An analytical method for three-dimensional location estimation using directional data

This article presents a new analytical method for estimating the location of a target using directional data. A three-dimensional (3-D) location estimation method is developed based on a nonlinear programming problem formulated for the line method, which is a well-known algorithm for 2-D location estimation. This method can be applied to situations in which one needs to find a target in space using observers on the ground or to find a target on the ground using observers at least one of which is not on the ground. In addition, based on the analysis of the maximum likelihood estimate of the target location, another 3-D location estimation method is developed for cases in which accuracies of directional data from different observers are different. The performance of the suggested methods is evaluated through simulation experiments; the results show that the methods give very accurate estimates in a reasonably short computation time.