Two-dimensional frequency estimation with multiplicative noise using non-causal minimum variance representation

In this paper, the problem of two-dimensional (2D) frequency estimation of a complex sinusoid embedded in a white Gaussian additive noise and a multiplicative noise is addressed. For this purpose, we derive a noncausal minimum variance representation, the coefficients of which are described according to the frequencies to be estimated. Therefore, estimates are given without a complete computation of the power spectral density over the 2D frequency plane, but directly from the coefficients. 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 directly achieved with the proposed model, even for signal embedded in multiplicative noise.