New generalized ESPRIT for direction estimation and its mathematical link to RARE method

The generalized ESPRIT (GESPRIT) method extends the conventional ESPRIT estimator to estimate the directions-of-arrival (DOAs) of multiple incident signals by using the array with more general geometrical configurations, where the translational invariance structure is not required. Unfortunately, the GESPRIT has serious ambiguous DOA estimates in some scenarios, and its performance degrades severely at low signal-to-noise ration (SNR) and with a small number of snapshots. Although a polynomial version of a new GESPRIT (NGESPRIT) method was given, but its derivation and estimation performance are unavailable in published literature. In this paper, in order to overcome the ambiguity of the GESPRIT and improve the estimation performance, the NGESPRIT method is derived explicitly. Moreover, the equivalence between the proposed NGESPRIT method and the rank reduction (RARE) method is clarified, while the former is more computationally efficient than the latter. Finally the effectiveness of the NGESPRIT method is substantiated through numerical examples.