Derivation of an Approximate Location Estimate in Angle-of-Arrival Based Localization in the Presence of Angle-of-Arrival Estimate Error and Sensor Location Error

We derive closed-form expression of an approximate location estimate in angle-of-arrival (AOA)-based localization. In this paper, it is assumed that there is estimation error in AOA estimation and that estimates of sensor location can be expressed as zero-mean Gaussian random variable. The derivation is based on Taylor series expansion and an approximate solution of an over-determined linear system. The effect of sensor location error and 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.