Rubaiyat Abu Hasnat Mohammad, Hallam Kyla M, Nichols Jonathan M, Hutchinson Meredith N, Li Shiying, Rohde Gustavo K
Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904 USA.
U.S. Naval Research Laboratory, Washington, DC 20375 USA.
IEEE Trans Signal Process. 2020;68:3312-3324. doi: 10.1109/tsp.2020.2997181. Epub 2020 May 25.
We present a new method for estimating signal model parameters using the Cumulative Distribution Transform (CDT). Our approach minimizes the Wasserstein distance between measured and model signals. We derive some useful properties of the CDT and show that the resulting estimation problem, while nonlinear in the original signal domain, becomes a linear least squares problem in the transform domain. Furthermore, we discuss the properties of the estimator in the presence of noise and present a novel approach for mitigating the impact of the noise on the estimates. The proposed estimation approach is evaluated by applying it to a source localization problem and comparing its performance against traditional approaches.
我们提出了一种使用累积分布变换（CDT）估计信号模型参数的新方法。我们的方法将测量信号与模型信号之间的瓦瑟斯坦距离最小化。我们推导了CDT的一些有用性质，并表明所得的估计问题虽然在原始信号域中是非线性的，但在变换域中变成了线性最小二乘问题。此外，我们讨论了存在噪声时估计器的性质，并提出了一种减轻噪声对估计影响的新方法。通过将所提出的估计方法应用于源定位问题并将其性能与传统方法进行比较来对其进行评估。
