Maximum likelihood estimation in mixed integer linear model with P-norm distribution

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.