Scientific- Research Quarterly of Geographical Data (SEPEHR)

Scientific- Research Quarterly of Geographical Data (SEPEHR)

Determination of the Additional Secondary Factor (ASF) of the ground-based navigation system (LPS) based on deep learning network

Document Type : Research Paper

Authors
Arman Saberi 1
Nemat Allah Ghahremani 2
Saeid Nasrollahi 3
Mohammad ali Keyvanrad 4
1 Ph.D Candidate of control engineering,, Faculty of electrical and computer engineering,, Malek Ashtar University of Technology, Tehran, Iran
2 Associate professor of control engineering,, Faculty of electrical and computer engineering,, Malek Ashtar University of Technology, Tehran, Iran
3 Assistant professor of control engineering,, Faculty of electrical and computer engineering,, Malek Ashtar University of Technology, Tehran, Iran
4 Assistant professor of artificial intelligence, Faculty of electrical and computer engineering, Malek Ashtar University of Technology, Tehran, Iran
10.22131/sepehr.2025.2049922.3118
Abstract
Extended Abstract
Introduction
   The Loran terrestrial navigation system is recognized as one of the key systems for providing precise positioning services and improving navigation performance on a global scale. These systems transmit low-frequency (LF) electromagnetic waves to deliver highly accurate timing signals to ground users, enabling access to high-precision positioning data. However, the performance of these systems is significantly influenced by environmental and geographical factors, including land cover, elevation, surface temperature, humidity, electrical conductivity, and thermal conductivity. These factors can introduce an additional secondary factor (ASF) error, causing changes in the path and intensity of electromagnetic waves, which consequently reduce the accuracy and reliability of signals. The importance of analyzing these factors and developing models to mitigate their effects is particularly critical in areas with diverse geographical characteristics. Additionally, the complexity of environmental factors such as topographical and climatic variations necessitates advanced methods for modeling and analyzing their impacts. In this context, combining numerical methods with deep learning has emerged as an effective solution to reduce errors arising from these factors and improve the performance of terrestrial navigation systems.
Materials and Methods
1. Numerical Modeling Using the FDTD Method
   The finite-difference time-domain (FDTD) method is a powerful numerical approach for simulating electromagnetic wave propagation under various environmental conditions. By discretizing Maxwell's equations, this method effectively models the interaction between electromagnetic waves and complex environmental features. In this study, the research area includes 17 distinct land cover classes such as dense forests, water bodies, and arid regions, enabling a comprehensive analysis of the environmental influences on ASF values. This modeling enhances our understanding of the interaction between electromagnetic waves and environmental conditions, paving the way for more accurate solutions to reduce errors stemming from these influences.
2. Integration of Meteorological Data
   One of the main challenges in this study was the limited availability of meteorological data from weather stations. To address this issue, data from nine weather stations in the study area were integrated with MODIS (Moderate Resolution Imaging Spectroradiometer) satellite imagery. Satellite data, with its extensive spatial coverage and high temporal resolution, provides more accurate inputs for predicting environmental parameter changes. Variables such as temperature, humidity, and air pressure were processed and combined to enhance the quality of the model inputs. This data integration not only increased spatial and temporal resolution but also improved the accuracy of ASF predictions.
3. Deep Learning Using LSTM Networks
   Long short-term memory (LSTM) networks, a type of advanced deep learning model, are particularly well-suited for analyzing sequential data. In this study, LSTM networks were employed to predict the spatiotemporal distribution of meteorological parameters. These networks, by identifying long-term temporal dependencies in the data, significantly improved the accuracy of ASF predictions. The integration of inputs derived from the FDTD method and meteorological information provided a robust framework for analyzing the nonlinear relationships among environmental variables.
Results and Discussion
Key Findings
1- Impact of Land Cover: The results revealed that areas with dense vegetation and high electrical and thermal conductivity exhibited higher ASF values. This can be attributed to the significant influence of these land covers on the absorption and reflection of electromagnetic waves. Conversely, arid regions with low conductivity showed lower ASF values.
