An improved atomic search algorithm for optimization and application in ML DOA estimation of vector hydrophone array

Peng Wang; Weijia He; Fan Guo; Xuefang He; Jiajun Huang; Peng Wang; Weijia He; Fan Guo; Xuefang He; Jiajun Huang

doi:10.3934/math.2022308

AIMS Mathematics

2022, Volume 7, Issue 4: 5563-5593. doi: 10.3934/math.2022308

Previous Article Next Article

Research article

An improved atomic search algorithm for optimization and application in ML DOA estimation of vector hydrophone array

Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China

Received: 30 September 2021 Revised: 22 December 2021 Accepted: 03 January 2022 Published: 10 January 2022
MSC : 65K05, 65K10

The atom search optimization (ASO) algorithm has the characteristics of fewer parameters and better performance than the traditional intelligent optimization algorithms, but it is found that ASO may easily fall into local optimum and its accuracy is not higher. Therefore, based on the idea of speed update in particle swarm optimization (PSO), an improved atomic search optimization (IASO) algorithm is proposed in this paper. Compared with traditional ASO, IASO has a faster convergence speed and higher precision for 23 benchmark functions. IASO algorithm has been successfully applied to maximum likelihood (ML) estimator for the direction of arrival (DOA), under the conditions of the different number of signal sources, different signal-to-noise ratio (SNR) and different population size, the simulation results show that ML estimator with IASO algorithum has faster convergence speed, fewer iterations and lower root mean square error (RMSE) than ML estimator with ASO, sine cosine algorithm (SCA), genetic algorithm (GA) and particle swarm optimization (PSO). Therefore, the proposed algorithm holds great potential for not only guaranteeing the estimation accuracy but also greatly reducing the computational complexity of multidimensional nonlinear optimization of ML estimator.
- atom search algorithm (ASO),
- improved ASO algorithm (IASO),
- maximum likelihood (ML),
- direction of arrival (DOA)
Citation: Peng Wang, Weijia He, Fan Guo, Xuefang He, Jiajun Huang. An improved atomic search algorithm for optimization and application in ML DOA estimation of vector hydrophone array[J]. AIMS Mathematics, 2022, 7(4): 5563-5593. doi: 10.3934/math.2022308

Related Papers:

Abstract

The atom search optimization (ASO) algorithm has the characteristics of fewer parameters and better performance than the traditional intelligent optimization algorithms, but it is found that ASO may easily fall into local optimum and its accuracy is not higher. Therefore, based on the idea of speed update in particle swarm optimization (PSO), an improved atomic search optimization (IASO) algorithm is proposed in this paper. Compared with traditional ASO, IASO has a faster convergence speed and higher precision for 23 benchmark functions. IASO algorithm has been successfully applied to maximum likelihood (ML) estimator for the direction of arrival (DOA), under the conditions of the different number of signal sources, different signal-to-noise ratio (SNR) and different population size, the simulation results show that ML estimator with IASO algorithum has faster convergence speed, fewer iterations and lower root mean square error (RMSE) than ML estimator with ASO, sine cosine algorithm (SCA), genetic algorithm (GA) and particle swarm optimization (PSO). Therefore, the proposed algorithm holds great potential for not only guaranteeing the estimation accuracy but also greatly reducing the computational complexity of multidimensional nonlinear optimization of ML estimator.

