Cardioid microphones/hydrophones in a collocated and orthogonal triad-A steerable beamformer with no beam-pointing error.

Cardioid sensors offer low sidelobes/backlobes compared to figure-8 bi-directional sensors (like velocity-sensors). Three cardioid sensors, in orthogonal orientation and in spatial collocation, have recently been proposed by Wong, Nnonyelu, and Wu [(2018). IEEE Trans. Sign. Process. 66(4), 895-906] and such a cardioid-triad's "spatial matched filter" beam-pattern has been analyzed therein. That beam-pattern, unfortunately, suffers pointing error, i.e., the spatial beam's actual peak direction deviates from the nominal "look direction." Instead, this paper will propose a steerable data-independent beamformer for the above-mentioned cardioidic triad to avoid beam-pointing error. Also analytically derived here (via multivariate calculus) is this beam-pattern's lobes' height ratio, beamwidth, directivity, and array gain.