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Improved GNSS integer ambiguity resolution method based on the column oriented Cholesky decomposition.

Yingxiang Jiao1, Kezhao Li2,3, Chendong Tian1

  • 1School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo, 454000, China.

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|March 18, 2023
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Summary
This summary is machine-generated.

A new Column-oriented Cholesky (C-Cholesky) algorithm improves Global Navigation Satellite System (GNSS) ambiguity resolution efficiency. This method enhances data processing speed by 12.34% without compromising integer ambiguity accuracy.

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Area of Science:

  • Geomatics Engineering
  • Computational Mathematics

Background:

  • Traditional Cholesky decomposition for Global Navigation Satellite System (GNSS) ambiguity resolution faces challenges with computational complexity and matrix structure.
  • Improving the efficiency of least squares ambiguity reduction correlation is crucial for carrier phase integer ambiguity solutions.

Purpose of the Study:

  • To enhance the computational efficiency of matrix decomposition in GNSS ambiguity resolution.
  • To reduce the calculation time for integer ambiguity reduction correlation.

Main Methods:

  • The study proposes an improved Cholesky decomposition algorithm, termed Column-oriented Cholesky (C-Cholesky).
  • The C-Cholesky algorithm divides the decomposition process into multiplication updates and a column reduction step for square root calculations.
  • The column reduction step handles square root and division calculations, while the update step manages multiplication tasks.

Main Results:

  • The proposed C-Cholesky algorithm demonstrates effectiveness and superiority in improving matrix decomposition efficiency.
  • This method achieves an average improvement of approximately 12.34% in data processing efficiency.
  • The integer ambiguity accuracy remains consistent with the traditional Cholesky algorithm.

Conclusions:

  • The C-Cholesky algorithm offers a significant improvement in computational efficiency for GNSS ambiguity resolution.
  • The enhanced efficiency is achieved without any loss in the accuracy of integer ambiguity determination.
  • This method provides a viable solution for faster and more efficient processing of GNSS carrier phase data.