Derivation of an explicit expression of an approximate location estimate in AOA-based localization

We derive closed-form expression of an approximate location estimate in AOA-based localization. The derivation is based on Taylor series expansion and an approximate solution of an overdetermined linear system. The effect of an angle-of-arrival (AOA) estimation error on the location estimate is explicitly shown in the derived expression, which implies that the result can be used for the closed-form expression of the mean-square-error of the location estimate.