A source number estimation method via determinant-trace criteria on Grassmann manifold

Estimating the number of sources in challenging scenarios with low signal-to-noise ratio (SNR), limited snapshots, or colored noise is a fundamental problem in array signal processing. This letter presents a method that recasts source number estimation from a statistical task into a problem of geometric feature detection, achieved by exploiting the invariants embedded within the data’s covariance structure. The method formulates dual determinant-trace criteria that leverage principal angle geometry to yield a characteristic cliff-like signature at the true source number. This signature is then harnessed by a unified framework integrating adaptive search and intelligent fusion, with hyperparameters optimized by an attentional Bayesian neural network. Experiments validate the method’s superior effectiveness and robustness against challenging conditions such as low-to-medium SNR, limited snapshots, and colored noise, where traditional techniques often falter.