References

[1]	B. Jiao, Z. Lian, X. Gu, A dynamic inertia weight particle swarm optimization algorithm, Chaos Soliton Fract, 37 (2008), 698–705. https://doi.org/10.1016/j.chaos.2006.09.063 doi: 10.1016/j.chaos.2006.09.063
[2]	D. E. Goldberg, Genetic algorithm in search optimization and machine learning, Addison Wesley, 8 (1989), 2104–2116. https://dl.acm.org/doi/book/10.5555/534133 doi: 10.5555/534133
[3]	S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, Optimization by simulated annealing, Readings Computer Vision, 220 (1983), 671–680. https://doi.org/10.1126/science.220.4598.671 doi: 10.1126/science.220.4598.671
[4]	S. Mirjalili, SCA: A Sine Cosine Algorithm for solving optimization problems, Knowl-based Syst., 96 (2016), 120–133. https://doi.org/10.1016/j.knosys.2015.12.022 doi: 10.1016/j.knosys.2015.12.022
[5]	Z. Zhang, J. Lin, Y. Shi, Application of artificial bee colony algorithm to maximum likelihood DOA estimation, J. Bionic. Eng., 10 (2013), 100–109. https://doi.org/10.1016/S1672-6529(13)60204-8 doi: 10.1016/S1672-6529(13)60204-8
[6]	S. Feng, Z. Zhang, Y. Shi, Introduction of bat algorithm into maximum likelihood DOA estimation, Modern Electronics Technique, 39 (2016), 26–29. https://doi.org/10.16652/j.issn.1004-373x.2016.08.007 doi: 10.16652/j.issn.1004-373x.2016.08.007
[7]	X. Fan, L. Pang, P. Shi, G. Li, X. Zhang, Application of bee evolutionary genetic algorithm to maximum likelihood direction-of-arrival estimation, Math. Probl. Eng., 2019 (2019), 1–11. https://doi.org/10.1155/2019/6035870 doi: 10.1155/2019/6035870
[8]	M. Jain, V. Singh, A. Rani, A novel nature-inspired algorithm for optimization: Squirrel search algorithm, Swarm Evol. Comput., 44 (2018), 148–175. https://doi.org/10.1016/j.swevo.2018.02.013 doi: 10.1016/j.swevo.2018.02.013
[9]	W. Zhao, L. Wang, Z. Zhang, Atom search optimization and its application to solve a hydrogeologic parameter estimation problem, Knowl-based Syst., 163 (2018), 283–304. https://doi.org/10.1016/j.knosys.2018.08.030 doi: 10.1016/j.knosys.2018.08.030
[10]	H. C. Corben, P. Stehle, Classical Mechanics, Physics Today, 6 (1953). https://doi.org/10.1063/1.3061288 doi: 10.1063/1.3061288
[11]	J. P. Ryckaert, G. Ciccotti, H. J. C Berendsen, Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes, J. Comput. Phys., 23 (1977), 327–341. https://doi.org/10.1016/0021-9991(77)90098-5 doi: 10.1016/0021-9991(77)90098-5
[12]	A. Stone, The theory of intermolecular forces, Pure. Appl. Chem., 51 (1979), 1627–1636. https://doi.org/10.1351/pac197951081627 doi: 10.1351/pac197951081627
[13]	J. E. Jones, On the determination of molecular fields Ⅱ. From the equation of state of a gas, P. Roy. Soc. A-Math. Phy., 106 (1924), 463–477. https://doi.org/10.2307/94265 doi: 10.2307/94265
[14]	W. Zhao, L. Wang, Z. Zhang, A novel atom search optimization for dispersion coefficient estimation in groundwater, Future Gener Comp. Sy., 91 (2018), 601–610. https://doi.org/10.1016/j.future.2018.05.037 doi: 10.1016/j.future.2018.05.037
[15]	A. M. Agwa, A. A. El-Fergany, G. M. Sarhan, Steady-State modeling of fuel cells based on atom search optimizer, Energies, 12 (2019), 1884. https://doi.org/10.3390/en12101884 doi: 10.3390/en12101884
[16]	A. Almagboul Mohammed, F. Shu, Y. Qian, X. Zhou, J. Wang, J. Hu, Atom search optimization algorithm based hybrid antenna array receive beamforming to control sidelobe level and steering the null, Aeu-int J. Electron. C., 111 (2019), 152854. https://doi.org/10.1016/j.aeue.2019.152854 doi: 10.1016/j.aeue.2019.152854
