Document Type : ResearchPaper


1 Faculty of Electrical Engineering, Shahrood University of Tecnology, Sharood, Iran

2 Department of Electrical Engineering, Faculty of Technical and Engineering, Imam Khomeini International University, Qazvin, Iran



In this paper, in addition to investigation and analyzing the dynamic model of a maneuver target, a new method based on the Interaction Multiple Model (IMM) method is presented to solve the tracking problem in presence of measurement noise. In this procedure, two models are used along with an extended Kalman filter for each model, for estimation of the states related to stochastic target model. To this end, a specific weight is calculated adaptively for each model and the final estimation of the target is obtained from the weighted sum of the modes related to each model. In this paper, second order Markov models are used to better describe the system behavior which leads to a decrease in the number of required motion models. This means that the previous two models are used to decide on the next model, and a much better algorithm is provided than the first-order IMM algorithm.


Main Subjects

[1] J.A. Fawcett, “Effect of course maneuvers on bearings-only range estimation,” IEEE Transactions On Acoustics Speech and Signal Processing, vol. 36, no.8, p.p. 1193–1199, 1988.
[2] Y. Oshman and P. Davidson, “Optimization of observer trajectories for bearings-only target localization,” IEEE Transactions on Aerospace and Electronic Systems, vol. 35, no. 3, p.p. 892–902, 1999.
[3] M. Gavish and A. J. Weiss, “Performance analysis of bearing-only target location algorithms,” IEEE Transactions on Aerospace and Electronic System, vol.28, no.3 , p.p 817–828, 1992.
[4] Popoli. R and S. Blackman, “Design and Analysis of Modern Tracking Systems,” Artech House radar library. Artech House 1 1999.  
[5] M. F. Huber, “Chebyshev polynomial Kalman filter,” Digital Signal Processing, vol. 23 ,no. 5,p. p. 1620–1629, 2013.
[6] T. Yang, P. G. Mehta, and S. P. Meyn, “Feedback particle filter,” IEEE Transactions on Automatic Control, vol.58,  no.10, p. p. 2465–2480, 2013.
[7] B. Jia, M. Xin, and Y. Cheng, “High-degree cubature Kalman filter,” Automatica,vol. 49, no. 2, p.p 510–518, 2013.
[8] L. Badriasl, and. K. Dogancay, “Three-Dimensional Target Motion Analysis Using Azimuth/Elevation Angles,” IEEE Transactions On Aerospace And Electronic System, vol.50, no.4, p.p. 3178-3194, 2014.
[9] L. Scala and M,B Morelande, “An analysis of the single sensor bearings-only tracking problem,” 11 th International Conference on Information Fusion, p.p 1-6, 2008.
[10] O. Straka, J. Dunik and M. Simandl, “Performance Evaluation of Local State Estimation Methods in Bearings-only Tracking Problems,” 14 th International Conference on Information Fusion,  p.p 1-8, 2011.
[11] A.G. Lindgren, K.F. Gong, “Position and Velocity Estimation Via Bearing Observations,” IEEE Transactions on Aerospace and electronic systems, vol.4, p.p 564-577, 1978.
[12] M. T. Sabet, A. R. Fathi, and H. R. Mohammadi Daniali, “Optimal design of the own ship maneuver in the bearing-only target motion analysis problem using a heuristically supervised extended Kalman filter,” Ocean Engineering, vol. 123, p.p 146–153, 2016.
[13] B. Ristic and M. S. Arulampalam, “Tracking a manoeuvring target using angle-only measurements: algorithms and performance,” Signal Processing ,vol.83,  p.p 1223–1238, 2003.
[14] H. E. Soken, C. Hacizade, and S. Sakai, “Simultaneous adaptation of the process and measurement noise covariances for the UKF applied to nanosatellite attitude estimation, IFAC Proceedings, vol. 47, no. 3 p.p 5921-5926, 2014.
[15] X. Wang, Z. You, and K. Zhao, “Inertial/celestial-based fuzzy adaptive unscented Kalman filter with Covariance Intersection algorithm for satellite attitude determination,” Aerospace Science and Technology,vol.48, p. p 214–222, 2016.
[16] B. Feng, M. Fu, H. Ma, Y. Xia, and B. Wang, “Kalman Filter With Recursive Covariance Estimation & Sequentially Estimating Process Noise Covariance,” IEEE Transactions on Industrial Electronics , vol.61, p.p 6253-6263, 2014.
[17] le Cadre, J-P., and S. Laurent-Michel, “Optimizing the receiver maneuvers for bearings-only tracking,” Automatica, vol.35, no.4, p.p 591–606, 1999.
[18] Li ,  X. Rong. and V. P. Jilkov, “Survey of maneuvering target tracking. Part I. Dynamic models,” IEEE Transaction on Aerospace and Elecreonic Systems, vol.39,  no.4, p.p 1333-1364, 2003.
[19] J. Lan, X. R. Li, V. P. Jilkov, and C. Mu, “Second-Order Markov Chain Based Multiple-Model Algorithm for Maneuvering Target Tracking,” IEEE Transactions on Aerospace and Electronic Systems,vol.49, no.1, p.p 3-19, 2013.
[20] Blom, AP. Henk, and  y. Bar-Shalom,.“The interacting multiple model algorithm for systems with Markovian switching coefficients,” IEEE Transactions on Automatic Control, vol.33, no.8, p.p 780-783, 1998.
[21] Nardone, C. Steven. and. M. L. Graham.,“A closed-form solution to bearings-only target motion analysis ,” IEEE Journal of Oceanic Engineering,vol.22,no.1 ,p. p. 168-178, 1997.
[22] B. Ristic, S. Arulampalam, and N. Gordon, “Beyond the Kalman Filter: Particle Filters for Tracking Applications,” Artech House,2003.
[23] A. Farina, “ Target tracking with bearings-Only measurements,” Signal Processing, vol78, no.1, p.p 61–78, 1999.
[24] S. E. Hammel, P.T. Liu, E.J. Hilliard,, “Optimal observer motion for localization with bearing measurements,” Computers and Mathematics with applications vol.18, no01-3 , p.p 171-180, 1989.
[25] S. E. Hammel, and V. J. Aidala, “Observability requirements for three dimensional tracking via angle measurements,” IEEE Transactions on Aerospace and Electronic Systems,  vol.2, p.p 200–207, 1985.
[26] S. C. Nardone, and  V. J. Aidala, “Observability criteria for bearings-only target motion analysis,” IEEE Transactions on Aerospace and Electronic systems vol.2 ,  p.p 162–166, 1981.
[27] Le Cadre , J.-P. and O. Tremois, “Bearings-only tracking for maneuvering sources,” IEEE Transactions on Aerospace and Electronic Systems, vol.34, no.1, p.p 179-193, 1998.
[28] Ristic , Branko, and B. Arulampalam., “Bernoulli Particle Filter with Observer Control for Bearings-Only Tracking in Clutter,” IEEE Transactions on Aerospace and Electronic Systems, vol.48, no.3, p.p 2405–2415, 2012.
[29] D. H. Dini, C. Jahanchahi, and D. P. Mandic, “Kalman filtering for widely linear complex and quaternion valued bearings only tracking,” IET Signal Processing, vol.6, no.5, p.p 435–445, 2012.
[30] K. Ito and K. Xiong, “Gaussian filters for nonlinear filtering problems,” IEEE Transactions on Automatic Control, vol 45, no.5, p.p 910–927, 2000.
[31] J. L. Kraige and  L. G. Meriam, “Engineering Mechanics: Dynamics 7th Edition: Dynamics,” Wiley, 2012.