Prediction-based Interacting Multiple Model Estimation Algorithm for Target Tracking with Large Sampling Periods

Transcription

1 44 Internatonal Jon Ha Journal Ryu, Du of Hee Control, Han, Automaton, Kyun Kyung and Lee, Systems, and Tae vol. Lyul 6, Song no., pp , February 8 Predcton-based Interactng Multple Model Estmaton Algorthm for Target Tracng wth Large Samplng Perods Jon Ha Ryu, Du Hee Han, Kyun Kyung Lee, and Tae Lyul Song* Abstract: An nteractng multple model (IMM) estmaton algorthm based on the mxng of the predcted state estmates s proposed n ths paper for a rght contnuous ump-lnear system model dfferent from the left-contnuous system model used to develop the exstng IMM algorthm. The dfference les n the modelng of the mode swtchng tme. Performance of the proposed algorthm s compared numercally wth that of the exstng IMM algorthm for nosy system dentfcaton. Based on the numercal analyss, the proposed algorthm s appled to target tracng wth a large samplng perod for performance comparson wth the exstng IMM. Keywords: osy system dentfcaton, predcton-based IMM, target tracng.. ITRODUCTIO Identfcaton of systems wth abrupt changes or unnown nose statstcs plays a crucal role n controller desgn, falure detecton, and maneuverng target tracng. When a sngle flter s used for system dentfcaton, accurate modelng s an mportant ssue for relable estmaton performance. However, obtanng accurate modelng may be dffcult n practce due to the lac of nowledge about the system and the practcal lmtatons mposed by computatonal complextes. Multple model estmaton assumng that the system under consderaton obeys one of a fnte number of models s ntroduced n []. Dependence of dentfcaton performance on modelng can be weaened n ths multple model approach due to the probablstc combnaton of the estmates generated from multple flters. A ban of flters utlzng dfferent models can also be appled to systems wth swtchng models [3,4]. The multple model estmaton technque has evolved nto the IMM algorthm []. The essental dfference between the IMM algorthm and the Manuscrpt receved August, 7; revsed December 7, 7; accepted December 4, 7. Recommended by Edtor Jae Weon Cho. Ths wor was supported by Defense Acquston Program Admnstraton and Agency for Defense Development under the contract UD754AD. Jon Ha Ryu and Kyun Kyung Lee are wth the School of Electrcal Engneerng and Computer Scence, Kyungpoo atonal Unversty, Daegu 7-7, Korea (e-mals: onha@dreamwz.com, lee@ee.nu.ac.r). Du Hee Han and Tae Lyul Song are wth the Department of Electroncs, Electrcal, Control and Instrumentaton Engneerng, Hanyang Unversty, 7 Sa- dong, Sangnogu, Ansan, Kyeongg-do 46-79, Korea (e-mals: {hduhee, tsong}@hanyang.ac.r). * Correspondng author. prevous multple model estmaton les n the tmng of hypotheses mxng, and t s nown for ts costeffectveness regardng computatonal complexty and performance. The IMM algorthm has been appled to a number of problems ncludng ar traffc control [5,8], target glnt flterng [6], maneuverng target tracng [7], radar management [8], system nose dentfcaton [9], tactcal ballstc mssle tracng [], and out-of-sequence measurements [9]. Recently, some modfed versons of the IMM to mprove estmaton performance have been developed, such as the adaptve IMM algorthm [4], the reweghted IMM algorthm [5], and IMM estmaton by smoothng [6,7]. The IMM algorthm was developed for a umplnear system called the left-contnuous system [], n whch the mpact of the new mode starts rght after the measurement samplng tme. In ths paper, a modfed verson of the IMM algorthm called the Predcton-based IMM (PBIMM) s developed for a ump-lnear system n whch the mpact of the new mode starts ust before the measurement samplng tme such that the system becomes rght-contnuous. It s thought that the mode n nature s a contnuous