Using of the SDP Relaxation Method for Optimization of the Satellites Set Chosen for Positioning

Lev Rapoport and Timofey Tormagov

Peer Reviewed

Abstract:	When processing multiple navigation satellite systems, including GPS, GLONASS, Galileo, Beidou, QZSS, the overall number of the pseudorange and carrier phase signals can exceed several tens. On the other hand, a much smaller number of them is usually sufficient to achieve necessary precision of positioning. Also, some parts of RTK algorithms, like carrier phase ambiguity resolution, are very sensitive to the problem dimension as they include the integer search. To reduce computational cost of positioning, the optimal choice of signals involved in computations should be performed. The PDOP or GDOP criterion is often used as a cost function to be optimized. Optimization is constrained by given number of satellite signals to be chosen for processing. This optimization problem falls into class of binary optimization problems which are hard for precise solution. The semi-definite relaxation approach (see [1]) is proposed in the paper for approximate solution of this problem. Computational results illustrating good performance of the proposed approach complete the paper.
Published in:	Proceedings of the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2018) September 24 - 28, 2018 Hyatt Regency Miami Miami, Florida
Pages:	3812 - 3820
Cite this article:	Rapoport, Lev, Tormagov, Timofey, "Using of the SDP Relaxation Method for Optimization of the Satellites Set Chosen for Positioning," Proceedings of the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2018), Miami, Florida, September 2018, pp. 3812-3820. https://doi.org/10.33012/2018.15994
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