Statistical angular resolution limit for point sources

We define a statistical angular resolution limit (ARL) on resolving two closely spaced point sources in a 3-D reference frame, using constraints on the probabilities of false alarm and detection for a hypothesis test. The ARL can be used as a performance measure for sensor arrays in localizing remote sources and is applicable to different measurement models and applications (e.g., radar, sonar, or astronomy). By considering the asymptotic performance of the generalized likelihood ratio test (GLRT), we derive the analytical expression of the ARL and show that it is proportional to the square root of the Cramer-Rao bound (CRB) on the angular source separation, or asymptotically the lower bound on the mean-square angular error (MSAE(CRB)). Numerical examples illustrate that the proposed ARL is practically computable and achievable with large data samples. Our analytical result can replace the commonly used ad hoc resolution limits in existing literature.