parameter that could be dscretzed and modeled n dfferent ways. Moreover, t s found n ths paper that the mode change tme dfference leads the PBIMM to have a dfferent algorthm from the IMM and to reveal a dfferent performance n nosy system dentfcaton and target tracng n an actve sonar applcaton. The PBIMM conssts of 4 steps: predcton, nteracton after mode change, measurement update, and combnaton. The order of the nteracton and predcton steps s changed from that of the IMM algorthm. It s found that the PBIMM and the IMM algorthms are dentcal f the Marovan parameters defnng the mode state are only related to the meas-

2 Predcton-based Interactng Multple Model Estmaton Algorthm for Target Tracng wth Large Samplng Perods 45 urement equaton. However, the algorthms are dfferent f the Marovan parameters are nvolved n the system dynamc equaton. The PBIMM s appled to nosy system dentfcaton problems, and the performance s compared numercally wth that of the IMM. Motvated by the numercal analyss, the PBIMM s further appled to target tracng by an actve sonar wth a large samplng perod. The results ndcate that the PBIMM outperforms the IMM and so could be used n practce for actve sonar systems that requre large samplng perods and yet need to produce accurate enough target state estmates.. DEVELOPMET OF THE PBIMM The ump-lnear system model for development of the IMM algorthm [,] s descrbed n () where the mode at tme, M, s assumed to be a Marovan parameter among the possble modes wth nown mode transton probabltes. x =Φ ( M) x + B( M) w ( M) w ( M)~ ( b( M), Q( M)), z = H( M) x + v( M) v ( M )~ ( c( M ), R( M )). It s also assumed that the mode + + () M s n effect for t t < t such that the mode ump process s assumed left-contnuous (.e., the mpact of the new mode starts at t + ) []. The ey feature of the IMM algorthm s mxng multple models usng mode probablty n order to allevate dependence of accuracy of target dynamc models and flter performance. As the samplng perod becomes large, flter performance s serously nfluenced by model accuracy. The allevaton of model dependence of the IMM algorthm may have a negatve effect on flter performance when one of the models of the IMM algorthm matches wth real target moton for tracng systems wth large samplng perods. It s expected to have better flter performance by reducng uncertanty of predcton through performng the nteractng step after the predcton step rather than vce versa. In order to mplement the above asserton, the mode ump process could be modeled n a dfferent way. The system model used n ths paper s ump-lnear, and the mode M s n effect for t t < t +. The proposed system dynamc model s expressed as x =Φ ( M ) x + B( M ) w ( M ) w ( M ) ~ ( b( M ), Q( M )), () z = H( M) x + v( M) v ( M ) ~ ( c( M ), R( M )), where Φ, BbQHc,,,, and R are consdered to vary wthn a fnte set. It s assumed that v and w are mutually ndependent Gaussan nose sequences and uncorrelated wth x. In (), the state x s consdered as a propagated varable nfluenced by the mode M and the mode s allowed to change to M ust before the measurement samplng tme t = t ; however, M does not nfluence x. The dfference between models () and () les n model swtch tme. In the IMM algorthm whch utlzes (), the mode s modeled to swtch ts value rght after the measurement samplng tme whle n ths paper, the mode s modeled to swtch ust before the measurement samplng tme. The mode or hypothess correspondng to the th Marovan parameter s denoted as the mode state M. A cycle of recursons for the evoluton of the condtonal probablty densty functons n the development of the IMM algorthm [] s summarzed as mode change, nteractng predcton update px ( M, Z ) px ( M, Z ) p( x M, Z ) px ( M, Z ) (3) where Z = { z, z,, z}. In the above, the nteractng step that s unque n the IMM algorthm enables the