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Ill-posed analysis and regularized estimation for seafloor geodetic acoustic single-difference positioning.

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Single-difference positioning enhances seafloor geodetic acoustic positioning accuracy by eliminating systematic errors. A novel L-curve Liu type method effectively addresses ill-posed problems inherent in this positioning technique.

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Area of Science:

  • Geodesy
  • Oceanography
  • Geophysics

Background:

  • Seafloor geodetic acoustic positioning accuracy is significantly impacted by long-term systematic errors.
  • The single-difference positioning method is crucial for mitigating these systematic errors.
  • Ill-posed problems, arising from poor observation geometry and collinearity, challenge single-difference positioning accuracy.

Purpose of the Study:

  • To analyze the spatial distribution of condition numbers in single-difference positioning under various track and heave conditions.
  • To investigate how observation structure optimization affects the ill-posed degree of single-difference positioning.
  • To propose and validate a novel method (L-curve Liu type) for addressing the unavoidable ill-posed problems in single-difference positioning.

Main Methods:

  • Analysis of condition numbers for single-difference positioning across different tracks and heaves.
  • Optimization of observation structures to reduce collinearity and ill-posedness.
  • Development and application of the L-curve Liu type method, utilizing the maximum curvature point of the L-curve (mean square error vs. residual two norm) for parameter and estimation optimization.

Main Results:

  • Circular tracks with equidistant measurements exacerbate collinearity, increasing the ill-posed degree.
  • Optimizing observation structure can effectively reduce the ill-posedness of single-difference positioning.
  • The proposed L-curve Liu type method successfully reduces the impact of ill-posed problems.

Conclusions:

  • Single-difference positioning is effective in eliminating systematic errors for seafloor geodetic acoustic positioning.
  • The L-curve Liu type method provides a robust solution for the ill-posed nature of single-difference positioning.
  • Experimental validation in the South China Sea and Panglong Lake confirms the efficacy of the proposed method.