MLE Solution Research for a Certain Kind of Two-dimensional Lognormal Distribution Function

Aimed at the puzzle that it is hardly possible to solve maximum likelihood estimate (MLE) of two-dimensional lognormal distribution function directly, the paper presents a novel solution based on extremum equivalent conversion. The puzzle could be transformed to solve the extremum of an equivalent function about independent variable, and then mathematical expression of the extremum was obtained by conventional differential method. Take the study on location in wireless sensor network as an example. The research shows that the method can obviously reduce difficulty of the puzzle and the algorithm complexity, so the presented method provides an effective solution for similar problems.