[17]	S. Barshandeh, A new hybrid chaotic atom search optimization based on tree-seed algorithm and Levy flight for solving optimization problems, Eng. Comput-germany, 37 (2021), 3079–3122. https://doi.org/10.1007/s00366-020-00994-0 doi: 10.1007/s00366-020-00994-0
[18]	K. K. Ghosh, R. Guha, S. Ghosh, S. K. Bera, R. Sarkar, Atom Search Optimization with Simulated Annealing-a Hybrid Metaheuristic Approach for Feature Selection, arXiv preprint arXiv: 2005.08642, (2020). https://arXiv.org/pdf/2005.08642v1
[19]	M. A. Elaziz, N. Nabil, A. A. Ewees, S. Lu, Automatic data clustering based on hybrid atom search optimization and Sine-Cosine algorithm, 2019 IEEE Congress on Evolutionary Computation (CEC), (2019), 2315–2322. https://doi.org/10.1109/CEC.2019.8790361 doi: 10.1109/CEC.2019.8790361
[20]	P. Sun, H. Liu, Y. Zhang, L. Tu, Q. Meng, An intensify atom search optimization for engineering design problems, Appl. Math. Model., 89 (2021), 837–859. https://doi.org/10.1016/j.apm.2020.07.052 doi: 10.1016/j.apm.2020.07.052
[21]	L. Xu, J. Chen, Y. Gao, Off-Grid DOA estimation based on sparse representation and rife algorithm, Microelectron J., 59 (2017), 193–201. https://doi.org/10.2528/PIERM17070404 doi: 10.2528/PIERM17070404
[22]	A. Peyman, Z. Kordrostami, K. Hassanli, Design of a MEMS bionic vector hydrophone with piezo-gated MOSFET readout, Prog. Electromagn Res. M., 98 (2020), 104748. https://doi.org/10.1016/j.mejo.2020.104748 doi: 10.1016/j.mejo.2020.104748
[23]	H. Song, M. Diao, T. Tang, J. Qin, Vector-Sensor Array DOA Estimation Based on Spatial Time-Frequency Distribution, 2018 Eighth International Conference on Instrumentation & Measurement, Computer, Communication and Control (IMCCC), (2020), 1351–1356. https://doi.org/10.1109/IMCCC.2018.00280 doi: 10.1109/IMCCC.2018.00280
[24]	M. Cao, X. Mao, L. Huang, Elevation, azimuth, and polarization estimation with nested electromagnetic vector-sensor arrays via tensor modeling, Eurasip J. Wirel. Comm., 2020 (2020), 153. https://doi.org/10.1186/s13638-020-01764-8 doi: 10.1186/s13638-020-01764-8
[25]	V. Baron, A. Finez, S. Bouley, F. Fayet, J. I. Mars, B. Nicolas, Hydrophone array optimization, conception, and validation for localization of acoustic sources in deep-Sea mining, IEEE J. Oceanic. Eng., 46 (2021), 555–563. https://doi.org/10.1109/JOE.2020.3004018 doi: 10.1109/JOE.2020.3004018
[26]	W. Wand, Q. Zhang, W. Shi, J. Shi, X. Wang, Iterative sparse covariance matrix fitting direction of arrival estimation method based on vector hydrophone array, Xibei Gongye Daxue Xuebao, 38 (2020), 14–23. https://doi.org/10.1051/jnwpu/20203810014 doi: 10.1051/jnwpu/20203810014
[27]	K. Aghababaiyan, R. G.Zefreh, V. Shah-Mansouri, 3D-OMP and 3D-FOMP algorithms for DOA estimation, Phys. Commun-amst, 31 (2018), 87–95. https://doi.org/10.1016/j.phycom.2018.10.005 doi: 10.1016/j.phycom.2018.10.005
[28]	K. Aghababaiyan, V. Shah-Mansouri, B. Maham, High-precision OMP-based direction of arrival estimation scheme for hybrid non-uniform array, IEEE Commun. Lett., 24 (2019), 354–357. https://doi.org/10.1109/LCOMM.2019.2952595 doi: 10.1109/LCOMM.2019.2952595
[29]	A. Nehorai, E. Paldi, , Acoustic vector-sensor array processing, IEEE T. Signal. Proces., 42 (1994), 2481–2491. https://doi.org/10.1109/ACSSC.1992.269285 doi: 10.1109/ACSSC.1992.269285