mxng of the estmates n a cost-effectve way whle enhancng the performance compared to the other algorthms wth smlar computatonal complextes []. Detaled dervaton of the IMM algorthm s referred to []. ow, the evoluton of the condtonal densty functons for the system model of () should be modfed to utlze the predcted estmates rather than the measurement-updated estmates n the nteractng step such as predcton mode change, nteractng px ( M, Z ) update px ( M, Z). px ( M, Z ) px ( M, Z ) (4) x and P represent the condtonal mean and covarance under the mode M gven Z such as Let ˆ px ( M, Z )~ x (, Pˆ ), ˆ ˆ (5) then the predcton step of (4) results n the predcted state estmaton algzorthm of a Kalman flter as one can see from the dynamc equaton of () and px ( M, Z ) satsfes

3 46 Jon Ha Ryu, Du Hee Han, Kyun Kyung Lee, and Tae Lyul Song px ( M, Z )~ x (, P). (6) To derve a representaton of the nteractng step of (4), the followng equaton s ntroduced from the Bayes formula px M Z P{ M Z } (, ) px ( M, Z ) =, (7) where the probablty of M for gven, Z P{ M Z } s calculated by the Chapman- Kolmogorov equaton as π = P{ M Z } = P{ M Z }, (8) where s the total number of the modes under consderaton and where π = P{ M M } s the mode transton probablty from M to M. The numerator of (7) can be expressed from the total probablty theorem as (, ) px M M Z M Z = px M Z π M Z = px M Z = = (,, )P{ } (, ) P{ }, (9) where the fact that for the system dynamc model of (), x s ndependent of s used. M M for the gven If we assume that px ( M, Z ) of (7) satsfes px ( M, Z )~ x (, P ), () then as x and = = P are obtaned from (6), (8) and (9) x π P{ M Z } x =, () π P{ M Z } P = = T + π ( P ( x x )( x x ) ) P{ M Z }. π P{ M Z } = Each of pars x and P s used as nput to a Kalman flter based on the mode M to yeld x ˆ, ˆ P n the update process of (4) such that px ( M, Z )~ x ( ˆ, P ˆ ). () Smlar to the IMM algorthm of [], the states and covarances are combned for output purpose only from = = T = + = xˆ xˆ P{ M Z }, Pˆ ( Pˆ ( xˆ xˆ )( xˆ xˆ ) )P{ M Z }, (3) where the mode probablty P{ M Z } s updated by M Z pz ( M, Z ) π P{ M Z } = h pz M Z π h M Z h= = P{ } =. (, ) P{ } ote that pz ( M, Z ) n (4) satsfes (4) pz ( M, Z ) exp ( ) T ( ) = z Hx S ( ), z Hx π S (5) where S T s defned as HP H + R. If we denote b as a parameter n the mode state M to be dentfed, then the estmate of b at t = t can also be obtaned from bˆ = b P{ M Z }, (6) where = M s the th mode assumng the value of b as b. The resultng algorthm called the PBIMM can be llustrated as Fg.. The PBIMM s the same as the IMM f the Marovan parameters are only nvolved n the measurement equaton so that Hc,, and R are desgnated to the mode state M, =,,,. However, t was found that the PBIMM and the IMM are dfferent f the mode set s defned n the system dynamcs so that Φ, Bb, and Q are desgnated to the mode states. The latter case has many mportant applcatons such as fault detecton, maneuverng target tracng, and process nose dentfcaton. As

4 Predcton-based Interactng Multple Model Estmaton Algorthm for Target Tracng wth Large Samplng Perods 47 Fg.. Schematc dagram of the PBIMM. shown n the above dervaton, f the dmenson of the state vector and the number of modes are the same n both algorthms, the PBIMM has dentcal computatonal complexty to the exstng IMM. Ths s due to the fact that both algorthms consst of dentcal nteractng, predcton and update steps; however, the order of steps and the nputs to each step are merely changed. For example, the updated state estmate xˆ of the IMM s replaced by the predcted state estmate x of the PBIMM as the nput to the nteractng step. 3. SIMULATIO RESULTS In the frst part of ths secton, performance of the PBIMM s tested and compared wth that of the IMM when the process nose of a second-order lnear system s to be