测绘学报

• 学术论文 •    

P范分布混合整数模型极大似然估计

李博峰1,沈云中2   

  1. 1. 同济大学测量与国土信息工程系
    2. 同济大学测量系现代工程测量国家测绘局重点实验室
  • 收稿日期:2008-11-26 修回日期:2009-05-30 出版日期:2010-04-22 发布日期:2010-04-22
  • 通讯作者: 李博峰

Maximum Likelihood Estimation in Mixed Integer Linear Model with P-Norm Distribution

,   

  • Received:2008-11-26 Revised:2009-05-30 Online:2010-04-22 Published:2010-04-22

摘要: 高精度GNSS定位和INSAR解缠都需要求解整数模糊度参数,从数学角度可抽象地提炼为含有实参数和整参数的混合整数模型。目前对混合整数模型的参数估计只是直接采用最小二乘准则。本文研究P范分布混合整数模型参数估计理论,首先采用极大似然理论,顾及实参数可导而整参数不可导,导出了P范分布整数搜索准则,并证明了最小二乘整数搜索准则是它的一个特例;然后给出了P范分布混合整数模型的p参数估计、整参数搜索和实参数求解的方法和计算流程;最后通过模拟算例分析和验证了本文模型和计算方法的正确性。

Abstract: The integer parameters must be primarily estimated in the GNSS and INSAR application, which essentially introduces a special mixed integer model with both real- and integer-valued parameters from mathematical point of view. Up to now, all methods for mixed integer model are based on the least squares criterion. In this paper, the parameter estimation will be investigated in mixed integer model with the P-norm distributed observation noises. First of all, we will employ the maximum likelihood estimation theory to derive the criterion for integer searching, considering the fact that only real parameters can be differentiated but not the integer parameters due to their discrete property, and further verify that least squares based integer searching criterion is just a case with normally distributed noises. Secondly, the approach and iterative procedure are given for estimating p, searching integers and solving real-valued parameters. Finally, the simulated experiments are implemented to verify the correctness of the derived formulae and proposed algorithm.