On 2-D Direction-of-Arrival Estimation Performance for Rank Reduction Estimator in Presence of Unexpected Modeling Errors

The rank reduction estimator (RARE) is one kind of autocalibration method used in the presence of sensor errors. It demonstrates high accuracy of direction-of-arrival (DOA) estimation in the absence of multidimensional search or iteration. However, its estimation performance is affected by “unexpected modeling errors.” There is a lack of research regarding the performance of 2-D RARE estimation, although 2-D RARE estimation is extensively employed in applications. This paper presents a theoretical derivation for the closed-form expression of the mean square error (MSE) of 2-D RARE estimation under the influence of small unexpected modeling errors in the first order analysis. First, three definitions of 2-D joint direction-finding success are introduced, in order to establish the criterion for estimate performance. Then corresponding theoretical formulas for three probabilities of direction-finding success are given with the circularly Gaussian assumption of unexpected modeling errors, and their relations are discussed. Finally, the results of simulations utilizing our analysis method are demonstrated, verifying the effectiveness of the MSE expression and the formulas for probabilities of success. Therefore, our first order approximation provides a good prediction of the necessary calibration accuracy in the presence of unexpected modeling errors in order to help RARE meet an expected performance specification.