dentfed. The system s descrbed by [9] T x T x = w, x + x + T x z = + v. x (7) The statonary process nose w s a Gaussan nose sequence wth unnown mean and varance whereas the measurement nose v s a zero-mean Gaussan nose sequence wth R =. Frstly, the unnown mean s dentfed by the PBIMM wth the two possble modes M : w ~ (,), and M : w ~ (,). The samplng perod T = s used as [9]. The transton probablty matrx of the two-mode system used s { π }.98. =,..98 (8) Table. Identfcaton of process nose mean wth b = and b =. true mean.3.5 IMM PBIMM true mean IMM PBIMM true mean IMM PBIMM true mean 9.7 IMM PBIMM whle the two ntal mode probabltes were both set to.5 snce no pror nformaton was avalable concernng the modes. The process nose mean was estmated accordng to the parameter dentfcaton algorthm expressed n (6). Table s a summary of the results of a seres of Monte Carlo smulaton runs as the true mean value s between and. Each result s the average quantty obtaned from smulaton runs wth 4 samplng perods per each run. The results ndcate that the PBIMM performs better than the IMM except n the cases where the true mean becomes very close to the lower and upper bounds b and b and where the true mean becomes close to the average value of b and b. When the true mean s close to the average of b and b, the PBIMM and the IMM show almost dentcal results. Hence, t s noteworthy that the PBIMM generates more accurate estmates than those of the IMM for the wde range of b as llustrated n Table, and that the PBIMM could be more usefully appled n practce snce the exact values of the upper and lower bounds are not exactly nown n general. ext, the process nose varance Q s to be dentfed wth the two possble modes M : w ~ (,), and M : w ~ (,). The other smulaton condtons are equvalent to the prevous case. The results are summarzed n Table. The results ndcate that the PBIMM performs better than the IMM except n the cases where the true process nose varance approaches the lower and upper bounds expressed as Q and Q, respectvely. The results also ndcate that the PBIMM may produce more accurate estmates of Q n practcal

5 48 Jon Ha Ryu, Du Hee Han, Kyun Kyung Lee, and Tae Lyul Song Table. Identfcaton of process nose varance wth Q = and Q =. true varance Q IMM PBIMM applcatons as the exact values of the upper and lower bounds are not nown, and the bounds are flter desgn parameters. The nfluence of the samplng perod T on estmatng the process nose mean b s analyzed next. The unnown mean s dentfed wth the two possble modes M : w ~ (,), and M : w ~ (,) for varous values for T {.,.5,,.5, }. Fg.. s a summary of tme averages of the estmates of b by the PBIMM and the IMM obtaned from runs of Monte Carlo smulaton. The results for T = are referred to n Table. Table and Fg. ndcate that the performance of the IMM s smlar to the performance of the PBIMM for dentfyng most of the true mean values when T s small. However, the PBIMM performs better than the IMM when T becomes large except n the cases where the true mean becomes model values for the flters. As the process nose mean b can be consdered as the target acceleraton, the above results motvate applcatons of the PBIMM to target tracng wth a large samplng perod as s seen n actve sonar practces. The frst example n ths secton s extended to - dmensonal underwater target tracng by an actve sonar system whch has a relatvely large samplng perod. The dscretzed system equatons for maneuverng target tracng are descrbed by x+ =Φ x +Γ ( a + w), z = H x + Gv, (9) where the state x conssts of target poston and.5 T=. sec IMM PBIMM.5 T=.5 sec IMM PBIMM.5.5 Estmaton Error Estmaton Error True mean True mean.5 T=.5 sec IMM PBIMM.5 T=. sec IMM PBIMM.5.5 Estmaton Error Estmaton Error True mean True mean Fg.. Estmaton error of process nose mean for varous samplng perods.

