Approximate maximum-likelihood algorithms for two-dimensional frequency estimation of a complex sinusoid

Starting with the maximum-likelihood (ML) formulation, three iterative algorithms for approximate ML frequency estimation of a two-dimensional (2-D) complex sinusoid in white Gaussian noise are developed. Mean and variance analyses of the proposed methods are provided, which show that they are approximately unbiased and their performance achieves Cramér-Rao lower bound (CRLB) at sufficiently high signal-to-noise ratio (SNR) conditions. Computer simulation results are included to corroborate the theoretical development as well as to contrast the performance of the proposed algorithms with Kay's estimators and the CRLB. © 2006 IEEE.