Strongly Consistent Model Order Selection for Estimating 2-D Sinusoids in Colored Noise

The problem of jointly estimating the number as well as the parameters of 2-D sinusoidal signals, observed in the presence of an additive colored noise field, is considered. We begin by establishing the strong consistency of the nonlinear least squares estimator of the parameters of 2-D sinusoids, when the number of sinusoidal signals assumed in the field is incorrect. Based on these results, we prove the strong consistency of a new family of model order selection rules.