On the Error Metrics Used for Direction of Arrival Estimation

In this article, the error metrics used for evaluating the performance of direction of arrival (DoA) estimation are thoroughly investigated to recommend the most suitable one. This investigation highlights the lack of consensus in the literature regarding the selection and definition of these metrics. We show that this disparity is particularly serious in 2D DoA estimation, an aspect often overlooked by many authors. Notably, certain widely accepted error metrics can yield inaccurate and misleading results. Therefore, this article advocates for the adoption of a specific error metric that ensures accurate and meaningful assessments of 2D DoA estimation. A set of numerical and experimental results is presented to demonstrate the potential of the proposed error metric compared to other well-known metrics. Unlike other metrics, our proposed error definition is frame-independent. Finally, practical use cases are briefly discussed to highlight the pervasive impact of this fundamental definition.