avigation, vol. 52, no., pp. 6-22, [7] S. Y. oh, J. B. Park, and Y. H. Joo, Intelligent tracking algorith for aneuvering target uing Kalan filter with fuzzy gain, IET Proceeding- Radar, Sonar and avigation, vol., no. 3, pp , 2007.

9 Hyun Seung Son, Jin Bae Park and Young Hoon Joo 263 [8] R. W. Oborne, III, Y. Bar-halo, and T. Kirubarajan, Radar eaureent noie variance etiation with everal target of opportunity, IEEE Tranaction on Aeropace and Electronic Syte, vol. 44, pp , [9] Hyun-Sik Ki, Joon-Goo Park, and Dongik Lee, Adaptive fuzzy IMM algorith for uncertain target tracking, International Journal of Control, Autoation, and Syte, vol. 7, no. 6, pp , [0] Singer, R. A. Etiating optial tracking filter perforance for anned aneuvering target, IEEE Tranaction Aeropace and Electronic Syte, AES-6, vol. 4, pp , 970. [] P. Gutan and V. Mordekhai Tracking target uing adaptive Kalan filtering, IEEE Tranaction on Aeropace and Electronic Syte, vol. 26, pp , 990. [2] Y. T. Chan, A. G. C. Hu, and J. B. Plant, A Kalan filter baed tracking chee with input etiation, IEEE Tranaction on Aeropace and Electronic Syte, vol. 5, pp , 979. [3] P. L. Bogler, Tracking a aneuvering target uing input etiation, IEEE Tranaction on Aeropace and Electronic Syte, vol. 23, pp , 987. [4] Y. Bar-Shalo and K. Biriwal, Variable dienion filter for aneuvering target tracking, IEEE Tranaction on Aeropace and Electronic Syte, vol. 8, pp , 982. [5] A. T. Alouani, P. Xia, T. R. Rice, and W. D. Blair, A two-tage Kalan etiator for tate etiation in the preence of rando bia and for tracking a aneuvering target, Proceeding of 30 th IEEE Conference on Deciion and Control, pp , 99. [6] G. A. Ackeron and K. S. Fu, On tate etiation in witching environent, IEEE Tranaction on Autoatic Control, vol. 5, pp. 0-7, 970. [7] C. B. Chang and M. Athan, State etiation for dicrete yte with witching paraeter, IEEE Tranaction on Aeropace and Electronic Syte, vol. 4, pp , 978. [8] H. A. P. Blo and Y. Bar-Shalo, The interacting ultiple odel algorith for yte with Markovian witching coefficient, IEEE Tranaction on Autoatic Control, vol. 33, pp , 988. [9] Y. Bar-Shalo, K. C. Chang, and H. A. P. Blo, Tracking a aneuvering target uing input etiation veru the interacting ultiple odel algorith, IEEE Tranaction on Aeropace and Electronic Syte, vol. 25, pp , 989. [20] E. Mazor, A. Averbuch, Y. Bar-Shalo, and J. Dayan, Interacting ultiple odel ethod in target tracking: a urvey, IEEE Tranaction on Aeropace and Electronic Syte, vol. 34, pp , 998. [2] D. P. Atherton and H. J. Lin, Parallel ipleenttation of IMM tracking algorith uing tranputer, IEE Proceeding-Radar, Sonar and avigation, vol. 4, pp , 994. [22] A. Munir and D. P. Atherton, Adaptive interacting ultiple odel algorith for tracking a aneuvering target, IEE Proceeding-Radar, Sonar and avigation, vol. 42, pp. -7, 995. Hyun Seung Son He received hi B.S. degree fro R.O.K aval Acadey in 2000 and hi M.S. degree in Electrical Engineering fro Yonei Univerity in 2007, repectively. He i currently a naval officer with R.O.K avy and a Ph.D. candidate tudent in Yonei Univerity. Hi reearch interet are target tracking, fuzzy logic control, and nonlinear control. Jin Bae Park He received hi B.S. degree in Electrical Engineering fro Yonei Univerity, Seoul, Korea, and hi M.S. and Ph.D. degree in Electrical Engineering fro Kana State Univerity, Manhattan, in 977, 985, and 990, repectively. Since 992, he ha been with the Departent of Electrical and Electronic Engineering, Yonei Univerity, Seoul, Korea, where he i currently a profeor. Hi ajor interet i ainly in the field of robut control and filtering, nonlinear control, intelligent obile robot, fuzzy logic control, neural network, Hadaard tranfor, chao theory, and genetic algorith. He erved a Editor-in- Chief for the International Journal of Control, Autoation, and Syte (IJCAS) ( ) and i erving a the Vice-Preident for the Intitute of Control, Robot, and Syte Engineer (ICROS) (2009-preent). Young Hoon Joo He received hi B.S., M.S., and Ph.D. degree in Electrical Engineering fro Yonei Univerity, Seoul, Korea, in 982, 984, and 995, repectively. He worked with Saung Electronic Copany, Korea, fro 986 to 995, a a project anager. He wa with the Univerity of Houton, Houton, TX, fro 998 to 999, a a viiting profeor in the Departent of Electrical and Coputer Engineering. He i currently a profeor in the Departent of Control and Robot Engineering, Kunan ational Univerity, Korea. Hi reearch interet include intelligent robot, intelligent control, and huan-robot interaction. He i erving a Editor for the International Journal of Control, Autoation, and Syte (IJCAS) (2008-preent).