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Designing INS/GNSS integrated navigation systems by using IPO algorithms

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Abstract

The application of soft computing techniques can be largely found in engineering sciences. These include the design and optimization of navigation systems for use in land, sea, and air transportation systems. In this paper, an attempt is made to leverage on novel metaheuristic optimization approaches for designing integrated navigation systems. For this purpose, a simplified version of the inclined planes system optimization (called SIPO) algorithm alongside its two standard and modified versions are used in comparison with the two conventional methods of genetic algorithm and particle swarm optimization. Considerations are made on an INS/GNSS problem with IMU MEMS modules. Outputs are presented in terms of statistical and performance indicators, such as runtime, fitness, convergence, navigation accuracy (velocity, latitude, longitude, altitude, roll, pitch, yaw), and routing along with the ranking of algorithms. Competitive performance and relative superiority of the standard IPO over other methods in evaluating results have been confirmed. So that compared to other state-of-the-art algorithms (GA, PSO, IPO, and MIPO), the best runtime rank with a value of 6/4 by SIPO and the best performance rank of fitness, navigation accuracy for the two assumed IMU modules, and the total rank with values of 4/4, 149/60, 165/60, and 332/128 obtained by IPO, respectively.

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Data availability statement

All data generated or analyzed during this study are included in this published article (and its supplementary information files).

References

  1. Bar-Shalom Y, Li XR, Kirubarajan T (2004) Estimation with applications to tracking and navigation: theory algorithms and software, 1st edn. Wiley

    Google Scholar 

  2. Brown RG, Hwang PYC (2012) Introduction to random signals and applied Kalman filtering: with MATLAB exercises and solutions, 4th edn. Wiley, Hoboken

    MATH  Google Scholar 

  3. Farrell J (2008) Aided navigation: GPS with high rate sensors, 1st edn. McGraw-Hill Inc, New York

    Google Scholar 

  4. Minkler G, Minkler J (1993) Theory and applications of Kalman filtering. Magellan Book Company

  5. Khan N, Jabbar A, Bilal H, Gul U (2020) Compensated closed-loop Kalman filtering for nonlinear systems. Measurement 151:107129

    Google Scholar 

  6. Cui Y, Wang Z (2021) “Auto-calibration Kalman filters for non-linear systems with direct feedthrough. IET Control Theory Appl 15(6):890–899

    Google Scholar 

  7. Urrea C, Agramonte R (2021) Kalman filter: historical overview and review of its use in robotics 60 years after its creation. J Sens 2021:9674015

    Google Scholar 

  8. Shakhtarin BI, Shen K, Neusypin KA (2016) Modification of the nonlinear kalman filter in a correction scheme of aircraft navigation systems. J Commun Technol Electron 61(11):1252–1258

    Google Scholar 

  9. Zheng B, Fu P, Li B, Yuan X (2018) A robust adaptive unscented kalman filter for nonlinear estimation with uncertain noise covariance. Sensors 18(3):1–15

    Google Scholar 

  10. Psiaki ML (2005) Backward-smoothing extended Kalman filter. J Guid Control Dyn 28(5):885–894

    Google Scholar 

  11. Nguyen NH, Doğançay K (2017) Improved pseudolinear Kalman filter algorithms for bearings-only target tracking. IEEE Trans Signal Process 65(23):6119–6134

    MathSciNet  MATH  Google Scholar 

  12. Chang L, Hu B, Chang G, Li A (2013) Robust derivative-free Kalman filter based on Huber’s M-estimation methodology. J Process Control 23(10):1555–1561

    Google Scholar 

  13. Rigatos G, Siano P, Zervos N, Cecati C (2015) Control and disturbances compensation for doubly fed induction generators using the derivative-free nonlinear Kalman filter. IEEE Trans Power Electron 30(10):5532–5547

    Google Scholar 

  14. Fang J, Gong X (2010) Predictive iterated Kalman filter for INS/GPS integration and Its application to SAR motion compensation. IEEE Trans Instrum Meas 59(4):909–915

