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Journal of Shanghai Jiaotong University(Science) >

2020 , Vol. 25 >Issue 6: 762 - 768

DOI: https://doi.org/10.1007/s12204-020-2200-5

Indirect-Inversion Algorithm via Precise Integration for Ill-Conditioned Matrix in Ambiguity Resolution

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  • (School of Coast Guard, Naval Aviation University, Yantai 264001, Shandong, China)

Online published: 2020-11-26

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Abstract

Global navigation satellite system (GNSS) positioning depends on the correct integer ambiguity resolution (AR). If the double difference equation for solving the float solution remains ill-conditioned, often happening due to the environment complexity and the equipment mobility, the correct AR is difficult to achieve. Concerningthe ill-conditioned problem, methods of modifying the equation coefficient matrix are widely applied, whose effects are heavily dependent on modifying parameters. Besides, the direct-inversion of the ill-conditioned coefficient matrix can lead to a reduction in the accuracy and stability of the float solution. To solve the problem of ill-conditioned matrix inversion and further improve the accuracy, the present study for the first time proves the positive definite symmetry of the coefficient matrix in AR model and employs precise integration method to the indirect inverse of coefficient matrix. AR model for the GNSS positioning and the general resolving strategies introduction are briefly introduced. An indirect-inversion algorithm via precise integration for ill-conditioned coefficient matrix is proposed. According to the simulations and comparisons, the proposed strategy has higher precision and stability on float solution, and less dependence on modifying parameters.

Key words： ill-condition; indirect-inversion; ambiguity resolution; precise integration; global navigation satellite
system positioning

Cite this article

ZHAO Fang, SUN Jin, ZHAO Jianjun, YANG Libin . Indirect-Inversion Algorithm via Precise Integration for Ill-Conditioned Matrix in Ambiguity Resolution[J]. Journal of Shanghai Jiaotong University(Science), 2020 , 25(6) : 762 -768 . DOI: 10.1007/s12204-020-2200-5

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