Utilizing principal singular vectors for two-dimensional single frequency estimation

In this paper, frequency estimation of a two-dimensional (2D) cisoid in the presence of additive white Gaussian noise is addressed. By utilizing the rank-one property of the 2D noise-free data matrix, the frequencies are estimated in a separable manner from the principal left and right singular vectors according to an iterative weighted least squares procedure. We have also derived the mean and variance expressions for the frequency estimates, which show that they are approximately unbiased and their accuracy achieves Cramér-Rao lower bound (CRLB) at sufficiently high signal-to-noise ratio conditions. Computer simulation results are included to corroborate the theoretical development as well as to contrast the performance of the proposed algorithm with the weighted phase averager and iterative quadratic maximum likelihood method as well as CRLB.