论文标题
估计叠加正弦的数量
Estimating the number of superimposed sinusoids
论文作者
论文摘要
在噪声存在下叠加正弦的数量的估计是统计信号处理中重要的模型订单选择（MOS）问题。在本文中，我们提出了一种新的方法来设计MOS算法，以估计叠加正弦的数量。我们提出的方法部分基于最小误差概率标准。此外，我们非常关注MOS算法的性能和一致性分析。在这项研究中，错误概率用作MOS算法的通用性能度量。我们提出了一个理论框架，使得提供一致性分析并获得有关广泛MOS算法的近似误差概率的封闭形式表达式。例如，我们将此框架应用于几种MOS算法的一致性和性能分析，以估计叠加正弦的数量。使用获得的结果，我们提供了所呈现的MOS算法的参数优化。最后，我们研究了MOS算法的设计和性能分析的一种准利氏菌方法。所提出的理论框架用于找到准利氏症方法的范围。
Estimation of the number of superimposed sinusoids in the presence of noise is an important model order selection (MOS) problem in statistical signal processing. In this paper, we propose a new approach to the design of MOS algorithms for estimating the number of superimposed sinusoids. Our proposed approach is partially based on the minimum error probability criterion. Also, we pay a lot of attention to the performance and consistency analysis of the MOS algorithms. In this study, an error probability is used as a universal performance measure of the MOS algorithms. We propose a theoretical framework that makes it possible to provide consistency analysis and to obtain closed-form expressions for the approximated error probabilities of a wide range of MOS algorithms. As an example, we applied this framework to the consistency and performance analysis of several MOS algorithms for estimating the number of superimposed sinusoids. Using the obtained results, we provide a parametric optimization of the presented MOS algorithms. Finally, we examine a quasilikelihood approach to the design and performance analysis of the MOS algorithms. The proposed theoretical framework is used to find the scope of the quasilikelihood approach.
