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

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

2008-01-18

arxiv.org/abs/0801.2790v1

Statistics

Methodology

Scientific paper

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.

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