American Institute of Mathematical Sciences

August & September 2019, 12(4&5): 1251-1264. doi: 10.3934/dcdss.2019086

Automatic tracking and positioning algorithm for moving targets in complex environment

 1 Unmanned Aerial Vehicle Research Institute, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2 Department of Mathematics UMBA, University of Mostaganem Algeria, Algeria

* Corresponding author: Rong Liu

Received  June 2017 Revised  November 2017 Published  November 2018

Nowadays, when moving targets are located in complex environment, the positioning algorithm takes longer time, and the result is not consistent with the actual positioning of the moving target, which has the problem of low positioning efficiency and inaccurate positioning results. In this paper, a moving target automatic tracking and positioning algorithm is proposed in the complex environment, which establishes the geodetic coordinate system and the space rectangular coordinate system, and completes the transformation between the geodetic coordinate system and the rectangular coordinate system, so as to improve the accuracy of the positioning result. The signal is rebuilt and the MIMO radar positioning model is used to complete the automatic tracking and positioning of the moving target in complex environment, to reduce the time consuming. The experimental results show that the proposed method can quickly and accurately track and locate the moving target in complex environment.

Citation: Rong Liu, Saini Jonathan Tishari. Automatic tracking and positioning algorithm for moving targets in complex environment. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1251-1264. doi: 10.3934/dcdss.2019086
References:
 [1] A. H. Abdullah and et al., Mathematics teachers' level of knowledge and practice on the implementation of higher-order thinking skills (hots), Eurasia Journal of Mathematics Science & Technology Education, 13 (2016), 3-17. [2] A. Ahadi and A. Dehghan, The inapproximability for the (0, 1)-additive number, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 217-226. [3] F. Altinay-Gazi Zehra—Altinay-Aksal, Technology as mediation tool for improving teaching profession in higher education practices, Eurasia Journal of Mathematics Science & Technology Education, 13 (2017), 803-813. [4] M. M. A. M. Aly and M. A. H. El-Sayed, Enhanced fault location algorithm for smart grid containing wind farm using wireless communication facilities, Iet Generation Transmission & Distribution, 10 (2016), 2231-2239. [5] L. B. and L. W. S., Indoor positioning method based on cosine similarity of fingerprint matching algorithm, Bulletin of Science and Technology, 3 (2017), 198-202. [6] T. P. S. Bains and M. R. D. Zadeh, Supplementary impedance-based fault-location algorithm for series-compensated lines, IEEE Transactions on Power Delivery, 31 (2016), 334-342. [7] A. Basar and M. Y. Abbasi, On ordered bi-ideals in ordered-semigroups, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 645-652. doi: 10.1080/09720529.2015.1130474. [8] T. Brough, L. Ciobanu, M. Elder and G. Zetzsche, Permutations of context-free, et0l and indexed languages, Discrete Mathematics & Theoretical Computer Science, 17 (2016), 167-178. [9] J. Byrka, S. Li and B. Rybicki, Improved Approximation Algorithm for k-level Uncapacitated Facility Location Problem (with Penalties), Theory Comput. Syst., 58 (2016), 19-44. doi: 10.1007/s00224-014-9575-3. [10] Y. Cao, Optimal investment-reinsurance problem for an insurer with jump-diffusion risk process: correlated of brownian motions, Journal of Interdisciplinary Mathematics, 20 (2017), 497-511. [11] M. Chen and C. X. Xu, Analysis of optimal utilization model of coastline resources in jiangsu province, Journal of Interdisciplinary Mathematics, 20 (2017), 1441-1444. [12] P. S. Davis and T. L. Ray, A branch ound algorithm for the capacitated facilities location problem, Naval Research Logistics, 16 (2015), 331-344. [13] W. Gao and W. Wang, A tight neighborhood union condition on fractional (g, f, n', m)-critical deleted graphs, Colloquium Mathematicum, 149 (2017), 291-298. doi: 10.4064/cm6959-8-2016. [14] W. Gao, L. Zhu, Y. Guo and K. Wang, Ontology learning algorithm for similarity measuring and ontology mapping using linear programming, Journal of Intelligent & Fuzzy Systems, 33 (2017), 3153-3163. [15] Y. Gao, Optimization design of fast query system for retrieval information from large amount of books, Modern Electronics Technique, 9 (2016), 422-425. [16] M. Ghorbani, An evolutionary algorithm for a new multi-objective location-inventory model in a distribution network with transportation modes and third-party logistics providers, International Journal of Production Research, 53 (2015), 1038-1050. [17] R. J. Hamidi and H. Livani, Traveling-wave-based fault-location algorithm for hybrid multiterminal circuits, IEEE Transactions on Power Delivery, 32 (2017), 135-144. [18] B. Hartke, Global cluster geometry optimization by a phenotype algorithm with niches: Location of elusive minima, and low rder scaling with cluster size, Journal of Computational Chemistry, 20 (2015), 1752-1759. [19] T. Jin, Y. F. Niu and L. Zhou, Methods of evaluating cognitive performance of products digital interface, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 295-308. [20] Z. Liu, M. Chao, J. Zhang, X. Zhang, Y. Liu and J. Zhang, Research on mathematical properties of localization algorithm based on sensor relative position in wsn, Journal of Jilin University(Information Science Edition, 6 (2015), 685-689. [21] G. Preston, Z. M. Radojevic, C. H. Kim and V. Terzija, New settings-free fault location algorithm based on synchronised sampling, Iet Generation Transmission & Distribution, 5 (2015), 376-83. [22] S. Sun, K. Dong, J. J. Xiu and Y. Liu, A passive source localization algorithm with multiple moving observers using tdoa/groa measurements based on cwls, Journal of China Academy of Electronics & Information Technology, 5 (2016), 540-546. [23] Y. Sun, J. Qi, R. Zhang, Y. Chen and X. Du, Mapreduce based location selection algorithm for utility maximization with capacity constraints, Computing, 97 (2015), 403-423. doi: 10.1007/s00607-013-0382-5. [24] P. H. Tseng and K. T. Lee, A femto-aided location tracking algorithm in lte-a heterogeneous networks, IEEE Transactions on Vehicular Technology, 66 (2017), 748-762. [25] G. Weckman, Applying genetic algorithm to a new location and routing model of hazardous materials, International Journal of Production Research, 53 (2015), 916-928. [26] W. Yi, Assessment study on brain wave predictive ability to policemen's safety law enforcement, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 193-204. [27] J. J. Zhang and K. Qiang, Modeling of complex information system based on hierarchical decision-making theory, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 137-148.

