Signal Parameter Estimation for Sparse Arrays

Abstract

For arrays with a small number of elements, such as those deployed in infrasound detection, the theoretical pattern of beam power associated with the incidence of a plane wave shows a broad main beam with strong side lobes. A novel approach to the estimation of the parameters of the incoming wave field is proposed based on the exploitation of the full beam pattern for the array. The pattern of beam power over a limited mask of beam points in slowness space is compared with the theoretical predictions over a set of narrow frequency bands and the set of signal parameters that give the best fit determined by an inversion using a Neighbourhood Algorithm (NA). The angle of incidence and azimuth provide a convenient parameter set since they can be used to include corrections for elevation differences between the sensors in the process of beamforming. Because the theoretical beam pattern depends only on the array geometry and frequency band, it can be computed on a dense grid and interpolation carried out to provide the beam power across the beam mask for a specified set of angular parameters. The NA inversion with an L1.3 measure of misfit in beam power is able to achieve good definition of the minimum misfit with only 120 trials, and the level of fit itself provides a good measure of the validity of the model of a single dominant plane wave. The NA approach is supplemented by a contracting grid method using a set of self-similar grid masks that can rapidly locate the position of maximum beam power. The two methods provide a valuable tool for real-time analysis, with both independent estimates of the angular parameters and a measure of the quality of the results.