Fast and accurate estimator for two-dimensional cisoids based on QR decomposition

In this paper, we apply the QR decomposition to parameter estimation for K two-dimensional (2-D) complex-valued sinusoids embedded in additive white Gaussian noise. By exploiting the rank-K and linear prediction (LP) properties of the 2-D noise-free data matrix, we show that the frequencies and damping factors of one dimension can be extracted from the first K rows of R, that is, the upper triangular matrix in the factorization. An iteratively weighted least squares (IWLS) algorithm is then proposed to estimate the LP coefficients from which the sinusoidal parameters in this dimension are computed. The frequencies and damping factors of the remaining dimension are estimated using a similar IWLS procedure such that the 2-D parameters are automatically paired. We thus refer our estimator to as the QR-IWLS algorithm. Moreover, we have analyzed its bias and mean square error performance. In particular, closed-form expressions are derived for the special case of K=1. The performance of the QR-IWLS method is also evaluated by comparing with several state-of-the-art 2-D harmonic retrieval algorithms as well as Cramér-Rao lower bound via computer simulations.