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

@article{Nnonyelu2019CardioidMI,
  title={Cardioid microphones/hydrophones in a collocated and orthogonal triad-A steerable beamformer with no beam-pointing error.},
  author={Chibuzo Joseph Nnonyelu and Kainam Thomas Wong and Yue Ivan Wu},
  journal={The Journal of the Acoustical Society of America},
  year={2019},
  volume={145 1},
  pages={
          575
        }
}
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… 
Hybrid Cramér-Rao bound of direction finding, using a triad of cardioid sensors that are perpendicularly oriented and spatially collocated.
TLDR
This analysis allows the cardioidicity index to be stochastically uncertain, applies to any cardioidic order (k), and is valid for any real-valued incident signal regardless of the signal's time-frequency structure.
On the Performance of L- and V-Shaped Arrays of Cardioid Microphones for Direction Finding
The L-shaped and V-shaped arrays of first-order cardioid microphones for direction finding are presented in this paper. A comparative study of the direction of arrival estimation performance of the