2008/01/18 by Mark Kliger, Kliger, Mark, Joseph M. Francos +1
Computer Science · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #Control Systems and Identification #Direction-of-Arrival Estimation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.0801.2790
arxiv created 2008/01/18 · openalex publication_date 2008/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of jointly estimating the number as well as the parameters of two-dimensional sinusoidal signals, observed in the presence of an additive colored noise field. We begin by elaborating on the least squares estimation of 2-D sinusoidal signals, when the assumed number of sinusoids is incorrect. In the case where the number of sinusoidal signals is under-estimated we show the almost sure convergence of the least squares estimates to the parameters of the dominant sinusoids. In the case where this number is over-estimated, the estimated parameter vector obtained by the least squares estimator contains a sub-vector that converges almost surely to the correct parameters of the sinusoids. Based on these results, we prove the strong consistency of a new model order selection rule.