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摘要
This paper realizes parameter estimation of canonical autoregressive decomposition (CARD) model by computing partially sparse solution to a linear inverse problem. By constructing an over-complete dictionary, it is demonstrated that the solution with respect to the sinusoids is sparse, while that with respect to the colored noise is not. To derive the solution, an alternating optimization algorithm, named Partially Sparse Solution Algorithm (PSSA), is proposed. PSSA is initialized by basis selection method, and updated alternately between estimation of the sinusoids and the colored noise. When updating the sinusoids estimation, diversity minimization is adopted as the criterion for the cost function. As for the estimation of the colored noise, Maximum likelihood (ML) criterion is used. Several numerical examples confirm validation and Superiority of PSSA. Firstly, it generalizes basis selection method to colored noise background. Secondly, the number of the sinusoids can be estimated based on the solution; so the predetermined number of the sinusoids needs not to be exact. Thirdly, PSSA shows little sensitivity to the choice of model order and is applicable to short data record. Furthermore, compared with ML method, PSSA attains higher estimation accuracy especially when the sinusoids are located near the peak of the noise spectrum.
