Maximum Likelihood Estimation in Mixed Integer Linear Models

We consider the maximum likelihood (ML) parameter estimation problem for mixed integer linear models with arbitrary noise covariance. This problem appears in applications such as single frequency estimation, phase contrast imaging, and direction of arrival (DoA) estimation. Parameter estimates are found by solving a closest lattice point problem, which requires a lattice basis. In this letter, we present a lattice basis construction for ML parameter estimation and conclude with simulated results from DoA estimation and phase contrast imaging.