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References:
 [1] A. H. Abdullah and et al., Mathematics teachers' level of knowledge and practice on the implementation of higher-order thinking skills (hots), Eurasia Journal of Mathematics Science & Technology Education, 13 (2016), 3-17. [2] A. Ahadi and A. Dehghan, The inapproximability for the (0, 1)-additive number, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 217-226. [3] F. Altinay-Gazi Zehra—Altinay-Aksal, Technology as mediation tool for improving teaching profession in higher education practices, Eurasia Journal of Mathematics Science & Technology Education, 13 (2017), 803-813. [4] M. M. A. M. Aly and M. A. H. El-Sayed, Enhanced fault location algorithm for smart grid containing wind farm using wireless communication facilities, Iet Generation Transmission & Distribution, 10 (2016), 2231-2239. [5] L. B. and L. W. S., Indoor positioning method based on cosine similarity of fingerprint matching algorithm, Bulletin of Science and Technology, 3 (2017), 198-202. [6] T. P. S. Bains and M. R. D. Zadeh, Supplementary impedance-based fault-location algorithm for series-compensated lines, IEEE Transactions on Power Delivery, 31 (2016), 334-342. [7] A. Basar and M. Y. Abbasi, On ordered bi-ideals in ordered-semigroups, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 645-652. doi: 10.1080/09720529.2015.1130474. [8] T. Brough, L. Ciobanu, M. Elder and G. Zetzsche, Permutations of context-free, et0l and indexed languages, Discrete Mathematics & Theoretical Computer Science, 17 (2016), 167-178. [9] J. Byrka, S. Li and B. Rybicki, Improved Approximation Algorithm for k-level Uncapacitated Facility Location Problem (with Penalties), Theory Comput. Syst., 58 (2016), 19-44. doi: 10.1007/s00224-014-9575-3. [10] Y. Cao, Optimal investment-reinsurance problem for an insurer with jump-diffusion risk process: correlated of brownian motions, Journal of Interdisciplinary Mathematics, 20 (2017), 497-511. [11] M. Chen and C. X. Xu, Analysis of optimal utilization model of coastline resources in jiangsu province, Journal of Interdisciplinary Mathematics, 20 (2017), 1441-1444. [12] P. S. Davis and T. L. Ray, A branch ound algorithm for the capacitated facilities location problem, Naval Research Logistics, 16 (2015), 331-344. [13] W. Gao and W. Wang, A tight neighborhood union condition on fractional (g, f, n', m)-critical deleted graphs, Colloquium Mathematicum, 149 (2017), 291-298. doi: 10.4064/cm6959-8-2016. [14] W. Gao, L. Zhu, Y. Guo and K. Wang, Ontology learning algorithm for similarity measuring and ontology mapping using linear programming, Journal of Intelligent & Fuzzy Systems, 33 (2017), 3153-3163. [15] Y. Gao, Optimization design of fast query system for retrieval information from large amount of books, Modern Electronics Technique, 9 (2016), 422-425. [16] M. Ghorbani, An evolutionary algorithm for a new multi-objective location-inventory model in a distribution network with transportation modes and third-party logistics providers, International Journal of Production Research, 53 (2015), 1038-1050. [17] R. J. Hamidi