Matching of the estimating covariance in bearings-only tracking algorithm for moving surface targets in multiple model filters

Document Type : Original Article

Authors

1 Faculty of Electrical and Robotic, Shahrood University of Technology, Shahrood, Iran

2 Faculty of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

: In this paper, an algorithm for bearings-only target tracking (BOT) problem is proposed using the resetting of the covariance matrix of the filter . Poor observability in BOT problem often leads to a bias error or even divergence of the filter. Therefore, due to non-uniqueness of the problem, the covariance value of the filter is not a sufficient condition to indicate the estimation error. In this paper, it is shown that the mutual effects between the covariance of the target range estimation and the Cramer-Rao lower error bound is similar to the stability of a Lyapunov function for detecting the divergence of the recursive filter. Then, this function is used as a correction coefficient of the estimating covariance matching. The multi-model/particle filters are also adopted for estimating the initial range of the target and calculating the Cramer-Rao lower error bound. Using the Monte Carlo simulation method, the proposed algorithm is compared with other conventional filters based on the criteria reported in the literature. Improvement of the results of the target range estimation is also shown, especially in case of observability reduction. All studies conducted in this paper are limited to the problem of surface floats tracking with passive sonar for a typical submarine.

Keywords

References

 [1] P. I. Reji and V. S. Dharun, “Recursive Multistage Estimator for Bearings only Passive Target Tracking in ESM EW Systems,” Indian Journal of Science and Technology, vol. 8, no. 26, pp. 1–7, 2015.
[2] B. Omkar Lakshmi Jagan, S. K. Rao, A. Jawahar, and S. B. Karishma, “Passive target tracking using intercept sonar measurements,” Indian Journal of Science and Technology, vol. 9, no. 12, pp. 10–13, 2016.
[3] عقیل عبیری، محمدرضا محزون، «ردیابی اهداف متحرک هوایی با استفاده از تخمین چگالی کرنل بر اساس الگوریتم فیلتر ذره»، مجله مهندسی برق دانشگاه تبریز، جلد 4، شماره 3، پاییز 94.
[4] B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman filter: Particle filters for tracking applications, Artech house, 2004.
[5] B. S. Yaakov, X. R. Li, and T. Kirubarajan. Estimation with applications to tracking and navigation: theory algorithms and software. John Wiley & Sons, 2004.
[6] J.P. Le Cadre, “Discrete-Time Observability and Estimability Analysis for Bearings-Only Target Motion Analysis,” IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 1, pp. 178-201, 1997.
[7] محمدمهدی عارفی، « طراحی یک رؤیت‌گر مقاوم تطبیقی برای دسته وسیعی از سیستم‌های غیرخطی در حضور دینامیک‌های مدل نشده»، مجله مهندسی برق دانشگاه تبریز، جلد 74 ، شماره 2، تابستان 96.
[8] S. E. Hammel, P. T. Liu, E. J. Hilliard, and K. F. Gong, “Optimal observer motion for localization with bearing measurements,” Computers and Mathematics with Applications, vol. 18, no. 1–3, pp. 171–180, 1989.
[9] 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, pp. 892–902, 1999.
[10] A. N. Bishop, “Bearing-Only Localization using Geometrically Constrained Optimization,” IEEE Transactions on Aerospace and Electronic Systems , vol. 45, no. 1, pp. 308-320, 2009.
[11] مهدی اردشیری، علیرضا الفی، «تعیین مسیر بهینه ناظر در ردیابی اهداف متحرک تنها با زاویه سمت با استفاده از چندجمله‌ای‌های چبی‌شف»، پذیرش شده در مجله کنترل، تیر 97.
[12] Reif, Konrad, et al. “Stochastic stability of the discrete-time extended Kalman filter.”  IEEE Transactions on Automatic control, vol. 44, no .4,  pp. 714-728, 1999.
[13] X. Chen, R. Tharmarasa, and T. Kirubarajan.“Multitarget Multisensor Tracking”. In Academic Press Library in Signal Processing, vol. 2, pp. 759-812. Elsevier, 2014.
[14] R. P. S. Mahler, Advances in statistical multisource-multitarget information fusion, Artech House, 2014.
[15] Lan, Jian, et al, “Second-order Markov chain based multiple-model algorithm for maneuvering target tracking,” IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 1, pp. 3-19, 2013.
[16] مهدی اردشیری، علیرضا الفی، «ارائه ابزار تشخیص هم‌گرایی روی‌خط در مسئله ره‌گیری تنها سمت هدف متحرک»، بیست و پنجمین کنفرانس برق ایران، دانشگاه خواجه نصیر تهران، 1396.
[17] مقداد محمدی، حسین قلی‌زاده نرم، «طبیق کواریانس های نویز فیلتر کالمن توسعه‌یافته در ردیابی هدف از روی سمت به روش بازگشتی»، مجله کنترل، جلد 10، تابستان، 1395.
[18] G. Quanbo et al. “Carrier tracking estimation analysis by using the extended strong tracking filtering,” IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 1415-1424, 2017.
[19] Liu, Kai-zhou, et al. "Navigation system of a class of underwater vehicle based on adaptive unscented Kalman fiter algorithm." Journal of Central South University, vol. 21, no .2, pp. 550-557, 2014.

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