Effects of coordinate system rotation on two novel closed-from localization estimators using azimuth/elevation

In this paper two novel solutions are developed for the 3D localization problem using azimuth/elevation angles by reformulating the nonlinear azimuth and elevation measurements in a linear way. The proposed solutions provide computationally non-demanding approaches for this problem and can be used for initializing iterative algorithms e.g., maximum likelihood estimator. This paper studies the effect of the xy-coordinate system rotation on the performance of these two estimators. It has been shown that the xy-coordinate system rotation can significantly change the performance of one of the estimators, while having no effect on the performance of the other one. This paper establishes this observation and provides a closed-form solution for finding the rotation angle that can effectively reduce the bias. The residual error criteria is used to compare the performance of the proposed estimators and select the one with better performance for different scenarios.