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Variance reduction of GNSS ambiguity in (inverse) paired Cholesky decorrelation transformation

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Abstract

It has been discovered that (a) the variance of all entries of the ambiguity vector transformed by a (inverse) paired Cholesky integer transformation is reduced relative to that of the corresponding entries of the original ambiguity vector; (b) the higher the dimension of the ambiguity vector, the more significantly the transformed variance will be decreased. The property of variance reduction is explained theoretically in detail. In order to better measure the property of variance reduction, an efficiency factor on variance reduction of ambiguities is defined. Since the (inverse) paired Cholesky integer transformation is generally performed many times for the GNSS high-dimensional ambiguity vector, the computation formula of the efficiency factor on the multi-time (inverse) paired Cholesky integer transformation is deduced. The computation results in the example show that (a) the (inverse) paired Cholesky integer transformation has a very good property of variance reduction, especially for the GNSS high-dimensional ambiguity vector; (b) this property of variance reduction can obviously improve the success rate of the transformed ambiguity vector.

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Acknowledgments

This study is supported by the Key Project of National Natural Science Foundation of China (No: 41231174). The authors thank the anonymous reviewers for their detailed comments and valuable suggestions that help us reform the manuscript into the current structure.

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Authors and Affiliations

  1. GNSS Research Center, Wuhan University, Wuhan, 430079, Hubei, China

    Yangmei Zhou & Zhibiao He

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  1. Yangmei Zhou
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  2. Zhibiao He
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Correspondence to Yangmei Zhou.

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Zhou, Y., He, Z. Variance reduction of GNSS ambiguity in (inverse) paired Cholesky decorrelation transformation. GPS Solut 18, 509–517 (2014). https://doi.org/10.1007/s10291-013-0347-3

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  • DOI: https://doi.org/10.1007/s10291-013-0347-3

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