    Google Scholar 

  15. Bai Y-T, Wang X-Y, Jin X-B, Zhao Z-Y, Zhang B-H (2020) A neuron-based Kalman filter with nonlinear autoregressive model. Sensors (Basel) 20(1):299

    Google Scholar 

  16. Julier SJ, Uhlmann JK (1997) New extension of the Kalman filter to nonlinear systems. Signal Process Sens Fus Target Recognit VI 3068:182–193

    Google Scholar 

  17. Ristic B, Arulampalam S, Gordon N (2004) Beyond the Kalman filter: Particle filters for tracking applications. Illustrate. Artech Print on Demand

  18. Sathiya V, Chinnadurai M (2019) Evolutionary algorithms-based multi-objective optimal mobile robot trajectory planning. Robotica 37(8):1363–1382

    Google Scholar 

  19. Jalali SMJ, Khosravi A, Kebria PM, Hedjam R, Nahavandi S (2019) Autonomous robot navigation system using the evolutionary multi-verse optimizer algorithm. In: 2019 IEEE international conference on systems, man and cybernetics (SMC), 2019, pp. 1221–1226.

  20. Liu Q, Li Y, Liu L (2020) A 3D simulation environment and navigation approach for robot navigation via deep reinforcement learning in dense pedestrian environment. In: 2020 IEEE 16th International Conference on Automation Science and Engineering (CASE), 2020, pp. 1514–1519

  21. Cong L, Yue S, Qin H, Li B, Yao J (2020) Implementation of a MEMS-based GNSS/INS integrated scheme using supported vector machine for land vehicle navigation. IEEE Sens J 20(23):14423–14435

    Google Scholar 

  22. Yi J-H, Lu M, Zhao X-J (2020) Quantum inspired monarch butterfly optimisation for UCAV path planning navigation problem. Int J Bio-Inspired Comput 15(2):75–89

    Google Scholar 

  23. Bellemare MG et al (2020) Autonomous navigation of stratospheric balloons using reinforcement learning. Nature 588(7836):77–82

    Google Scholar 

  24. Al Bitar N, Gavrilov AI (2020) Neural networks aided unscented Kalman filter for integrated INS/GNSS systems. In: 2020 27th Saint Petersburg International Conference on Integrated Navigation Systems (ICINS), 2020, pp. 1–4.

  25. Wang J, Ma Z, Chen X (2021) Generalized Dynamic Fuzzy NN Model Based on Multiple Fading Factors SCKF and its Application in Integrated Navigation. IEEE Sens J 21(3):3680–3693

    Google Scholar 

  26. Gul F, Rahiman W, Alhady SSN, Ali A, Mir I, Jalil A (2021) Meta-heuristic approach for solving multi-objective path planning for autonomous guided robot using PSO–GWO optimization algorithm with evolutionary programming. J Ambient Intell Humaniz Comput 12(7):7873–7890

    Google Scholar 

  27. Zieliński P, Markowska-Kaczmar U (2021) 3D robotic navigation using a vision-based deep reinforcement learning model. Appl Soft Comput 110:107602

    Google Scholar 

  28. Gao D, Lyu X, Qin F, Chang L, Hu B (2021) A real time gravity compensation method for high precision INS based on neural network. In: 2021 28th Saint Petersburg international conference on integrated navigation systems (ICINS), 2021, pp. 1–5

  29. Wen S, Wen Z, Zhang D, Zhang H, Wang T (2021) A multi-robot path-planning algorithm for autonomous navigation using meta-reinforcement learning based on transfer learning. Appl Soft Comput 110:107605

    Google Scholar 

  30. Al Bitar N, Gavrilov A (2021) A novel approach for aiding unscented Kalman filter for bridging GNSS outages in integrated navigation systems. Navigation 68(3):521–539

    Google Scholar 

  31. Yan F, Li S, Zhang E, Guo J, Chen Q (2021) An adaptive nonlinear filter for integrated navigation systems using deep neural networks. Neurocomputing 446:130–144

