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.
- Least squares estimation
- model order selection
- strong consistency
- two-dimensional random fields