Abstract
Complex urban environments limit the reception of global navigation satellite system (GNSS) signals, increasing the difficulty of ambiguity resolution (AR) for GNSS attitude determination based on carrier-phase observations. To constrain the Least-squares Ambiguity Decorrelation Adjustment (LAMBDA) and improve the success rate and accuracy of AR, a fixed length between the antennas is proposed. Heading angle- and length-constrained LAMBDA (HLC-LAMBDA) and converted baseline vector-constrained LAMBDA (VC-LAMBDA) were proposed because baseline length-constrained LAMBDA (BC-LAMBDA) cannot guarantee three-dimensional accuracy. Because BC-LAMBDA, HLC-LAMBDA, and VC-LAMBDA are based on multi-antenna attitude determination, this study introduces heading angle-constrained LAMBDA (HC-LAMBDA), which can also be applied to single-antenna GNSS attitude determination scenarios. To identify the optimal ambiguity candidate in BC-LAMBDA, HLC-LAMBDA, HC-LAMBDA, and VC-LAMBDA, search and shrink strategy were performed based on the boundary function rather than an exhaustive search. Additionally, a simple validation was implemented to ensure the reliability of the ambiguous candidates during the search process. The car experiment was conducted in an urban environment using a low-cost Ublox-F9p. The test of different maximum candidate numbers indicated that the accuracy of the baseline solution did not continue to increase as the maximum candidate number increased in the search space. The constrained LAMBDAs (C-LAMBDAs) with the boundary function had a higher fix rate and smaller bias than those of the exhaustive search; however, the consumed time by the boundary function was larger owing to the Modified Search (M-Search) in the shrink process. The results also show that different constraints have different effects; HC-LAMBDA has a similar performance to HLC-LAMBDA in terms of heading angle, which should be considered when the baseline length is unknown. The baseline vector of VC-LAMBDA performed better in three dimensions if there was an accurate constraint on the baseline vector.
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The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable requests.
Abbreviations
- AC-LAMBDA:
-
Affine-constrained LAMBDA
- AFM:
-
Ambiguity function method
- AR:
-
Ambiguity resolution
- BC-LAMBDA:
-
Baseline length-constrained LAMBDA
- C-LAMBDA:
-
Constrained LAMBDA
- CPU:
-
Central processing unit
- DD:
-
Double-difference
- E:
-
East
- GNSS:
-
Global navigation satellite system
- HC-LAMBDA:
-
Heading angle-constrained LAMBDA
- HLC-LAMBDA:
-
Heading angle- and length-constrained LAMBDA
- IAR:
-
Integer ambiguity resolution
- ILS:
-
Integer least-squares
- IMU:
-
Inertial measurement unit
- INSs:
-
Inertial navigation systems
- LAMBDA:
-
Least-squares ambiguity decorrelation adjustment
- MC-LAMBDA:
-
Multivariate-constrained LAMBDA
- N:
-
North
- NSAT:
-
Number of satellites
- PDOP:
-
Position dilution of precision
- RMSE:
-
Root-mean-square error
- U:
-
Up
- VC-LAMBDA:
-
Vector-constrained LAMBDA
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Acknowledgements
We would like to thank the students in the laboratory at the Tokyo University of Marine Science and Technology for their help throughout the collection of the experimental data. This work was sponsored by the National Natural Science Foundation of China (No. 41771475), Social Development Project of Science and Technology Innovation Action Plan of Shanghai (No. 20dz1207107), and the authors gratefully acknowledge the financial support from China Scholarship Council. This work was also supported by JSPS KAKENHI Grant Number JP19H02355.
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CZ did the experiment and wrote the manuscript. DD helped solve the key problem, gave suggestions, and modified the manuscript. NK provided the idea, gave suggestions, and modified the manuscript. KK collected the data and gave suggestions on the program. NK and WC provided the funding support. JW gave suggestions on the writing of this manuscript and the support of experiment.
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Zhang, C., Dong, D., Kubo, N. et al. Evaluation of different constrained LAMBDAs for low-cost GNSS attitude determination in an urban environment. GPS Solut 28, 42 (2024). https://doi.org/10.1007/s10291-023-01584-5
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DOI: https://doi.org/10.1007/s10291-023-01584-5