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Multiple-model Rao-Blackwellized particle CPHD filter for multitarget tracking

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Abstract

To overcome high computational complexity and imprecise target estimates in existing multitarget tracking (MMT), a multiple-model Rao-Blackwellized particle cardinalized probability hypothesis density (CPHD) filter is presented in this paper. First, we derive the multiple-model CPHD filter to model maneuvering multitarget with uncertainties of each individual state and then make full use of the Rao-Blackwellization to divide the target state space into the nonlinear and linear parts to reduce space dimension. Furthermore, the nonlinear state is estimated by the particle filter with the sequential Monte Carlo method, and the linear part is predicted by the Kalman filter with the information embedded in the estimated nonlinear state. With respect to the tracking precision, we find that the proposed filter has small Wasserstein distance by eliminating unstable target number-estimates. Especially, the computational cost is significantly reduced due to the saved particles. Finally, the illustrative numerical studies are provided to demonstrate the tracking performance of the proposed filter is superior.

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References

  1. Mahler, R.: PHD filters for nonstandard target. In: 12th Conference on Information Fusion, Seattle, pp. 915–921 (2009)

  2. Lundquist, C., Granstrom, K., Orguner, U.: Estimating the shape of targets with a PHD filter. In: 14th International Conference on Information Fusion, Chicago, pp. 1–8 (2011)

  3. Panta, K., Clark, D.E., Vo, B.N.: Data association and track management for the Gaussian mixture probability hypothesis density filter. IEEE Trans. Aerosp. Electron. Syst. 45(3), 1003–1016 (2009)

    Article  Google Scholar 

  4. Li, W.L., Jia, Y.M., Du, J.P., Yu, F.S.: Gaussian mixture PHD smoother for jump Markov models in multiple maneuvering targets tracking. In: American Control Conference, San Francisco, pp. 3025–3029 (2011)

  5. Vo, B.N., Ma, W.K.: The Gaussian mixture probability hypothesis density filter. IEEE Trans. Signal Process. 5(11), 3291–3304 (2006)

    Google Scholar 

  6. Mahelr, R.: Statistical Multisource–Multitarget Information Fusion. Artech House, Norwood (2007)

    Google Scholar 

  7. Vo, B.T.: Random Finite Set in Multi-Object Filtering. The University of Western Australia, Perth (2008)

    Google Scholar 

  8. Mahler, R.: PHD filters of higher order in target number. IEEE Trans. Aerosp. Electron. Syst. 43(4), 1532–1543 (2007)

    Article  Google Scholar 

  9. Zheng, X.T., Song, L.P.: Improved CPHD filtering with unknown clutter rate. In: 10th World Congress Conference on Intelligent Control and Automation, Beijing, pp. 4326–4331 (2012)

  10. Ristic, B., Clark, D., Vo, B.N., Vo, B.T.: Adaptive target birth intensity for PHD and CPHD filters. IEEE Trans. Aerosp. Electron. Syst. 48(2), 1656–1668 (2012)

    Article  Google Scholar 

  11. Zhou, W.D., Zhang, H.B., Ji, Y.R.: Multi-target tracking algorithm based on SMC–CPHD filter. J. Astron. 33, 443–450 (2012)

    Google Scholar 

  12. Delande, E., Uney, M., Houssineau, J., Clark, D.E.: Regional variance for multi-object filtering. IEEE Trans. Signal Process. 32(13), 3415–3428 (2014)

    Article  MathSciNet  Google Scholar 

  13. Daniel, M., Stephan, R., Benjamin, W., Klaus, D.: Road user tracking using a Dempster–Shafer based classifying multiple-model PHD filter. In: 16th International Conference on Information Fusion, Istanbul, pp. 1236–1242 (2013)

  14. Hong, S.H., Shi, Z.G., Chen, K.S.: Novel multiple-model probability hypothesis density filter for multiple maneuvering targets tracking. In: Asia Pacific Conference on Postgraduate Research in Microelectronics and Electronics, Shanghai, pp. 189–192 (2009)

  15. Pasha, A., Vo, B.N., Tuan, H.D., Ma, W.K.: A Gaussian mixture PHD filter for jump Markov systems models. IEEE Trans. Aerosp. Electron. Syst. 46(3), 919–936 (2009)