2- Impact of Elevation: Higher elevations were associated with increased ASF values. This increase is due to variations in atmospheric pressure and temperature at these elevations, which affect the path and intensity of electromagnetic waves.
3- Meteorological Relationships: The findings demonstrated a direct relationship between temperature, humidity, and ASF values. Warmer and more humid conditions amplified ASF errors, while cooler and drier conditions reduced these errors.
4- Temporal Variations: ASF values exhibited daily and seasonal variations, influenced by fluctuations in temperature and humidity over time. These variations necessitate periodic adjustments to maintain the accuracy of navigation systems.
Integration of Numerical Modeling and Deep Learning
   The results of this study demonstrated that combining the FDTD method with LSTM-based deep learning models provides an effective approach for mitigating ASF errors. The FDTD method accurately simulated complex environmental conditions, while the LSTM model identified long-term temporal patterns. This combination significantly enhanced the reliability of terrestrial navigation systems and reduced errors arising from environmental conditions.
Conclusion
   This study successfully integrated numerical modeling and deep learning to address the challenges associated with ASF errors in terrestrial navigation systems. The findings clearly highlighted the importance of considering environmental factors such as elevation, land cover, and meteorological conditions in improving the accuracy and performance of these systems. The proposed combined approach not only ensures the reduction of errors due to environmental conditions but also lays a foundation for future research in navigation and geospatial analyses.
Keywords
Additional Secondary Factor
Loran navigation system
Positioning
Deep learning network
Time difference error
Finite-difference time-domain method

Subjects

1.   Ali, S., & Smith, K. A. (2006). On learning algorithm selection for classification. Applied Soft Computing, 6(2), 119–138. https://doi.org/10.1016/j.asoc.2005.02.002
2.   Ali-Khah-Asal, M., & Naseri, D. (2017). Assessment of land cover change trends in the Khair Gota watershed using remote sensing methods. Journal of Environmental Science and Technology, 19
3.   Anderson, M. C., et al. (2008). A thermal-based remote sensing technique for routine mapping of land-surface carbon, water, and energy fluxes from field to regional scales. Remote Sensing of Environment, 112(12), 4227–4241. https://doi.org/10.1016/j.rse.2008.07.009
4.   Anismov, O. (2001). Prediction pattern of near surface air temperature using empirical data. Climatic Change, 50:297–315.
5.   Bai, S., Kolter, J. Z., & Koltun, V. (2018). “An empirical evaluation of generic convolutional and recurrent networks for sequence modeling.” arXiv preprint arXiv:1803.01271.
6.   Bannayan, M., & Hoogenboom, G. (2008). Daily weather sequence prediction realization using the non-parametric nearest neighbor re-sampling technique. Int. J. Climatol., 28(10), 1357–1368.
7.   Bannayan, M., & Hoogenboom, G. (2008). Weather Analogue: A tool for lead time simulation of daily weather data based on modified K-nearest-neighbor approach. Environmental Modeling and Software, 23, 703–713.
8.    Bhutiyani, M. R., Kale, V. S., & Pawar, N. J. (2007). Long-term trends in maximum, minimum and mean annual air temperatures across the Northwestern Himalaya during the twentieth century. Climatic Change, 85:159–177.
9.   Bolstad, P. V., Swift, L., Collins, F., & Regniere, J. (1998). Measured and predicted air temperatures at basin to regional scales in the southern Appalachian Mountains. Agricultural and Forest Meteorology, 91:161–176.
10.  Crespi, M., De Vendictis, L., Poli, D., Wolff, K., Colosimo, G., Gruen, A., & Volpe, F. (2008). Radiometric quality and DSM generation analysis of Cartosat-1 stereo imagery.
11. Fang, T. H., Kim, Y., Park, S. G., Seo, K., & Park, S. H. (2020). GPS and eLoran integrated navigation for marine applications using augmented measurement equation based on range domain. International Journal of Control, Automation and Systems, 18(9), 234–2359.
