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GNSS best integer equivariant estimation combining with integer least squares estimation: an integrated ambiguity resolution method with optimal integer aperture test

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Abstract

Accurate and reliable carrier phase ambiguity resolution (AR) is the key to global navigation satellite system (GNSS) high-precision navigation and positioning applications. The integer least squares (ILS) estimation and the best integer equivariant (BIE) estimation are two widely used AR method, with the former considered to have the highest success rate and the latter to be optimal in the minimum mean squared error (MSE) sense. We analyzed three key issues of applying the BIE method in detail, including the use boundary of BIE, the number of candidates to be involved, and the weight determination among ambiguity candidates. It has been demonstrated that the BIE estimator is superior to ILS estimator from an overall perspective, but not always the best in each specific epoch. Therefore, we recommend constructing an integrated ambiguity resolution scheme that combines BIE with ILS, and we propose to adopt the optimal integer aperture (OIA) test as a criterion to distinguish the two. Moreover, a new criterion referred to the OIA test is proposed to determine the number of candidates involved in the BIE estimator. We also attempt to add the quadratic forms of baseline residuals into the weight function of BIE, aiming to reach a more accurate estimator. Finally, an integrated AR method that combines ILS with BIE and distinguished by the OIA test is proposed, named OIA-BIE. A set of real-measured vehicle data are tested to evaluate its performance, compared to least squares (LS), ILS, and the original BIE. The results show that the positioning accuracy of OIA-BIE is a little better than BIE, better than ILS, and significantly better than LS. Moreover, the average time consumption of ILS, BIE, and OIA-BIE are also evaluated, with 1.15, 14.62, and 3.71 ms, respectively, and OIA-BIE is four times more efficient than BIE.

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The data used in this manuscript are available from the corresponding author upon request.

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Acknowledgements

This study was supported by the National Key R&D Program of China (Grant No. 2021YFC3000501), the National Natural Science Foundation of China (Grant Nos. 41961144015, 41804020), the China Postdoctoral Science Foundation (Grant No. 2020M682484), the Wuhan Science and Technology Project (Grant No. 2020010601012185).

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Authors and Affiliations

  1. GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Liye Ma & Yidong Lou

  2. School of Geomatics, East China University of Technology, 418 Guanglan Road, Nanchang, 330013, Jiangxi, China

    Liguo Lu

  3. School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Wanke Liu & Feng Zhu

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  1. Liye Ma
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  2. Yidong Lou
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  3. Liguo Lu
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  4. Wanke Liu
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  5. Feng Zhu
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Correspondence to Yidong Lou.

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Ma, L., Lou, Y., Lu, L. et al. GNSS best integer equivariant estimation combining with integer least squares estimation: an integrated ambiguity resolution method with optimal integer aperture test. GPS Solut 26, 100 (2022). https://doi.org/10.1007/s10291-022-01285-5

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