Robust adaptive vector sensor processing in the presence of mismatch and finite sample support

We present analytical results which quantify the effect of system mismatch and finite sample support on acoustic vector sensor array performance. One noteworthy result is that the vector aspect of the array ldquodampensrdquo the effect of array mismatch, enabling deeper true nulls. This is accomplished because the variance of the vector sensor array spatial response (due to rotational, positional and filter gain/phase perturbations) decreases in the sidelobes, unlike arrays of omnidirectional hydrophones. When sensor orientation is measured within a reasonable tolerance, the beampattern variance dominates the average sidelobe power response. Our analysis also suggests that vector sensor array gain performance is less sensitive to rotational than to positional perturbations in the regions of interest. We analytically characterize the eigen-SNR threshold, which depends on the signal and noise covariance and the number of noise-only and signal-plus-noise snapshots, below which (asymptotically speaking) reliable detection using sample eigenvalue based techniques is not possible. Thus for a given number of snapshots, since the dimensionality of the snapshot in a vector sensor array is larger than that of a hydrophone-only array, the eigen-SNR detection threshold will be greater whenever the eigenvector information is discarded. We present processing techniques customized to the unique characteristics of vector sensors, which exploit information encoded in the sample eigenvectors and are robust to the mismatch and finite sample support issues. These methods include adaptive processing techniques with multiple white noise constraints.