    Google Scholar 

  32. Wu Y (2021) A survey on population-based meta-heuristic algorithms for motion planning of aircraft. Swarm Evol Comput 62:100844

    Google Scholar 

  33. Silva C, Ribeiro B (2003) Navigating mobile robots with a modular neural architecture. Neural Comput Appl 12(3):200–211

    Google Scholar 

  34. Braga APS, Araújo AFR (2003) A topological reinforcement learning agent for navigation. Neural Comput Appl 12(3):220–236

    Google Scholar 

  35. Do Q, Jain L (2010) Application of neural processing paradigm in visual landmark recognition and autonomous robot navigation. Neural Comput Appl 19(2):237–254

    Google Scholar 

  36. Kan EM, Lim MH, Ong YS, Tan AH, Yeo SP (2013) Extreme learning machine terrain-based navigation for unmanned aerial vehicles. Neural Comput Appl 22(3):469–477

    Google Scholar 

  37. El-Shafie A, Najah A, Karim OA (2014) Amplified wavelet-ANFIS-based model for GPS/INS integration to enhance vehicular navigation system. Neural Comput Appl 24(7):1905–1916

    Google Scholar 

  38. Guo C, Li F, Tian Z, Guo W, Tan S (2020) Intelligent active fault-tolerant system for multi-source integrated navigation system based on deep neural network. Neural Comput Appl 32(22):16857–16874

    Google Scholar 

  39. Hodge VJ, Hawkins R, Alexander R (2021) Deep reinforcement learning for drone navigation using sensor data. Neural Comput Appl 33(6):2015–2033

    Google Scholar 

  40. Fu C et al (2022) Memory-enhanced deep reinforcement learning for UAV navigation in 3D environment. Neural Comput Appl 34(17):14599–14607

    Google Scholar 

  41. Luo Q, Shao Y, Li J, Yan X, Liu C (2022) A multi-AUV cooperative navigation method based on the augmented adaptive embedded cubature Kalman filter algorithm. Neural Comput Appl 34(21):18975–18992

    Google Scholar 

  42. Millán-Arias C, Fernandes B, Cruz F (2022) Proxemic behavior in navigation tasks using reinforcement learning. Neural Comput Appl

  43. Herrera EP, Kaufmann H (2010) Adaptive methods of Kalman filtering for personal positioning systems. In: Proceedings of the 23rd international technical meeting of the satellite division of the institute of navigation (ION GNSS 2010), 2010, pp. 584–589

  44. Mohamed AH, Schwarz KP (1999) Adaptive Kalman filtering for INS/GPS. J Geod 73(4):193–203

    MATH  Google Scholar 

  45. Hide C, Moore T, Smith M (2003) Adaptive Kalman filtering for low-cost INS/GPS. J Navig 56(1):143–152

    Google Scholar 

  46. Hide C, Moore T, Smith M (2004) Adaptive Kalman filtering algorithms for integrating GPS and low cost INS. In: PLANS 2004. Position location and navigation symposium (IEEE Cat. No.04CH37556), 2004, pp. 227–233

  47. Gao W, Yang Y, Cui X, Zhang S (2007) Application of adaptive Kalman filtering algorithm in IMU/GPS integrated navigation system. Geo-spatial Inf Sci 10(1):22–26

    Google Scholar 

  48. Zhang L, Wang S, Selezneva MS, Neusypin KA (2021) A new adaptive Kalman filter for navigation systems of carrier-based aircraft. Chinese J Aeronaut (in Press)

  49. Mozaffari MH, Abdy H, Zahiri SH (2016) IPO: an inclined planes system optimization algorithm. Comput Inform 35(1):222–240

    MathSciNet  MATH  Google Scholar 

  50. Mohammadi A, Zahiri SH (2017) IIR model identification using a modified inclined planes system optimization algorithm. Artif Intell Rev 48(2):237–259

    Google Scholar 

  51. Mohammadi-Esfahrood S, Mohammadi A, Zahiri SH (2019) A Simplified and efficient version of inclined planes system optimization algorithm. In: 2019 5th Conference on Knowledge Based Engineering and Innovation (KBEI), 2019, pp. 504–509

  52. Gonzalez R, Giribet JI, Patino HD (2015) NaveGo: a simulation framework for low-cost integrated navigation systems. J Control Eng Appl Inform 17(2):110–120

    Google Scholar 

  53. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Publishing Company

  54. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, 1995, vol 4, pp. 1942–1948.

