We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform of the given equidistant signal values. We show that ESPIRA can be interpreted as a matrix pencil method applied to Loewner matrices. These Loewner matrices are closely connected with the Hankel matrices which are usually employed for signal recovery. Due to the construction of the Loewner matrices via an adaptive selection of index sets, the matrix pencil method is stabilized. ESPIRA achieves similar recovery results for exact data as ESPRIT and the matrix pencil method but with less computational effort. Moreover, ESPIRA strongly outperforms ESPRIT and the matrix pencil method for noisy data and for signal approximation by short exponential sums.
翻译:我们引入了一种基于超常合理接近(ESPIRA)对稀散指数值进行信号参数估计的新方法。 我们的算法使用AA算法合理接近给定的等离散Fourier信号值的离散Fourier转换。 我们显示,ESPIRA可以被解释为适用于Lewner矩阵的矩阵铅笔方法。 这些Lewner矩阵与通常用于信号恢复的Hankel矩阵紧密相连。由于通过对指数集进行适应性选择来构建Lewner矩阵,矩阵铅笔方法已经稳定下来。 ESPIRA在精确数据方面取得了类似于ESPRIT和矩阵铅笔方法的回收结果,但计算努力却较少。 此外,ESPIRA明显地超越了ESPRIT和用于噪音数据和短指数信号近似的矩阵铅笔方法。