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.

中文翻译：

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使用累积分布变换的参数化信号估计

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。我们的方法最小化了测量信号和模型信号之间的 Wasserstein 距离。我们推导出 CDT 的一些有用特性，并表明由此产生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特性，并提出了一种减轻噪声对估计影响的新方法。通过将其应用于源定位问题并将其性能与传统方法进行比较来评估所提出的估计方法。