Abstract TheMultiple Targets Tracking(MTT) problem is addressed in signal and image processing.When thestate and measurement models are linear, we can find several algorithms that yield good performances in MTT problem, among them, theMultiple Hypotheses Tracker(MHT) and theJoint Probabilistic Data Association Filter(JPDAF).However, if the state and measurement models are nonlinear, these algorithms break down.In this paper we propose a method based on particle filters bank, where the objective is to make a contribution for estimating the trajectories of several targets using only bearings measurements. The main idea of this algorithm is to combine theMultiple Modelapproach (MM) withSequential Monte Carlo methods (SMC). The result from this combination is aNonlinear Multiple Model Particle Filtersalgorithm (NMMPF) ableto estimate the trajectories of multiple targets.

References

[1]Bar-Shalom Y.and Tse E., Tracking in a Cluttered EnvironmentwithProbabilistic Data Association, Automatica, vol.11, no.5,pp.451- 460, 1975.

[2]Bar Shalom Y., Li X., and Thiagalingam K., Estimation withApplicationstoTrackingand Navigation, USA, 2001.

[3]Blom H.and Bloem E., TrackingMultiple TargetsbyJoint Combinationsof IMM and PDA, inProceeding of the42ndIEEE Real traj Esteemed traj Real traj Esteemed traj Time stepk Real traj Esteemed traj (18) Parallel Particle Filters for Multiple Target Tracking713 Conference onDecision and Control,pp.2965- 2970, 2003.

[4]Boers Y.andDriessen H., AMultiple Model Multiple Hypothesis Filterfor Markovian Switching Systems, Automatica, vol.41,no. 4, pp.709-716, 2005.

[5]Chang K.and Bar-Shalom Y., Joint Probabilistic Data AssociationforMulti target TrackingwithPossibly Unresolved MeasurementsandManeuvers, IEEE Transactionof Automation and Control, vol.29, no. 7,pp.585-594,1984.

[6]Chen B. and Tugnait J., Tracking ofMultiple Maneuvering TargetsinClutterusing IMM/JPDAFilteringandFixed-lagSmoothing, Automatica,vol.37,no. 2,pp. 239-249,2001.

[7]Djouadi M., Sebbagh A., and Berkani D., A Nonlinear Algorithm for Manoeuvrings Target Visual-based Tracking, IEEE Proceedingsof the 2ndInternational Conferenceon intell Sens and Infor Proc, ICISIP,Chennai, India,pp.61-66, 2005.

[8]Doucet A., Convergence of sequential Monte CarloMethods, TechnicalReport, Signal Processing Group, Department of Engineering, University of Cambridge, 2000.

[9]Doucet A., OnSequential Simulation-based Methodsfor BayesianFiltering, Technical Report, Department of Engineering. University of Cambridge, 1998.

[10]Doucet A., De Freitas N., and Gordon N., Sequential Monte Carlo Methods in Practice, New York:Springer,pp. 525-532, 2001.

[11]Gordon N., AHybrid Bootstrap FilterforTarget TrackinginClutter, IEEE Transactionon Aerospace and Electronic Systems,vol.33, no.1, pp.353-358,1997.

[12]Gordon N., Salmond D., and Smith A., Novel ApproachtoNonlinear/Non-Gaussian Bayesian State Estimation, in Proceedings of F-Radar and Signal Processing,pp. 107-113,1993.

[13]Hue C., Le Cadre J., and P rez P., Sequential Monte CarloMethodsforMultiple Target TrackingandData Fusion, IEEETransactionon Signal Processing,vol.50 no.2,pp.309-325, 2002.

[14]Hue C.,Le Cadre J., and P rezP., Tracking Multiple ObjectswithParticle Filtering, available at: http://www.irisa.fr/vista/Papers/2002_aes_hue.pd f,last visited2002.

[15]Isard M.and Blake A., Condensation ConditionalDensity PropagationforVisual Tracking, International Journal of Computer Vision, vol.29, no.1,pp.5-28,1998.

[16]Kong A., Liu J., and Wong W., Sequential Imputation MethodandBayesian Missing Data Problems, available at: http://stat.rutgers.edu/home/rongchen/papers/Kon gLiuWong.pdf,last visited1994

[17]Li X. and Bar-Shalom Y., Design of an Interacting Multiple Model AlgorithmforAir Traffic Control Tracking, IEEE Transactions on Control Systems Technology,vol. 1,no. 3,pp. 186-194,1993.

[18]Liu J., MetropolizedIndependent Samplingwith ComparisontoRejection Samplingand Importance Sampling, Statistics and Computing, vol. 6,no. 2,pp.113-119, 1996.

[19]Sebbagh A.andTebbikh H., NonlinearMultiple Model Particle Filters AlgorithmforTracking Multiple Targets, Archives ofControl Sciences, vol.21, no. 1,pp.37-60,2011.

[20]Van Der Merwe R., Doucet A., De Freitas N., and Wan E., TheUnscented Particle Filte, TechnicalReport, Cambridge University Engineering Department, 2000.

[21]Vermaak J., Godsill S., and Perez P., Monte CarloFilteringforMulti-Target Trackingand Data Assoication,IEEE Transactions on Aerospace and Electronic Systems, vol. 41, no. 1, pp. 309-332, 2005.

[22]Wang H., Kirubarajan T., and Bar Shalom Y., Precision Large Scale Air Traffic Surveillance Using an IMM Estimator with Assignment, IEEE Transactions on Aerospace and Electronic Systems, vol.35, no.1,pp.255-266,1999.

[23]Yang N., Tian W., Jin Z., and Zhang C., Particle FilterforSensor Fusionin aLand Vehicle Navigation System, Measurement Science and Technology, vol.16,no. 3,pp.677- 681, 2005.

[24]Zahidul I., Chi-Min O., and Chil-Woo L., Effect of Resampling Steepness on ParticleFiltering Performance in Visual Tracking, The International Arab Journal of Information Technology, vol. 10,no. 1, pp. 102-109, 2013.

[25]Zheng T., Chao S., and Zongwei L., The Tracking Algorithm for Maneuvering Target Based on Adaptive Kalman Filter, The International Arab Journal of Information Technology, vol. 10,no. 5, pp. 453-459, 2013. SebbaghAbdennouris aDoctoral candidate inElectritechnicand Automatic Departmentof 08 May 1945 Guelma University, Algeria. He received hisautomatic engineer degree from the University of Annabain 2000andhis Magister degreefrom the Polytechnic military school (EMP) of Algiers, Algeria in 2004. His research interests include automatic control and tracking targets. 714The International Arab Journal of Information Technology,Vol. 13, No. 6, November 2016 TebbikhHichamis a professor in automatic and signal processing of 08 may 1945 Guelma University, Algeria. He received his electronic engineer degree from the University of Annaba in 1984 and his doctorate degree from the I.N.P of Grenoble, France in 1988. His research interests include modeling andfractionalcontrolsystems, modeling and control of hybriddynamic systems and automatic pattern recognition.He was in chargeof several scientificand administrativeresponsibilitiesincluding Chair of the ScientificCouncil ofthe Faculty of Scienceand Technolog. He alsoparticipated,as a memberon severalnational science and technology committees including theSectorStanding Committee (CSP) of theMESRS from 2009 to 2012,the Central Committeeof thenew technologies ofinformation and communicationoftheMESRSfrom 2002.Currently he is a director ofautomatic andcomputing laboratory of guelma (LAIG).