and H. Livani, Traveling-wave-based fault-location algorithm for hybrid multiterminal circuits, IEEE Transactions on Power Delivery, 32 (2017), 135-144. [18] B. Hartke, Global cluster geometry optimization by a phenotype algorithm with niches: Location of elusive minima, and low rder scaling with cluster size, Journal of Computational Chemistry, 20 (2015), 1752-1759. [19] T. Jin, Y. F. Niu and L. Zhou, Methods of evaluating cognitive performance of products digital interface, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 295-308. [20] Z. Liu, M. Chao, J. Zhang, X. Zhang, Y. Liu and J. Zhang, Research on mathematical properties of localization algorithm based on sensor relative position in wsn, Journal of Jilin University(Information Science Edition, 6 (2015), 685-689. [21] G. Preston, Z. M. Radojevic, C. H. Kim and V. Terzija, New settings-free fault location algorithm based on synchronised sampling, Iet Generation Transmission & Distribution, 5 (2015), 376-83. [22] S. Sun, K. Dong, J. J. Xiu and Y. Liu, A passive source localization algorithm with multiple moving observers using tdoa/groa measurements based on cwls, Journal of China Academy of Electronics & Information Technology, 5 (2016), 540-546. [23] Y. Sun, J. Qi, R. Zhang, Y. Chen and X. Du, Mapreduce based location selection algorithm for utility maximization with capacity constraints, Computing, 97 (2015), 403-423. doi: 10.1007/s00607-013-0382-5. [24] P. H. Tseng and K. T. Lee, A femto-aided location tracking algorithm in lte-a heterogeneous networks, IEEE Transactions on Vehicular Technology, 66 (2017), 748-762. [25] G. Weckman, Applying genetic algorithm to a new location and routing model of hazardous materials, International Journal of Production Research, 53 (2015), 916-928. [26] W. Yi, Assessment study on brain wave predictive ability to policemen's safety law enforcement, Journal of Discrete Mathematical Sciences and Cryptography, 20 (2017), 193-204. [27] J. J. Zhang and K. Qiang, Modeling of complex information system based on hierarchical decision-making theory, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 137-148.
Model of pin hole imaging
Diagram of corner system $\varphi, \omega$ and $\kappa$
Comparison of the calculated position and the actual position of a ship
Comparison of calculate longitude and actual longitude of ship
Comparison of the calculated latitudes and the actual latitudes of the ship
the time used for positioning by the three different methods
test data table of the target location algorithm
 Target Ship 1 Ship 2 Ship 3 Ship 4 Algorithm parameters $\Phi (^{\circ})$ 32 39 31 29 $\omega (^{\circ})$ -1 -1 -1 -1 $\kappa (^{\circ})$ 0.2 0.2 0.2 0.2 x(mm) 14 -16 -1 -23 y(mm) 9 2 -9 -7 f(mm) 148.51 155 148.51 133 X$_{C}$(m) -2734008.694 -2733672.0788 -2734008.694 -2733672.0788 Y$_{C}$(m) 5120687.4680 5121154.1044 5120687.4680 5121154.1044 Z$_{C}$(m) 2634082.8485 2633528.7010 2634082.8485 2633528.7010 Calculated coordinate 118$^{\circ}$05.872'E, 118$^{\circ}$05.572'E, 118$^{\circ}$05.883'E, 118$^{\circ}$05.586'E, 24$^{\circ}$33.109'N 24$^{\circ}$32.779'N 24$^{\circ}$33.112'N 24$^{\circ}$32.773'N Actual coordinate 118$^{\circ}$05.906'E, 118$^{\circ}$05.493'E, 118$^{\circ}$05.896'E, 118$^{\circ}$05.464'E, 24$^{\circ}$33.055'N 24$^{\circ}$32.700'N 24$^{\circ}$33.050'N 24$^{\circ}$32.655'N Error Longitude/' 0.034 0.079 0.013 0.122 Latitude/' 0.054 0.079 0.062 0.118
