下三角Cholesky分解的整数高斯变换算法

发布时间：2018-04-16 21:29

本文选题：整周模糊度 + 整数最小二乘　；参考：《测绘科学》2017年12期

【摘要】：针对全球导航卫星系统(GNSS)载波相位测量中,基于整数最小二乘估计准则解算整周模糊度问题。目前以LAMBDA降相关算法和Lenstra-Lenstra-Lovász(LLL)为代表的规约算法应用最为广泛。由于不同算法采用的模糊度方差-协方差阵的分解方式不同,导致难以合理地进行不同算法性能的比较。该文通过分析LAMBDA算法的降相关特点,从理论上推出基于下三角Cholesky分解多维情形下的整数高斯变换的降相关条件及相应公式,并与分解方式不同的LAMBDA和LLL算法作了对比。实验结果表明,降相关采用的分解方式将会直接影响计算复杂度和解算性能,因此该文推导的整数高斯变换算法便于今后基于下三角Cholesky分解的降相关算法间的合理比较。
[Abstract]:The integer least square estimation criterion is used to solve the integer ambiguity problem in GNSS carrier phase measurement.At present, the protocol algorithm, represented by LAMBDA algorithm and Lenstra-Lenstra-Lov 谩 szl algorithm, is the most widely used.Due to the different decomposition methods of ambiguity variance-covariance matrix, it is difficult to compare the performance of different algorithms reasonably.By analyzing the characteristics of LAMBDA algorithm, the paper theoretically deduces the condition of reducing correlation and the corresponding formula of integer Gao Si transform based on lower triangular Cholesky decomposition in multidimensional case, and compares it with LAMBDA and LLL algorithms with different decomposition methods.The experimental results show that the decomposition method of reducing correlation will directly affect the computational complexity and performance. Therefore, the integer Gao Si transform algorithm derived in this paper is convenient for the reasonable comparison between the reduced correlation algorithms based on the lower triangular Cholesky decomposition in the future.
【作者单位】：东华理工大学测绘工程学院;武汉大学测绘学院;
【基金】：国家自然科学基金项目(41774031,91638203,41374007,41464001) 江西省自然科学基金项目(2017BAB203032)
【分类号】：P228.4

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