Abstract
Time-relative positioning (TRP), a global navigation satellite system (GNSS) dead reckoning method with low-cost and highly autonomous characteristics, accumulates the position increments calculated by time-differenced carrier phase (TDCP) between adjacent epochs to extrapolate position. It suffers from error accumulation over time, so it is necessary to judge the availability of positioning services based on predicted accuracy. We propose a new model to predict the accuracy (the root-mean-square error, RMSE) of TRP in real time by determining systematical errors and random errors. The proposed model consists of the following two steps: first, extracting the systematic errors and correlation of position increment errors before position extrapolation; second, predicting RMSE of the positioning results based on the error propagation law during position extrapolation. The experimental results show that after considering the correlation, the predicted RMSE sequences can envelop the actual positioning error more closely. In the case of having static observation before position extrapolation, the predicted RMSEs of extrapolation position in both horizontal and vertical directions decrease by approximately 53.8% compared to the results without considering correlation; in the case where real-time kinematic (RTK) dynamic results are obtained before extrapolation, the predicted RMSE of extrapolation position can decrease by 36.7% in horizontal direction and decrease by 27.9% in vertical direction. The proposed model will be able to provide an important accuracy reference to judge the availability of positioning services when the TRP method is used to extrapolate position under the condition of the augmentation information of RTK interruption.
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The data analyzed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
We are very grateful to the reviewers and editor for their helpful remarks in improving the manuscript. This study is financially supported by the National Key Research and Development Program of China (Grant No. 2021YFC3000504), the Key Research and Development Program of Technology Evolution Plan of Hubei Province (Grant No. 2023BAB068), the Natural Science Foundation of Hunan Province, China (Grant No. 2024JJ8377), and the Research Foundation of the Department of Natural Resources of Hunan Province (Grant No. 20230104CH).
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XZ and ZL wrote the main manuscript text; WT designed the structure and ideas of the paper; YW and YL conducted testing and verification and prepared Tables 1, 2; SZ and YZ assisted in completing data analysis and prepared all figures. All authors reviewed the manuscript.
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Zou, X., Li, Z., Tang, W. et al. A real-time accuracy prediction model on time-relative positioning method considering the correlation of position increment errors. GPS Solut 28, 110 (2024). https://doi.org/10.1007/s10291-024-01654-2
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DOI: https://doi.org/10.1007/s10291-024-01654-2