12. Galway, J. G. (1956). The lifted index as a predictor of latent instability. Bulletin of the American Meteorological Society, 37, 528–529. https://doi.org/10.1175/1520-0477-37.10.528
13. Gao, B.-C., & Kaufman, Y. J. (2000). The MODIS near-IR water vapor algorithm. Product ID: MOD05 -Total Precipitable Water. NASA MODIS Technical Report Series.
14. Hongjuan, Y., Lili, W., Yurong, P., & Xiaoli, X. (2017, October). Analysis of diurnal variation on long-wave ground wave propagation delay. In 2017 Sixth Asia-Pacific Conference on Antennas and Propagation (APCAP) (pp. 1–3). IEEE.
15. Jingmei, Y., & Jinhuan, Q. (1996). The empirical expressions of the relation between precipitable water and ground water vapor pressure for some areas in China. Scientia Atmospherica Sinica, 5.
16. Johler, J. R. (1956). Phase of the low frequency ground wave (Vel 573). US Department of Commerce, National Bureau of Standards.
17. Kazemi, M. Y., Mahdavi, Y., & Other Authors. (2011). Estimation of land cover and land use changes using remote sensing techniques and geographic information system
18. Kerr, Y. H., Lagouarde, J. P., & Imbernon, J. (1992). Accurate land surface temperature retrieval from AVHRR data with use of an improved split window algorithm. Remote Sensing of Environment, 41(2–3), 197–209. https://doi.org/10.1016/0034-4257(92)90063-P
19. Khesali, E., & Mobasheri, M. R. (2018). Air temperature image production at different times from a satellite pass time using weather stations data. 13th Symposium on Advances in Science and Technology.
20. Khesali, E., & Mobasheri, M. R. (2019). Prediction of areas at risk of frost using the NEAT model. Scientific-Research Quarterly of Geographical Data (SEPEHR), 28(111), 41–52.
21. Khesali, E., & Mobasheri, M. R. (2020). A method in near surface estimation of air temperature (NEAT) in times following the satellite passing time using MODIS images. Advances in Space Research, 65(10), 2339–2347.
22. Khesali, E., & Mobasheri, M. R. (2023). Near Surface Air Temperature Estimation Through Parametrization of Modis Products. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 10, 405-410.
23. Last, J. D., Williams, P., Peterson, B., & Dyksta, K. (2000, November). Propagation of Loran-C signals in irregular terrain: Modeling and measurements Part 1: Modeling. In 29th Annual Convention and Technical Symposium, International Loran Association, Washington DC, Washington USA (pp. 13–15).
24. Li, X. R., Zhu, Y., Wang, J., & Han, C. (2003). Optimal linear estimation fusion I. Unified fusion rules. IEEE Transactions on Information Theory, 49(9), 2192–2208.
25. Li, Z.-L., Tang, B.-H., Wu, H., Ren, H., Yan, G., Wan, Z., & others. (2013). Satellite-derived land surface temperature: Current status and perspectives. Remote Sensing of Environment, 131, 14–37. https://doi.org/10.1016/j.rse.2012.12.008
26. Li, Z. L., et al. (2018). “Satellite-derived land surface temperature: Current status and perspectives.” Remote Sensing of Environment.
27. Lomme, J. P., & Guilioni, L. (2004). A simple model for minimum crop temperature forecasting during nocturnal cooling. Agricultural and Forest Meteorology, 123(1–2), 55–68.
28. Lo, S., Enge, P., Boyce, L., Peterson, B., Gunther, T., Wenzel, B., & Carroll, K. (2002, September). The Loran integrity performance panel. In Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002) (pp. 1002–1012).
29. Lo, S., Leatham, M., Offermans, G., Gunther, G. T., Peterson, B., Johnson, G., & Enge, P. (2009). Defining primary, secondary, additional secondary factors for RTCM minimum performance specification. Research & Radionavigation.
