A bootstrap technique for rank estimation

A crucial step in many signal processing applications is the determination of the effective rank of a noise corrupted multi-dimensional signal, i.e. the dimension of the signal subspace. Standard techniques for rank estimation, such as the minimum description length, often have shortcomings in practice, an example being when noise parameters are unknown. An alternative scheme is proposed for rank detection. From successive pairs of the ordered eigenvalues of the array covariance, a series of statistics is formed. The statistics are chosen such that their distributions for noise eigenvalue pairs are close. The actual distributions are unknown and are estimated with the bootstrap. The rank is then found by a sequential comparison of the estimated distributions using a Kolmogorov-Smirnov test