中文摘要：

针对新一代GPS的轮廓信号和几何误差成分特点，引入一种具有自适应能力的非平稳信号分析新方法——希尔伯特-黄变换（Hilbert—HuangTransform，HHT）用于轮廓滤波和几何误差成分分析。研究了HHT中固有模态函数（IntrinsicModeFunction，IMF）的特点，指出各阶IMF分量按特征时间尺度从小到大的顺序排列，构建了基于经验模态分解（EmpiricalModeDecomposition，EMD）的滤波器并将其用于轮廓滤波。分析了EMD分解中剩余项的特点，根据各阶IMF的瞬时频率和幅值函数以及Hilbert—Huang谱，确定了各周期性分量以及非周期性趋势项。几何误差仿真信号分析结果表明，与小波神经网络方法的相比，HHT方法获取的初始阶段信号更好；对实测轮廓曲线，采用HHT和小波变换进行了滤波试验验证，结果表明HHT方法获取的轮廓曲线更平滑。

英文摘要：

Focusing on the new generation of GPS profile signal and geometric error component characteristics, the paper introduces a non-stationary signal analysis new approach Hilbert-Huang Transform（HHT） for profile filtering and geometric error components analysis. Characteristics of Intrinsic Mode Function（IMF） of HHT is studied. Pointed out that each order IMF component characteristic time scales from small to high order, on this basis, EMD-based filter constructor is poprosed. Studied the characteristics of the remaining items, according to instantaneous frequency and amplitude function of each order IMF and the Hilbert-Huang spectrum, this paper determines the cyclical component as well as non-periodic trend term. The geometric error simulation signal analysis results show that, compared with wavelet neural network method, the HHT method to obtain the initial phase of the signal is better. Profile curve analysis results show that, the use of HHT and wavelet transform filtering experimental verification, profile curve obtained using the HHT method is the smoother.