6 Predcton-based Interactng Multple Model Estmaton Algorthm for Target Tracng wth Large Samplng Perods 49 velocty components n X and Y axes such that T x = ( X, Y, X, Y ), w s a zero-mean whte Gaussan process nose vector wth covarance Q, and v s a zero-mean measurement nose vector wth covarance R. System matrces for (9) are defned as I TI Φ=, I T I Γ=, TI H =, G = I, () and a = ( X, Y ) T s the target acceleraton vector. The PBIMM algorthm approxmates the evoluton of the target true acceleraton wthn a fnte set of acceleraton values. The 4 modes descrbng - dmensonal target acceleraton vectors are selected as T M = (.5,.5) (m /sec ), M = (.5,.5) T (m/ sec ), M 3 = (.5,.5) T (m/sec ) and M 4 = (.5, T.5) (m / sec ). For the target tracng problem, Q=.5 I (m / sec ), R = I (m) are used, the samplng perod s chosen to be 3sec, and the mode transton probablty matrx s selected to be { π } = () ote that the measurement nose covarance results n a standard devaton of 4.4m n the range drecton error. The ntal poston of the target s (6m, 6m) T and the ntal velocty of the target s T (, 3m/ sec). For the tme nterval sec t < 7 sec, the target moves n a crcular path of radus 344m wth a constant velocty and acceleraton of.6 m/sec. The target traectory s shown n Fg. 3. Fgs. 4-6 show the RMSE values of, runs of Monte Carlo smulaton resultng from employng the IMM and the proposed PBIMM. The results ndcate that the PBIMM outperforms the IMM for target poston, velocty, and acceleraton estmaton. The results ndcate that the PBIMM can be used for practcal target tracng wth large samplng perods as requred n actve sonar systems and sonar resource management practces []. Fnally, the PBIMM and the IMM algorthms wth orth[m] East[m] Fg. 3. Target traectory. Fg. 4. RMSE of target poston estmates. Fg. 5. RMSE of target velocty estmates.

7 5 Jon Ha Ryu, Du Hee Han, Kyun Kyung Lee, and Tae Lyul Song Fg. 6. RMSE of target acceleraton estmates. two dfferent dynamc models are appled to underwater actve sonar target tracng. The dynamc models used n the smulaton study are the constant velocty (CV) model and the constant turn rate (CTR) model. The CV model employs the dscretzed system equaton of (9) wth a =, and the system matrces are the same as descrbed n (). The state of the CTR model conssts of target poston, velocty, and acceleraton components, and the system equatons are expressed n the same form as the CV model, but wth dfferent dmensons. The system matrces are expressed as follows [,]. snωt cosωt I I I ω ω snωt O cos ωti I, ω O ωsnωti cosωti H =, G I, = ωt snωt 3 I ω cosωt I, ω snωt I ω Φ= Γ= () where ω s the turn rate. For ths target tracng problem, R = I (m), Q CV =. I (m/sec ), Q CTR =.5 I (m/sec 3 ) are used and the mode transton probablty matrx s selected to be { π }.8. =...8 (3) The target s assumed as a submarne, whch executes an evasve maneuver to avod a stuaton of beng traced by a target moton analyss scheme. The T ntal poston of the target s (6m, 6m), and the target s ntally movng n a straght lne wth a constant speed of 3(m / sec) wth 67.5 of headng angle from the Y-axs. The target moves wth an ntal course of 67.5 for sec t < 5sec, and then the target executes a perodc moton wth ω =± (deg/ sec) wth a swtchng perod of 35 seconds. ote that f an actve sonar system s used to detect a target located near m from the system, a samplng perod of 3sec s requred. The target traectory s depcted n Fg. 7. Fgs. 8- show the results extracted from, Monte Carlo smulaton runs to demonstrate the superor performance of the proposed PBIMM by comparson wth the IMM. Lsted n these fgures are Fg. 7. Target traectory. Fg. 8. RMSE of target poston estmates.

