This paper presents a new analytical method for estimating the location of a target using directional data. Based on a nonlinear programming (NLP) problem formulated for the line method, which is a well known algorithm for two-dimensional location estimation, we present a method to find an optimal solution for the problem. Then we present a two-stage method for better location estimation based on the NLP problem. In addition, another two-stage method is presented for location estimation problems in which different types of observers are used to obtain directional data based on the analysis of the maximum likelihood estimate of the target location. The performance of the suggested method is evaluated through simulation experiments, and results show that the two-stage method is computationally efficient and highly accurate.