Identifiability Analysis of Positioning and Synchronization Errors in Airborne Distributed Coherence Aperture Radars

Positioning and synchronization are fundamental problems before multiplatform signal coherence on a potential target, for the purpose of detection, in airborne distributed coherent aperture radars (ADCARs). Hence, in this paper, the identifiability analysis of positioning and synchronization errors, including platform position errors (PPEs), time alignment errors (TAEs), and initial phases (IPs), is investigated using calibrating scatterers separated in disjoint Doppler resolution bins. Firstly, the hybrid Cramér-Rao lower bounds (HCRLBs) of these three perturbations are derived in an assumed observation geometry determined by the platform formation and scatterer placement. Then based on application scenarios, we conduct identifiability analysis using the HCRLB tool in the following three different cases: In the PPE-absent case, with one scatterer, relative errors are identifiable, whereas their absolute ones are not. In the PPE-only case, at least three distributed scatterers exist to identify PPEs except for ill-posed observation geometries. In the ADCAR case, both the two previous conditions are required for the whole identifiability. We assert that relative errors are identifiable because of the extra degree of freedoms (DoFs) brought by different transmit/receive pairs. Moreover, the ill-posed geometries leading to PPEs unidentifiability, from hybrid Fisher information matrix (HFIM) and time difference of arrival (TDOA) perspectives, are also elaborated. Finally, numerical experiments validate our conclusions, and the scatterer-based calibration achieves signal coherence on transmitting and receiving.