Abstract
The global navigation satellite system (GNSS) is widely employed in location-based services (LBS) as a pivotal technology for high-precision navigation and positioning. However, measurement errors cannot be fully eliminated in practical applications, potentially impacting positioning accuracy and reliability. Based on robust estimation and fractional calculus, we construct a robust fractional-order extended Kalman filter (RFEKF) model with a Huber function model. First, we introduce a fractional-order extended Kalman filter (FEKF) model. Second, the RFEKF is constructed by incorporating an equivalence weight matrix that introduces redundancy and the statistical properties of predicted residuals. The RFEKF model adapts the gain matrix through iterative adjustment, obtaining optimal solutions and enhancing the operational efficiency of the model. Finally, simulation experiment and practical implementation are carried out to verify the proposed RFEKF model in GNSS navigation and positioning. The results demonstrate that the RFEKF significantly improves the accuracy of navigation and positioning in the presence of gross errors, surpassing the performance of the REKF.
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Upon a reasonable request, the simulation test and the field test can be obtained from the first author (1108130421004@stu.bucea.edu.cn).
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Acknowledgements
We are grateful to the anonymous reviewers for their helpful, constructive suggestions and comments that helped to improve the article quality significantly. This study is supported by Beijing Natural Science Foundation: 8222011, the National Natural Science Foundation of China: 41874029 and the BUCEA Doctor Graduate Scientific Research Ability Improvement Project: DG2023006.
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JZ and JW were involved in conceptualization and validation; JZ and HH assisted with methodology; TJ helped with the software; JZ was responsible for formal analysis, data curation and writing—original draft preparation; JW contributed to resources, supervision, project administration and funding acquisition; and HH took part in writing—reviewing and editing. All authors have read and agreed to the published version of the manuscript.
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Zhao, J., Wang, J., Han, H. et al. A study on the model of robust fractional-order extended Kalman filtering with gross error. GPS Solut 28, 87 (2024). https://doi.org/10.1007/s10291-024-01613-x
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DOI: https://doi.org/10.1007/s10291-024-01613-x