vbICA code

The independent component analysis (ICA) is a popular technique adopted to approach the so-called blind source separation (BSS) problem, i.e., the problem of recovering and separating the original sources that generate the observed data. However, the independence condition is not easy to impose, and it is often necessary to introduce some approximations. Here we provide a MATLAB code which implement a modified variational Bayesian ICA (vbICA) method for the analysis GNSS time series. The vbICA method models the probability density function (pdf) of each source signal using a mix of Gaussian distributions, allowing for more flexibility in the description of the pdf of the sources with respect to standard ICA, and giving a more reliable estimate of them. In particular, this method allows to recover the multiple sources of ground deformation even in the presence of missing data. This material is based on the original work of Choudrey (2002) and Choudrey and Roberts (2003), subsequently adapted by Gualandi et al. (2016) and Serpelloni et al. (2018) for the study of GNSS position time series.

独立成分分析（ICA）是解决盲源分离（BSS）问题的主流技术之一，该问题旨在恢复并分离出生成观测数据的原始信源。然而，独立性约束往往难以直接施加，通常需要引入近似处理手段。本文提供一段MATLAB代码，实现了改进变分贝叶斯独立成分分析（vbICA）方法，用于全球导航卫星系统（GNSS）时序数据分析。vbICA方法采用混合高斯分布对各信源信号的概率密度函数（pdf）进行建模，相较于标准ICA，该方法能够更灵活地刻画信源的概率密度分布，从而得到更为可靠的信源估计结果。尤为关键的是，即便存在缺失数据，该方法仍可恢复出多组地面形变信源。本材料基于Choudrey（2002）以及Choudrey与Roberts（2003）的原创研究成果，后经Gualandi等人（2016）和Serpelloni等人（2018）适配，用于GNSS位置时序的相关研究。

搜集汇总

背景与挑战

背景概述

该数据集提供了一个MATLAB实现的变分贝叶斯独立成分分析（vbICA）代码，专门用于GNSS时间序列分析，能够灵活处理源信号的概率密度函数并支持缺失数据情况下的源信号估计。