2qth-Order cumulants based virtual array of a single acoustic vector sensor

Abstract

A spatially co-located four-element single acoustic vector sensor offers numerous advantages over the scalar pressure sensor array such as compact size, ability to handle spatially undersampled systems, and the intrinsic two-dimensional directivity independent of the range, frequency, and bandwidth of the incoming signal. Despite all these advantages, a single acoustic vector sensor finds limited application in the field of the direction of arrival estimation as it can only resolve a maximum of two sound sources using classical second-order statistics-based methods. This paper proposes a 2qth-order circular cumulants based processing (q is an integer, and q≥1) by utilizing the concept of virtual array, to enhance the degree of freedom and hence to maximize the sources resolvability of a single acoustic vector sensor. Additionally, this paper derives a theoretical upper bound on the maximum number of the identifiable two-dimensional direction of arrivals of statistically independent, non-Gaussian sources by exploiting the proposed virtual array of a single acoustic vector sensor. The upper bound on the maximum number of the identifiable two-dimensional direction of arrivals by exploiting the proposed virtual array is found to be 3, 8, and 14, for q=1, 2, and 3, respectively, if both the elevations and azimuths are distinct for all the given statistically independent, non-Gaussian sources. Furthermore, the upper bound on the maximum number of the identifiable two-dimensional direction of arrivals by exploiting the proposed virtual array is found to be 2, 4, and 6, for q=1, 2, and 3, respectively, if all the given statistically independent, non-Gaussian sources are lying in a single azimuth (or elevation) plane with distinct elevations (or azimuths).