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Optimal reduction and conversion of range-difference measurements for positioning

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  • M Hou

Abstract

For positioning an object with m references, there are m−1 linearly independent range differences and measuring them is essential. However, none of m(m−1) possible range differences should be considered redundant unless their measurements are free of noise and locations of the references are exactly known. From all available range-difference measurements, m range measurements are obtained for positioning based on the least squares principle. The problem formulation treats missing and weighted range-difference measurements simultaneously. The exact relationships among several formulations of least squares positioning are established. A numerical example illustrates the results.

Suggested Citation

  • M Hou, 2022. "Optimal reduction and conversion of range-difference measurements for positioning," PLOS ONE, Public Library of Science, vol. 17(8), pages 1-12, August.
    • Handle: RePEc:plo:pone00:0273617
    DOI: 10.1371/journal.pone.0273617
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