8 Predcton-based Interactng Multple Model Estmaton Algorthm for Target Tracng wth Large Samplng Perods 5 Fg. 9. RMSE of target velocty estmates. Fg.. RMSE of target poston estmates of the IMM algorthm. Fg.. RMSE of target acceleraton estmates. the RMSE values of the estmates of the target poston, velocty, and acceleraton. The results ndcate that the proposed PBIMM has a superor performance to the IMM, and that t has advantages n calculatng future target postons such as are requred n combat management systems. In addton to these results, Fgs. and show the senstvtes of the IMM and the PBIMM to the same varatons of R. The scalar s a flter parameter used n flter algorthms such that the flters assume that the measurement nose covarance s R nstead of the true value of R. The smulaton results show that the PBIMM s less senstve to the flter parameter snce the RMSE values of the IMM are much more wdely dspersed than those of the PBIMM as vares, whch ndcates that the PBIMM has some practcal advantages snce the true measurement nose Fg.. RMSE of target poston estmates of the PBIMM algorthm. covarance may not be avalable n dverse underwater tracng envronments. 4. COCLUSIO The PBIMM algorthm based on the mxng of the predcted state estmates s developed and appled to process nose dentfcaton of a lnear system and a - dmensonal target tracng wth a large samplng perod. Smlar to the exstng IMM algorthm, the PBIMM algorthm s cost effectve regardng computatonal complexty and performance compared to the other multple model approaches. The PBIMM produces the same results as the IMM f the Marovan parameters are only nvolved n the system measurement whle producng dfferent results f the Marovan parameters are nvolved n the

9 5 Jon Ha Ryu, Du Hee Han, Kyun Kyung Lee, and Tae Lyul Song system dynamcs. A study of Monte Carlo smulaton runs ndcates that the PBIMM produces more accurate estmates of mean and covarance of process nose than the IMM f the samplng perod becomes larger whle producng a smlar performance for small samplng perods. Based on the numercal analyss, the PBIMM s appled to underwater target tracng wth an actve sonar system of whch the samplng perod s 3sec. The results of the Monte Carlo smulaton runs ndcate that the PBIMM outperforms the IMM n ths applcaton. It s also shown that the PBIMM has more freedom than the IMM to select flter parameter values for maneuverng target tracng such that ths burden can be allevated for flter parameter tunng. A seres of smulaton studes shows that the PBIMM s a vable soluton to target tracng systems operated wth large samplng perods. REFERECES [] H. A. P. Blom and Y. Bar-Shalom, The nteractng multple model algorthm for systems wth Marovan swtchng coeffcents, IEEE Trans. on Automatc Control, vol. 33, no. 8, pp , August 988. [] D. T. Magll, Optmal adaptve estmaton of sampled stochastc processes, IEEE Trans. on Automatc Control, vol., pp , Aprl 965. [3] R. L. Moose, M. K. Sstanzadeh, and G, Sagford, Adaptve estmaton for a system wth unnown measurement bas, IEEE Trans. on Aerospace and Electronc Systems, vol., no. 6, pp , ovember 986. [4] P. S. Maybec and P. D, Halon, Performance enhancement of multple model adaptve estmator, IEEE Trans. on Aerospace and Electronc Systems, vol. 3, no. 4, pp. 4-54, October 995. [5] X. R. L and Y. Bar-Shalom, Desgn of an nteractng multple model algorthm for ar traffc control tracng, IEEE Trans. on Control Technology, vol., no. 3, pp , September 993. [6] E. Daepour and Y. Bar-Shalom, An nteractng multple model approach for target tracng wth glnt nose, IEEE Trans. on Aerospace and Electronc Systems, vol. 3, no., pp , Aprl 995. [7] Y. Bar-Shalom, K. C. Chang, and H. A. P. Blom, Tracng a maneuverng