Low frequency three-dimensional DOA estimation for underwater gliders using an arbitrary tetrahedral array

This study proposes a method for estimating the three-dimensional (3-D) direction of arrival (DOA) of low-frequency line spectra with an arbitrary tetrahedral array on a moving underwater platform, such as underwater glider (UG). First, we provide the theoretical derivations of the 3-D DOA estimation algorithm. Four sensors are matched pairwise without duplication and the time difference of arrival (TDOA) of each pair is estimated using the cross-spectral method. The geometric relation between the space coordinate vector of the paired sensors and direction vector of the incoming signal is combined with the TDOA to establish the overdetermined equations. The algorithm solves the overdetermined equations to obtain the azimuth and elevation of the line spectra, and exploits all the information from sensors to enhance the accuracy of DOA estimation. And the Cramer–Rao lower bound (CRLB) of an arbitrary tetrahedral array is derived as a function of the signal-to-noise ratio (SNR), integration time, signal bandwidth, frequency, array arrangement, and DOA of the signal. Second, simulations and a sea trial verify the feasibility of the 3-D DOA estimation algorithm using a tetrahedral array on a moving UG. Finally, several factors that influence the algorithm are analyzed, including the DOA of the source, frequency, SNR, sensor position error and phase error. The upper frequency limit to avoid spatial aliasing is also derived as a function of the array aperture. The study shows that the tetrahedral array is suitable for various underwater mobile platforms owing to its small scale and irregularity.