  55. Georgy JFW (2010) Advanced nonlinear techniques for low cost land vehicle navigation. Queen’s University

  56. Abdul Rahim K (2012) Heading drift mitigation for low-cost inertial pedestrian navigation. University of Nottingham

  57. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press

  58. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B. 26(1):29–41

  59. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    MathSciNet  MATH  Google Scholar 

  60. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (Ny) 179(13):2232–2248

    MATH  Google Scholar 

  61. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  62. Price K, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer-Verlag, Berlin Heidelberg

    MATH  Google Scholar 

  63. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31

    Google Scholar 

  64. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  65. Lin C-W, Zhang B, Yang K-T, Hong T-P (2014) Efficiently hiding sensitive itemsets with transaction deletion based on genetic algorithms. Sci World J 2014:398269

    Google Scholar 

  66. Lin JC-W, Liu Q, Fournier-Viger P, Hong T-P, Voznak M, Zhan J (2016) A sanitization approach for hiding sensitive itemsets based on particle swarm optimization. Eng Appl Artif Intell 53:1–18

    Google Scholar 

  67. Djenouri Y, Djenouri D, Belhadi A, Fournier-Viger P, Lin JC-W (2018) A new framework for metaheuristic-based frequent itemset mining. Appl Intell 48(12):4775–4791

    MATH  Google Scholar 

  68. Lin JCW, Lv Q, Yu D, Srivastava G, Chen CH (2022) Adaptive particle swarm optimization model for resource leveling. Evol. Syst

  69. Mohammadi A, Sheikholeslam F, Emami M (2022) Metaheuristic algorithms for integrated navigation systems. In: Computational Intelligence for Unmanned Aerial Vehicles Communication Networks, First Edit., M. Ouaissa, I. U. Khan, M. Ouaissa, Z. Boulouard, and S. B. Hussain Shah, Eds. Cham: Springer International Publishing, 2022, pp. 45–72

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Ali Mohammadi & Farid Sheikholeslam

  2. Department of Electrical and Computer Engineering, Esfarayen University of Technology, Esfarayen, 96619-98195, Iran

    Ali Mohammadi

  3. Department of Electrical and Computer Engineering, Yazd University, Yazd, 89158-18411, Iran

    Mehdi Emami

  4. Centre for Artificial Intelligence Research and Optimization, Torrens University Australia, Brisbane, Australia

    Seyedali Mirjalili

  5. Yonsei Frontier Lab, Yonsei University, Seoul, South Korea

    Seyedali Mirjalili

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  1. Ali Mohammadi
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  2. Farid Sheikholeslam
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  4. Seyedali Mirjalili
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Correspondence to Ali Mohammadi.

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Publisher's Note

All data generated or analyzed during this study are included in this published article (and its supplementary information files).

Appendix

Appendix

Note that variables with subscript (-) correspond to the previous sample (such as t(k-1)), and (+) to the next sample (such as t(k+1)); the tilde symbol (-) is for noisy measurements, and the estimated variables based on these measurements also have a hat (^); Finally, an entry-wise product is expressed by the symbol ‘○’.

All source codes are fully and publicly available at https://github.com/ali-ece

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Mohammadi, A., Sheikholeslam, F., Emami, M. et al. Designing INS/GNSS integrated navigation systems by using IPO algorithms. Neural Comput & Applic 35, 15461–15475 (2023). https://doi.org/10.1007/s00521-023-08517-w

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  • DOI: https://doi.org/10.1007/s00521-023-08517-w

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