Eigenvalue Analysis For Source Detection With Narrowband Passive Arrays

Knowing the number of sources in the acoustic field of a narrowband passive array can be very useful when determining the bearing of these sources relative to the array; many of the "high resolution" bearing estimation algorithms assume that the number of sources is known. The sphericity test is a well-known algorithm for estimating the number of sources from the eigenvalues of the spatial correlation matrix of the array. A new sphericity test statistic is proposed whose distribution approaches the asymptotic $\chi\sp2$ distribution much faster than previously proposed statistics and, consequently, weaker sources are more readily detected. The capability of this algorithm to detect closely spaced sources in white Gaussian noise is examined and compared to the resolution capabilities of well-known bearing estimation algorithms. The sphericity test statistic is modified for use in non-white noise and the resolution in this situation is also analyzed.