Two-dimensional Determination of the Decision Boundary for a Radar Detection Method in the Moment Space

The radar detection with decision making in the moments space (DRACEC method) is based on a statistical analysis to determine the boundary between the background (absent target) and the anomaly (present target) classes. In this article, the boundary is taken as an ellipse and is calculated for two dimensions, emphasizing its geometric interpretation. The procedures to establish the shape, location, and size of the ellipse are highlighted, guaranteeing the probability of false alarm by applying the Neyman-Pearson criterion. The proposal establishes a methodology for calculation of the boundary when it is required to use the moments directly as a sufficient decision statistic.