4.7 Article

A Shrink-Branch-Bound Algorithm for eLoran Pseudorange Positioning Initialization

Journal

REMOTE SENSING
Volume 14, Issue 8, Pages -

Publisher

MDPI
DOI: 10.3390/rs14081781

Keywords

pseudorange positioning; branch and bound; nonlinear least squares; eLoran; trust region reflective algorithm; initialization

Funding

  1. Chinese Academy of Sciences Light of West China Program [E017YR1R10]
  2. Youth Innovation Promotion Association CAS [1188000YCZ]

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eLoran is an important backup and supplement for global navigation satellite systems, and pseudorange positioning is a key issue. A new shrink-branch-bound algorithm is proposed to solve the initialization problem of eLoran pseudorange positioning without any initial value information.
Currently, eLoran is the ideal backup and supplement for global navigation satellite systems. The time synchronization accuracy between stations in the eLoran system has improved, providing conditions for eLoran pseudorange positioning. The pseudorange positioning of eLoran is a nonlinear least-squares problem and the location of the eLoran transmitting stations may cause the above problem to be non-convex. This makes the conventional pseudorange positioning al-gorithm strongly depend on the initial value when solving the eLoran pseudorange positioning. We propose a shrink-branch-bound (SBB) algorithm to solve the eLoran pseudorange positioning initialization problem. The algorithm first uses a shrink method to reduce the search space of the position estimator. Then, optimization is performed using a branch and bound algorithm within the shrunk region, where a trust region reflective algorithm is used for the lower bound process. The algorithm can help the receiver to complete the initial positioning without any initial value information. Simulation experiments verify that the algorithm has a success rate of more than 99.5% in solving the initialization problem of eLoran pseudorange positioning, and can be used as an initialization algorithm for pseudorange positioning problems for eLoran or other long-range terrestrial-based radio navigation system.

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