High-Resolution Signal and Noise Field Estimation Using theL1 (Least Absolute Values) Norm

Publisher Website
Google Scholar
Abstract
Abstmct-In this paper a new method for obtaining a quantitative estimate of an acoustic field consisting of a set of discrete sources and background noise is described. The method is based on the L1 (least absolute values) norm solution to an underdetermined system of linear equations defining the Fourier transform of the signal series. Implemen- tations of the method with either equality or inequality constraints are presented and discussed. The much faster and more compact equality constraint version with a provision for modeling the noise field is recommended in practice. Experience with real data has shown the necessity of correcting for an observed Gaussian decay on the covari- ances. A simple means of estimating this effect and taking it into account in the signal estimation procedure is discussed, and the implications of this effect in high-resolution beamforming are considered. The effective- ness and versatility of the L1 method indicate that it has a useful role in high-resolution signal estimation. CENTRAL problem in array signal processing is the estimation of a set of discrete signals in the presence of background noise. In the classical approach to this problem, conventional beamforming is applied to a set of covariances derived from the outputs of an array of sensors to yield an estimate of the strength of the acoustic field in the direction of the beam. Since the method of conventional beamforming is based on the Fourier spatial power spectrum of the array, the resolution of discrete signals by this procedure is limited by the aperture of the array. Because of this, closely spaced discrete arrivals will be detected only as a single broadened peak in the beamforming output. In addition, a strong source may mask a weaker arrival of interest by sidelobe leakage. Thus it is desirable to consider alternatives to conventional beamforming which have higher resolution and lower levels of sidelobe interference. The problem of obtaining direction estimates of a noise field is mathematically equivalent to estimating a spatial spectrum for the array. In recent years, many alternatives to the classical Fourier methods for spectral estimation have been developed ( 11. The application of several of these methods to direction estimation, including maximum likelihood, linear prediction, eigenvector and maximum entropy algorithms, has been discussed by Johnson (2), who showed that each approach is