P-范分布混合整数模型极大似然估计

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

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P-范分布整数搜索准则,并证明最小二乘整数搜索准则是它的一个特例;然后给出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本文模型和计算方法的正确性。

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.