Combining the Liouville equations for polar motion (PM) with forecasted geophysical effective angular momentum (EAM) functions can significantly improve the accuracy of Earth's PM predictions. These predictions rely on deconvolution and convolution methods. Deconvolution derives the geodetic EAM function from the PM observations, while convolution uses both the geodetic and geophysical EAM functions to reproduce and predict the PM values. However, there are limitations in existing numerical realisations of deconvolution and convolution that must be addressed. These limitations include low-frequency biases, high-frequency errors, and edge errors, which can negatively impact the accuracy of PM prediction. To overcome these concerns, we develop the Convolution Least Squares (Conv-LS) scheme through a multi-perspective analysis in the frequency domain, PM domain, and EAM domain. By comparing representative approaches for reproducing three different PM series (IERS C01, IERS C04, and IGS) with varying sampling intervals (18.25 days, daily, and 6 h), we demonstrate that the Conv-LS scheme can effectively eliminate the usually present spurious signals and also integrate high-accuracy deconvolution algorithms to reduce reproduced errors further. Compared to the traditional approacsh (using a low-accuracy discrete PM equation for deconvolution and numerical integration for convolution), our new approach (utilising a high-accuracy deconvolution algorithm along with the Conv-LS scheme for convolution) reduces the standard deviations of the residuals' x-component by 31.0%, 60.1%, and 13.7% for C01, C04, and IGS PM series, respectively, while also reducing the y-component by 17.3%, 47.0%, and 14.0%, respectively. These results highlight the superiority of the Conv-LS scheme, leading us to recommend it for practical applications.

将极地运动 （PM） 的 Liouville 方程与预测的地球物理有效角动量 （EAM） 函数相结合，可以显著提高地球 PM 预测的准确性。这些预测依赖于反卷积和卷积方法。反卷积从 PM 观测值中得出大地测量 EAM 函数，而卷积则同时使用大地测量和地球物理 EAM 函数来重现和预测 PM 值。然而，现有的反卷积和卷积数值实现存在必须解决的局限性。这些限制包括低频偏差、高频误差和边缘误差，它们可能会对 PM 预测的准确性产生负面影响。为了克服这些问题，我们通过在频域、PM 域和 EAM 域进行多视角分析，开发了卷积最小二乘法 （Conv-LS） 方案。通过比较以不同的采样间隔（18.25 天、每天和 6 小时）再现三种不同 PM 系列 （IERS C01、IERS C04 和 IGS） 的代表性方法，我们证明了 Conv-LS 方案可以有效消除通常存在的杂散信号，还可以集成高精度反卷积算法以进一步减少再现的误差。与传统的 approacsh 相比（使用低精度离散 PM 方程进行反卷积，使用数值积分进行卷积），我们的新方法（利用高精度反卷积算法和 Conv-LS 方案进行卷积）将 C01、C04 和 IGS PM 系列残差的 x 分量的标准差分别降低了 31.0%、60.1% 和 13.7%，同时还将 y 分量减少了 17.3%， 分别为 47.0% 和 14.0%。 这些结果突出了 Conv-LS 方案的优越性，因此我们推荐将其用于实际应用。