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Optimal reduction and conversion of range-difference measurements for positioning.

M Hou1

  • 1Department of Engineering, University of Hull, Hull, United Kingdom.

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|August 29, 2022
PubMed
Summary
This summary is machine-generated.

Accurate object positioning requires measuring range differences between m references. This study presents a least squares method to handle noisy or missing measurements for precise positioning.

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Area of Science:

  • Geomatics and Geodesy
  • Signal Processing
  • Navigation Systems

Background:

  • Object positioning relies on range difference measurements.
  • Redundancy in range difference measurements is often assumed but not always valid due to noise and reference location uncertainties.
  • Existing methods may not adequately handle missing or weighted range-difference data.

Purpose of the Study:

  • To develop a robust positioning method using range differences.
  • To address the challenge of non-redundant range difference measurements in positioning.
  • To establish relationships between different least squares positioning formulations.

Main Methods:

  • Utilizing m-1 linearly independent range differences for positioning.
  • Applying the least squares principle to derive m range measurements from available data.
  • Simultaneously formulating problems with missing and weighted range-difference measurements.

Main Results:

  • Demonstrated that range difference measurements are not always redundant.
  • Established exact relationships among various least squares positioning formulations.
  • Provided a numerical example validating the proposed methodology.

Conclusions:

  • The proposed least squares approach effectively handles noisy and incomplete range difference data for object positioning.
  • Understanding the non-redundancy of range differences is crucial for accurate positioning.
  • The method offers a unified framework for least squares positioning with diverse measurement conditions.