Shape parameter estimation of wavefronts with known waveform

Abstract Active sensor arrays are useful to parametrically estimate the wavefronts in most applications where the excitation signal (waveform) is known or can be consistently estimated (e.g., in remote sensing, radar and communication systems). For the estimation of the shape parameters (SPs) of the wavefronts several algorithms have been summarized from the literature and compared. The algorithm proposed here is based on singular value decomposition (SVD) and has been proven to be effective in reducing coherent noise arising from interfering wavefronts. The problem of SP estimation is treated as a whole for plane and curved wavefronts, for different geometries (1-D and 2-D array of sensors), and for wide and narrowband waveforms. Wavefield distortion due to propagating medium inhomogeneities is analyzed for increasing distortion. Compared with the methods adapted for SP estimation of narrowband wavefront, the maximum likelihood estimator (ML) and the method based on SVD show better resolution of the wavefront arrival time since they correlate with the known waveform. The Cramer–Rao bound is derived and some useful properties are also established. Finally the paper contains a numerical study of the SP estimators for incoherent and coherent noise.