Optimality Analysis of Sensor-Target Geometries for Bearing-Only Passive Localization in Three Dimensional Space

ZHONG Yu; WU Xiaoyan; HUANG Shucai; LI Chengjing; WU Jianfeng

doi:10.1049/cje.2016.03.029

Volume 25 Issue 2

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Article Navigation > Chinese Journal of Electronics > 2016 > 25(2): 391-396

ZHONG Yu, WU Xiaoyan, HUANG Shucai, et al., “Optimality Analysis of Sensor-Target Geometries for Bearing-Only Passive Localization in Three Dimensional Space,” Chinese Journal of Electronics, vol. 25, no. 2, pp. 391-396, 2016, doi: 10.1049/cje.2016.03.029

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ZHONG Yu, WU Xiaoyan, HUANG Shucai, et al., “Optimality Analysis of Sensor-Target Geometries for Bearing-Only Passive Localization in Three Dimensional Space,” Chinese Journal of Electronics, vol. 25, no. 2, pp. 391-396, 2016, doi: 10.1049/cje.2016.03.029

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Optimality Analysis of Sensor-Target Geometries for Bearing-Only Passive Localization in Three Dimensional Space

doi: 10.1049/cje.2016.03.029

Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China

Received Date: 2013-12-18
Rev Recd Date: 2015-03-08
Publish Date: 2016-03-10

Abstract

Abstract

Optimality analysis of sensor to target observation geometry for bearing-only passive localization is of practical significance in engineering and military applications and this paper generalized predecessors' researches in two-dimensions into three dimensional space. Based on the principles of Cramer-Rao lower bound (CRLB), Fisher information matrix (FIM) and the determinant of FIM derived by Cauchy-Binet formula, this paper configured the optimal observation geometry resulted from maximizing the determinant of FIM. Optimal observation geometry theorems and corresponding propositions were proved for N≥2 sensors in three dimensions. One conjecture was proposed, i.e., when each range of N(N≥4) sensors to the single target is identical, configuring the optimal geometry is equivalent to distributing N points uniformly on a unit sphere, which is one of the worldwide difficult problem. Studies in this paper can provide helpful reference for passive sensor deployment, route planning of detection platform and so on.

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References(23)

References

Z.K. Sun, F.C. Guo, D.W. Feng, et al., Passive Location and Tracking Technology by Single Observer, National Defense Industry Press, Beijing, China, 2008. (in Chinese)

S.C. Nardone, A.G. Lindgren and K.F. Gong, "Fundamental properties and performance of conventional bearings-only target motion analysis", IEEE Transactions on Automatic and Control, Vol.29, No.9, pp.775-787, 1984.

S.E. Hammel and V.J. Aidala, "Observability requirements for three-dimensional tracking via angle measurements", IEEE Transactions on Aerospace and Electronic Systems, Vol.21, No.2, pp.200-207, 1985.

M. Ben Ghalia and A.T. Alouani, "Observability requirements for passive target tracking", Proc. of Twenty-Fifth Southeastern Symposium on System Theory, Tuscaloosa, Alabama, USA, pp.253-257, 1990.

C. Jauffret, "Observability and fisher information matrix in nonlinear regression", IEEE Transactions on Aerospace and Electronic Systems, Vol.43, No.2, pp.756-759, 2007.

J.E. Le Cadre and C. Jauffret, "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.

E. Castillo, A.J. Conejo, R.E. Pruneda, et al., "Observability analysis in state estimation: A unified numerical approach", IEEE Transactions on Power Systems, Vol.21, No.2, pp.877-886, 2006.

S.C. Stubberud, K.A. Kramer and J.A. Geremia, "Analysis of the effects of bearings-only sensors on the performance of the neural extended Kalman filter tracking system", Proc. of IEEE International Conference on Computational Intelligence for Measurement Systems and Applications (CIMSA), Istanbul, Turkey, pp.54-59. 2008.

Z. Xu, C.W. Qu, C.H. Wang, et al., "Research on a passive localization algorithm based on minimizing the generalized Rayleigh Quotient", Acta Electronica Sinica, Vol.40, No.12, pp.2446-2450, 2012. (in Chinese)

Y. Oshman and P. Davidson, "Optimization of observer trajectories for bearings-only target", IEEE Transactions on Localization Aerospace and Electronic Systems, Vol.35, No.3, pp.892-902, 1999.

I. Kadar, "Optimum geometry selection for sensor fusion", Proc.of SPIE Conference on Signal Processing, Sensor Fusion, and Target Recognition II, Orlando, Florida, USA, pp.96-107, 1998.

A.N. Bishop, B. Fidan and B.D.O. Anderson, et al., "Optimality analysis of sensor-target geometries in passive localization: Part 1-bearing-only localization", Proc. of 3rd International Conference on Intelligent Sensors, Sensor Networks and Information( ISSNIP), Melbourne, Australia, pp.7-12, 2007.

A.N. Bishop, B. Fidan and B.D.O. Anderson, et al., "Optimality analysis of sensor-target geometries in passive localization: Part 2-time-of-arrival based localization", Proc. of 3rd International Conference on Intelligent Sensors, Sensor Networks and Information (ISSNIP), Melbourne, Australia, pp.13-18, 2007.

Y. Zhao, "Study on target tracking algorithm of LEO satellite constellation", Ph.D.Thesis, National University of Defense Technology, Changsha, China, 2011. (in Chinese)

R.X. Wang, Mathematical Statics, Xi'an Jiaotong University Press, Xi'an, China, 1986. (in Chinese)

C.Z. Han, H.Y. Zhu and Z.S. Duan, et al., Multi-source Information Fusion, Tsinghua University Press, Beijing, China, 2010.

M.S. Yao, Higher Algebra, Fudan University Press, Shanghai, China, 2003.

B.L. Chen, Theory and Algorithm of Optimization, Tsinghua University Press, Beijing, China, 2005. (in Chinese)

R. Alexander, "On the sum of distances between n points on a sphere", Acta Mathematica Academiae Scientiarum Hungaricae, Vol.23, No.3-4, pp.443-448, 1972.

A.B.J. Kuijlaars, E.B. Saff and X. Sunc, "On separation of minimal Riesz energy points on spheres in Euclidean spaces", Journal of Computational and Applied Mathematics, Vol.199, No.1, pp.172-180, 2007.

X.W. Hou and J.W. Shao, "Spherical distribution of 5 points with maximal distance sum", Discrete and Computational Geometry, Vol.46, No.1, pp.156-174, 2011.

C.L. del Arco-Calderón, P.I. Viñuela and J.C.H. Castro, "Distribuci ón de cargas en una esfera mediante estrategias evolutivas", IEEE Latin America Transactions, Vol.2, No.2, pp.149-155, 2002. (in Spanish)

E.B. Saff and A.B.J. Kuijlaars, "Distributing many points on a sphere", Mathematical Intelligencer, Vol.19, No.1, pp.5-11, 1997.

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