下三角Cholesky分解的整数高斯变换算法

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。

Integer Gauss transformation algorithm based on low triangular Cholesky decomposition

In view of the ambiguity resolution problems in GNSS carrier phase measurement,usually integer least-squares(ILS)estimation criterion was taken advantage of to resolve ambiguity.At present,the least-squares ambiguity decorrelation adjustment (LAMBDA) decorrelation algorithm and Lenstra-Lenstra-Lovász(LLL) reduction algorithm are most popular and widely used in many fields.However,different ambiguity resolution algorithms using different decompositions of ambiguity variance-covariance matrix results in difficulty to reasonably compare the performance of different algorithms.In this paper,we firstly deduced the decorrelation conditions and relating formulas of integer Gauss transformation based on low triangular Cholesky decomposition under multi-dimension situations through analyzing decorrelation characteristic of LAMBDA algorithm,and then compared with LAMBDA and LLL algorithm which had different decompositions.Simulations and real data validations clearly showed that different decompositions would lead to significant differences on decorrelation computation complexity and resolution performance.Therefore,this method would be benefitial to the reasonable comparison of decorrelation algorithms based on low triangular Cholesky decomposition.