Two-dimensional frequency estimation using autocorrelation phase fitting

The problem of two-dimensional (2D) frequency estimation of a complex sinusoid embedded in a additive white Gaussian noise is addressed. A new frequency estimator based on a least squares plane fitting of the estimated autocorrelation phase of the signal is derived. This algorithm requires a 2D phase unwrapping step which can be easily done. This algorithm is shown to be unbiased and attains the Cramer Rao bounds for high signal-to-noise ratio (SNR > 0 dB). Accuracy and robustness of this new 2D frequency estimator are statistically assessed by Monte Carlo simulations. The results obtained show that a good local frequency estimation can be achieved with a very simple algorithm, and a very small number of points are used for the autocorrelation estimation.