一种求解复指数逼近问题的黑箱方法
A black box method for solving the complex exponentials approximation problem
AI总结：
针对从含噪数据中估计阻尼正弦波数量及其参数的问题，提出一种随机扰动方法，在低信噪比下优于最大似然方法，且超参数可固定，形成黑箱方法。
摘要：
一个在许多不同应用背景下出现的常见问题是，估计加权和最佳拟合一组有限含噪数据的指数衰减正弦波的数量，并估计其参数。为此存在许多不同的方法。其中最好的方法基于近似最大似然估计，假设已知阻尼正弦波的数量，然后可以通过阶数选择程序进行估计。由于该问题可能严重不适定，提出了一种随机扰动方法，在信噪比较低时比基于最大似然的方法提供更好的结果。该方法依赖于一些超参数，这些超参数实际上与应用无关。因此，它们可以一次性固定，从而产生一种黑箱方法。
英文摘要：
A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different methods exist to this purpose. The best of them are based on approximate Maximum Likelihood estimators, assuming to know the number of damped sinusoids, which can then be estimated by an order selection procedure. As the problem can be severely ill posed, a stochastic perturbation method is proposed which provides better results than Maximum Likelihood based methods when the signal-to-noise ratio is low. The method depends on some hyperparameters which turn out to be essentially independent of the application. Therefore they can be fixed once and for all, giving rise to a black box method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
