Conical Angle Localization: A Linear Solution

Although linear arrays cannot measure elevation and azimuth in 3-D, they can still be used to localize an emitter in 3-D by measuring conical angles (CA). A CA is the angle between an array's longitudinal axis and the line connecting the array reference to the emitter, establishing a conical surface on which the emitter lies. Localizing the emitter involves finding the intersection of these cones, a nonlinear problem that typically requires complex computations or restricts array placement. This correspondence introduces a method that uses pairs of linear arrays, sharing a common reference, and provides a two-stage weighted linear least squares closed-form solution. The proposed estimator is shown to be optimal at reasonable noise levels, as demonstrated by simulation results.