 Target Ship 1 Ship 2 Ship 3 Ship 4 Algorithm parameters $\Phi (^{\circ})$ 32 39 31 29 $\omega (^{\circ})$ -1 -1 -1 -1 $\kappa (^{\circ})$ 0.2 0.2 0.2 0.2 x(mm) 14 -16 -1 -23 y(mm) 9 2 -9 -7 f(mm) 148.51 155 148.51 133 X$_{C}$(m) -2734008.694 -2733672.0788 -2734008.694 -2733672.0788 Y$_{C}$(m) 5120687.4680 5121154.1044 5120687.4680 5121154.1044 Z$_{C}$(m) 2634082.8485 2633528.7010 2634082.8485 2633528.7010 Calculated coordinate 118$^{\circ}$05.872'E, 118$^{\circ}$05.572'E, 118$^{\circ}$05.883'E, 118$^{\circ}$05.586'E, 24$^{\circ}$33.109'N 24$^{\circ}$32.779'N 24$^{\circ}$33.112'N 24$^{\circ}$32.773'N Actual coordinate 118$^{\circ}$05.906'E, 118$^{\circ}$05.493'E, 118$^{\circ}$05.896'E, 118$^{\circ}$05.464'E, 24$^{\circ}$33.055'N 24$^{\circ}$32.700'N 24$^{\circ}$33.050'N 24$^{\circ}$32.655'N Error Longitude/' 0.034 0.079 0.013 0.122 Latitude/' 0.054 0.079 0.062 0.118
test data table of the target location algorithm
 Target Ship 5 Ship 6 Ship 7 Ship 8 Algorithm parameters $\Phi (^{\circ})$ 21 24 25 25 $\omega (^{\circ})$ $-$1 $-$1 $-$1 $-$1 $\kappa (^{\circ})$ 0.2 0.2 0.2 0.2 x(mm) $-$7 $-$9 $-$11 $-$2 y(mm) $-$12 $-$11 $-$5 $-$5 f(mm) 166 155 155 126.6 X$_{C}$(m) $-$2733672.0788 $-$2733672.0788 $-$2733672.0788 $-$2733672.0788 Y$_{C}$(m) 5121154.1044 5121154.1044 5121154.1044 5121154.1044 Z$_{C}$(m) 2633528.7010 2633528.7010 2633528.7010 2633528.7010 Calculated coordinate 118$^{\circ}$05.587'E, 118$^{\circ}$05.586'E, 118$^{\circ}$05.583'E, 118$^{\circ}$05.580'E, 24$^{\circ}$32.774'N 24$^{\circ}$32.775'N 24$^{\circ}$32.773'N 24$^{\circ}$32.776'N Actual coordinate 118$^{\circ}$05.594'E, 118$^{\circ}$05.480'E, 118$^{\circ}$05.427'E, 118$^{\circ}$05.459'E, 24$^{\circ}$32.798'N 24$^{\circ}$32.676'N 24$^{\circ}$32.669'N 24$^{\circ}$32.690'N Error Longitude/' 0.007 0.106 0.156 0.121 Latitude/' 0.024 0.099 0.104 0.086
 Target Ship 5 Ship 6 Ship 7 Ship 8 Algorithm parameters $\Phi (^{\circ})$ 21 24 25 25 $\omega (^{\circ})$ $-$1 $-$1 $-$1 $-$1 $\kappa (^{\circ})$ 0.2 0.2 0.2 0.2 x(mm) $-$7 $-$9 $-$11 $-$2 y(mm) $-$12 $-$11 $-$5 $-$5 f(mm) 166 155 155 126.6 X$_{C}$(m) $-$2733672.0788 $-$2733672.0788 $-$2733672.0788 $-$2733672.0788 Y$_{C}$(m) 5121154.1044 5121154.1044 5121154.1044 5121154.1044 Z$_{C}$(m) 2633528.7010 2633528.7010 2633528.7010 2633528.7010 Calculated coordinate 118$^{\circ}$05.587'E, 118$^{\circ}$05.586'E, 118$^{\circ}$05.583'E, 118$^{\circ}$05.580'E, 24$^{\circ}$32.774'N 24$^{\circ}$32.775'N 24$^{\circ}$32.773'N 24$^{\circ}$32.776'N Actual coordinate 118$^{\circ}$05.594'E, 118$^{\circ}$05.480'E, 118$^{\circ}$05.427'E, 118$^{\circ}$05.459'E, 24$^{\circ}$32.798'N 24$^{\circ}$32.676'N 24$^{\circ}$32.669'N 24$^{\circ}$32.690'N Error Longitude/' 0.007 0.106 0.156 0.121 Latitude/' 0.024 0.099 0.104 0.086
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