target usng nput estmaton versus the nteractng multple model algorthm, IEEE Trans. on Aerospace and Electronc Systems, vol., no. 6, pp , ovember 986. [8] T. Krubaraan, Y. Bar-Shalom, W. D. Blar, and G. A, Watson, IMMPDAF for radar management and tracng benchmar wth ECM, IEEE Trans. on Aerospace and Electronc Systems, vol. 34, no. 4, pp. 5-34, October 998. [9] X. R. L and Y. Bar-shalom, A recursve multple model approach to nose dentfcaton, IEEE Trans. on Aerospace and Electronc Systems, vol. 3, no. 3, pp , July 994. [] Y. Bar-Shalom and X. R. L, Estmaton and Ttracng, Prncples, Technques, and Software, Artech House, 993. [] S. S. Ahmeda, I. Harrson, and M. S, Woolfson, Adaptve probablstc data-assocaton algorthm for tracng n cluttered envronment, IEE Proc.-Radar, Sonar, avgaton, vol. 43, no., pp. 7-, February 996. [] R. L. Cooperman, Tactcal ballstc mssle tracng usng the nteractng multple model algorthm, Proc. of the Ffth Internatonal Conference on Informaton Fuson, vol., pp , July. [3] T. L. Song and D. G. Lee, Effectve flterng of target glnt, IEEE Trans. on Aerospace and Electronc Systems, vol. 36, no., pp. 34-4, January. [4] Y. He, Z.-J. Guo, and J.-P. Jang, Desgn of the adaptve nteractng multple model algorthm, Proc. of the Amercan Control Conference, Anchorage, AK May 8-, pp ,. [5] L. A. Johnston and V. Krshnamurthy, An mprovement to the nteractng multple model (IMM) algorthm, IEEE Trans. on Sgnal Processng, vol. 49, no., pp , December. [6] V. P. Jlov, X. R. L, and L. Lu, Performance enhancement of the IMM estmaton by smoothng, Proc. of the Ffth Internatonal Conference on Informaton Fuson, vol., pp. 73-7, July. [7] B. Chen and J. K. Tugnat, Interactng multple model fxed-lag smoothng algorthm for Marovan swtchng systems, IEEE Trans. on Aerospace and Electronc Systems, vol. 36, no., pp. 43-5, January. [8] T. Krubaraan and Y. Bar-Shalom, Kalman flter versus IMM Estmator : When do we need the latter?, IEEE Trans. on Aerospace and Electronc Systems, vol. 39, no. 4, pp , October 3. [9] Y. Bar-Shalom and H. Chen, IMM estmator wth out-of-sequence measurements, IEEE Trans. on Aerospace and Electronc Systems, vol. 4, no., pp. 9-98, January 5. [] X. Rong L and V. P. Jlov, Survey of maneuverng target tracng. part I: Dynamc models, IEEE Trans. on Aerospace and Electronc Systems, vol. 39, no. 4, pp , October 3.

10 Predcton-based Interactng Multple Model Estmaton Algorthm for Target Tracng wth Large Samplng Perods 53 [] X. Rong L and V. P. Jlov, Survey of maneuverng target tracng. Part V: Multplemodel methods, IEEE Trans. on Aerospace and Electronc Systems, vol. 4, no. 4, pp. 55-3, October 5. Jon Ha Ryu receved the M.S. degree n Electroncs and Electrcal Engneerng from Kyungpoo atonal Unversty n 99. He s currently a Ph.D. canddate n Kyungpoo atonal Unversty. Hs research nterests nclude target tracng and target moton analyss. Du Hee Han receved the M.S. degree n Electroncs, Electrcal, Control and Instrumentaton Engneerng from Hanyang Unversty n 5. He s currently a Ph.D. canddate n Hanyang Unversty. Hs research nterests nclude target tracng systems, gudance and control. tracng. Kyun Kyung Lee receved the Ph.D. degree n Electrcal and Computer Engneerng from Unversty of Texas at Austn n 987. He s a Professor n the School of Electrcal Engneerng and Computer Scence, Kyungpoo atonal Unversty. Hs research nterests nclude underwater acoustc sgnal processng, target detecton and Tae Lyul Song receved the Ph.D. degree n Aerospace Engneerng from Unversty of Texas at Austn n 983. He s a Professor n the Department of Elec-troncs, Electrcal, Control and Instrumentaton Engneerng, Hanyang Unversty. Hs research nterests nclude target state estmaton, gudance, navgaton and control.