    Article  Google Scholar 

  16. Punithakumar, K., Kirubarajan, T., Sinha, A.: Multiple-model probability hypothesis density filter for tracking maneuvering targets. IEEE Trans. Aerosp. Electron. Syst. 44(1), 87–98 (2008)

    Article  Google Scholar 

  17. Georgescu, R., Willet, P.: Multiple model cardinalized probability hypothesis density filter. In: SPIE Signal and Data Processing of Small Targets, San Diego, 81370L (2011)

  18. Doucet, A., Freitas, N.D., Murphy, K., Russell, S.: Rao-Blackwellised particle filtering for dynamic Bayesian networks. In: 16th Conference on Uncertainty in Artificial Intelligence, San Francisco, pp. 176–183 (2000)

  19. Zia, K., Baich, T., Dellaert, F.: A Rao-Blackwellized particle filter for target tracking. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 980–986 (2004)

  20. Liu, Y.J., Zheng, Y.Q.: Adaptive robust fuzzy control for a class of uncertain chaotic systems. Nonlinear Dyn. 57(3), 431–439 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Zhang, S.C., Li, J.X., Wu, L.B.: A novel multiple maneuvering targets tracking algorithm with data association and track management. Int. J. Control Autom. Syst. 11(5), 947–956 (2013)

    Article  MathSciNet  Google Scholar 

  22. Liu, Y.J., Chen, C.L.P., Wen, G.X., Tong, S.C.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22(7), 1162–1167 (2011)

    Article  Google Scholar 

  23. Yang, J.L., Ji, H.B.: A novel track maintenance algorithm for PHD/CPHD filter. Signal Process. 92, 2371–2980 (2012)

    Article  Google Scholar 

  24. Han, Y.B.: A Rao-Blackwellized particle filter for adaptive beamforming with strong interference. IEEE Trans. Signal Process. 60(6), 2952–2961 (2012)

    Article  MathSciNet  Google Scholar 

  25. Xu, X.Y., Li, B.X.: Adaptive Rao-Blackwellized particle filter and its evaluation for tracking in surveillance. IEEE Trans. Image Process. 16(3), 838–849 (2007)

    Article  MathSciNet  Google Scholar 

  26. Schon, T., Gustafsson, F.: Marginalized particle filters for mixed linear/nonlinear state-space models. IEEE Trans. Signal Process. 53(7), 2279–2289 (2005)

    Article  MathSciNet  Google Scholar 

  27. Nordlumd, P.J.: Sequential Monte Carlo Filter and Integrated Navigation. Linkoping University, Sweden (2002)

    Google Scholar 

  28. Yin, J.J., Zhang, J.Q., Mike, K.: The marginal Rao-Blackwellized particle filter for mixed linear/nonlinear state space models. Chin. J. Aeronaut. 20, 348–354 (2007)

    Article  Google Scholar 

  29. Li, B., Pang, F.W.: Improved probability hypothesis density filter for multitarget tracking. Nonlinear Dyn. 76(1), 367–376 (2014)

    Article  MathSciNet  Google Scholar 

  30. Zhuang, Z.S., Zhang, J.Q., Yin, J.J.: Rao-Blackwellized particle probability hypothesis density filter. Acta Aeronautica et Astronautica Sinica 30(4), 699–705 (2009)

  31. Vo, B.N., Singh, S., Doucet, A.: Sequential Monte Carlo methods for multi-target filtering with random finite sets. IEEE Trans. Aerosp. Electron. Syst. 41(4), 1224–1245 (2005)

    Article  Google Scholar 

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Acknowledgments

This work was supported by the Subject of Electronics and Information Engineering College in Liaoning University of Technology (DX201416), and Natural Science Foundation of China (61104017, 61473139). The authors thank the reviewers for their valuable comments and suggestions which helped to improve the quality and presentation of this paper.

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  1. College of Electronics and Information Engineering, Liaoning University of Technology, Jinzhou, 121001, China

    Bo Li

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  1. Bo Li
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Correspondence to Bo Li.

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Li, B. Multiple-model Rao-Blackwellized particle CPHD filter for multitarget tracking. Nonlinear Dyn 79, 2133–2143 (2015). https://doi.org/10.1007/s11071-014-1799-x

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