A range and azimuth estimator based on forming the spatial Wigner distribution

Abstract

We show that for a linear, equally spaced array, wavefront curvature produces a quadratic phase variation across the array for a single arrival frequency from a target within the Fresnel zone of the array. The Wigner distribution for a quadratic phase signal peaks at the instantaneous frequency or, in our case, at the wave number versus array position. By relating this to wavefront curvature, a range estimate is produced.

Structure-Aware Bayesian Compressive Sensing for Near-Field Source Localization Based on Sensor-Angle Distributions

“…The sensor-angle distribution (SAD) is used to represent the phase progression in the joint space and spatial frequency domain with a signature that resembles those of instantaneously narrowband frequency-modulated (FM) signals in the joint time-frequency domain [9,10]. In this respect, the signal processing algorithms introduced for quadratic timefrequency analysis can be readily applied for the processing of the SAD for near-field source localization.…”

“…In this respect, the signal processing algorithms introduced for quadratic timefrequency analysis can be readily applied for the processing of the SAD for near-field source localization. It is important to note that, while the SAD was originally developed in the form of spatial Wigner distribution [9,10], which is effective only for second-order (linear FM) spatial frequency signatures, we consider it in the general form within Cohen's class with a proper time-frequency kernel for improved sensor-angle relationship [11]. The proposed technique permits the sensordependent phase progression as a high-order polynomial phase signal (PPS) to account for close sources, whereas the coefficients are estimated from the SAD signature with simple least squares fitting, which does not require parameter searching.…”