[30]	K. T. Wong, M. D. Zoltowski, Root-MUSIC-based azimuth-elevation angle-of-arrival estimation with uniformly spaced but arbitrarily oriented velocity hydrophones, IEEE T. Signal. Proces., 47 (1999), 3250–3260. https://doi.org/10.1109/78.806070 doi: 10.1109/78.806070
[31]	K. T. Wong, M. D. Zoltowski, Uni-vector-sensor ESPRIT for multisource azimuth, elevation, and polarization estimatio, IEEE T. Antenn. Propag., 45 (1997), 1467–1474. https://doi.org/10.1109/8.633852 doi: 10.1109/8.633852
[32]	I. Ziskind, M. Wax, Maximum likelihood localization of multiple sources by alternating projection, IEEE Trans. Acoust. Speech Signal Process, 36 (1988), 1553–1560. https://doi.org/10.1109/29.7543 doi: 10.1109/29.7543
[33]	M. Feder, E. Weinstein, Parameter estimation of superimposed signals using the EM algorithm, IEEE Trans. Acoust. Speech Signal Process, 36 (1988), 477–489. https://doi.org/10.1109/29.1552 doi: 10.1109/29.1552
[34]	Y. Zheng, L. Liu, X. Yang, SPICE-ML Algorithm for Direction-of-Arrival Estimation, Sensors, 20 (2019), 119. https://doi.org/10.3390/s20010119 doi: 10.3390/s20010119
[35]	Y. Hu, J. Lu, X. Qiu, Direction of arrival estimation of multiple acoustic sources using a maximum likelihood method in the spherical harmonic domain, Appl. Acoust., 135 (2018), 85–90. https://doi.org/10.1016/j.apacoust.2018.02.005 doi: 10.1016/j.apacoust.2018.02.005
[36]	J. W. Paik, K. H. Lee, J. H. Lee, Asymptotic performance analysis of maximum likelihood algorithm for direction-of-arrival estimation: Explicit expression of estimation error and mean square error, Applied Sciences, 10 (2020), 2415. https://doi.org/10.3390/app10072415 doi: 10.3390/app10072415
[37]	S. Jesus, Efficient ML direction of arrival estimation assuming unknown sensor noise powers, arXiv preprint arXiv: 2001.01935, (2020), https: //arXiv: 2001.01935
[38]	Y. Yoon, Y. H. Kim, Optimizing taxon addition order and branch lengths in the construction of phylogenetic trees using maximum likelihood, J. Bioinf. Comput. Biol., 18 (2020), 837–859. https://doi.org/10.1142/S0219720020500031 doi: 10.1142/S0219720020500031
[39]	P. Vishnu, C. S. Ramalingam, An improved LSF-based algorithm for sinusoidal frequency estimation that achieves maximum likelihood performance, 2020 International Conference on Signal Processing and Communications (SPCOM), (2020), 1–5. https://doi.org/10.1109/SPCOM50965.2020.9179546
[40]	M. Li, Y. Lu, Genetic algorithm based maximum likelihood DOA estimation, RADAR 2002, 2002 (2002), 502–506. https://doi.org/10.1109/RADAR.2002.1174766 doi: 10.1109/RADAR.2002.1174766
[41]	A. Sharma, S. Mathur, Comparative analysis of ML-PSO DOA estimation with conventional techniques in varied multipath channel environment, Wireless Pers. Commun., 100 (2018), 803–817. https://doi.org/10.1007/s11277-018-5350-0 doi: 10.1007/s11277-018-5350-0
[42]	P. Wang, Y. Kong, X. He, M. Zhang, X. Tan, An improved squirrel search algorithm for maximum likelihood DOA estimation and application for MEMS vector hydrophone array, IEEE Access, 7 (2019), 118343–118358. https://doi.org/10.1109/ACCESS.2019.2936823 doi: 10.1109/ACCESS.2019.2936823
[43]	L. Cai, H. Tian, H. Chen, J. Hu, A random maximum likelihood algorithm based on limited PSO initial space, Computer Modernization, 282 (2019), 60–65. https://doi.org/10.3969/j.issn.1006-2475.2019.02.011 doi: 10.3969/j.issn.1006-2475.2019.02.011

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)