30. Loran, C. (1992). User Handbook. US Department of Transportation, US Coast Guard, Commandant Publication P16562.5.
31. Martha, T. R., Kerle, N., van Westen, C. J., Jetten, V., & Vinod Kumar, K. (2010). Effect of sun elevation angle on DSMs derived from Cartosat-1 data. Photogrammetric Engineering and Remote Sensing, 76, 429–438.
32. Meng, B., Xi, X. L., & Li, J. (2009, July). ASF seasonal correction of Loran-C based on artificial neural network. In Proceedings of the IEEE 2009 National Aerospace & Electronics Conference (NAECON) (pp. 304–307). IEEE.
33. Mohsen, F., & Authors Group. (2009). Introduction to the positioning of Malek Ashtar University of Technology.
34- Moran, M. S., & Jackson, R. D. (1991). Assessing the spatial distribution of evapotranspiration using remotely sensed inputs. Journal of Environmental Quality, 20(4), 725–737. https://doi.org/10.2134/jeq1991.00472425002000040022x
35. Nandakumar, R., Amitabh Chamy, M. P. T., Kopparthi, S. S. S., Paswan, G., Prakash, S., & Singh, S. (2008). Synthesis of investigations under ISPRS-ISRO Cartosat-1 scientific assessment programme primarily for DSM generation. http://www.isprs.org/proceedings/XXXVII/congress/1_pdf/218.pdf
36. Paterson, B., Hartnett, R., Bruckner, D., Hetherington, R., & Fiedlers, R. (1998). Integrated GPS/Loran: Structures and issues. Navigation, 45(3), 183–193.
37. Peterson, B. B., Lo, S., & Enge, P. (2008, September). Integrating Loran and GNSS for safety of life applications. In Proceedings of the Institute of Navigation GNSS Conference, Savannah, GA.
38.   Pu, Y., Yang, H. J., Wang, L. L., Zhao, Y. C., Luo, R., & Xi, X. L. (2019). Analysis and modeling of temporal variation properties for LF ground-wave propagation delay. IEEE Antennas and Wireless Propagation Letters, 18(4), 641–645.
39.   Pu, Y. Zheng, X. Wang, D. & Xi, X. (2021). Accuracy improvement model for predicting propagation delay of Loran-C signal over a long distance. IEEE Antennas and Wireless Propagation Letters, 20(4), 582-586.
40. Rosenthal, W., et al. (2017). “Air temperature estimation using MODIS LST and surface emissivity.” Journal of Climate Science.
41. Townshend, J. R. G., Justice, C., Skole, D., Malingreau, J. P., Cihlar, J., Teillet, P., & others. (1994). The 1 km resolution global data set: Needs of the International Geosphere Biosphere Programme. International Journal of Remote Sensing, 15(17), 3417–3441. https://doi.org/10.1080/01431169408954395
42. Tzanis, A. (2017). “Electromagnetic wave propagation in complex environments.” Geophysical Journal International, 182(2), 469-487.
43. Wang, J., et al. (2019). “Deep learning for daily temperature forecasting: Feasibility and challenges.” Advances in Atmospheric Sciences, 36(4), 390-405.
44. Wang, L. L. Liang, Z. C. Pu, Y. R. & Xi, X. L. (2021). Method for Loran-C Additional Secondary Factor Correction Based on Neural Network and Transfer Learning. IEEE Antennas and Wireless Propagation Letters, 21(2), 332-336.
45. Wang, Y. Wang, W. & Luo, R. (2021). Research on Loran-C ASF Correction Method Based on GA-BP Neural Network. In China Satellite Navigation Conference (CSNC 2021) Proceedings (pp. 487-495). Springer, Singapore.
46. Williams, P. & Last, D. (2000), Mapping the ASF of the Northwest European Loren -C System. The Journal of Navigation, 53( 2), 225-235.
47.  Zhou, L. Xu, X. Zhang, J. & Pu, Y. (2013). A new method for Lon-CASF calculation over irrgular terrain.IEEE Tansactions on Aercospace and Electronic System, 49(3), 1738-1744.