Frequency-azimuth-elevation determination with a single acoustic vector-sensor involved in a reflecting boundary

The temporally regularized multiresolution ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm is proposed to exploit the second-order information present in the superposition of incidence of direct and reflected monochromatic acoustic waves for uni-vector-sensor direction finding in the presence of a reflecting boundary. The data are organized such that the phase shifts for frequency estimation of each signal corresponding to two distinct sampling rates are separately embedded in the modulus and argument of the ESPRIT eigenvalue, whereas the direction cosines for azimuth-elevation direction-of-arrival (DOA) estimation dwell in the associated ESPRIT eigenvector, and thus the matching procedure for aligning the output of multidimensional and multi-invariant data manipulation is avoided. The temporal multiresolution herein realized is iteration free and needs merely one lower-dimensional eigendecomposition. The simplified version of the presented method offers a similar performance while requiring only two time-delayed data sets and thus has a comparable computational complexity with the traditional single resolution ESPRIT. This ESPRIT-type method is also blind to the reflection coefficient which generally depends on the boundary nature, medium property, and signal parameters still to be estimated, viz. DOAs and signal frequencies. Simulation results are included to validate the proposed algorithm.