奇异谱分析在GPS站坐标监测序列分析中的应用

Application in Analysis of coordinate series based on the Singular Spectral Analysis

摘要:

利用奇异谱分析（SSA）对测站坐标时间序列进行数据处理，包括数据补缺、趋势项和周期项的识别和提取。奇异谱分析是一种从时间序列的动力重构出发并与经验正交函数相联系的统计技术，可以较好地从含噪声的有限尺度时间序列中提取趋势和周期等信息，目前已应用于多种时间序列的分析中。文章将奇异谱分析的优点应用到GPS时间序列分析中：利用奇异谱分析对中国地壳运动观测网络GPS数据服务提供的测站坐标（NEU）时间序列（以BJFS站为例）进行补缺，各向插补的均方误差均为毫米级；根据降噪重构序列提取坐标时间序列中的趋势成分（N：-11.688mm/a，E：29.585mm/a ，U：2.557mm/a）和周期成分（N、U方向上存在年周期和半年周期，U方向上还存在着1.5年和0.25年左右的周期，E方向上只存在年周期）；对完整序列进行重构降噪，即从原始序列中提取有用信息而丢弃一些干扰信息，起着平滑作用。试验结果表明，BJFS站的各方向上均存在显著的变动周期和明显的趋势，也有较多的噪声信息。

Abstract:

Singular spectrum analysis (SSA) was introduced to data processing of station coordinates, including treatment of missing values, identification and extraction of trends and cycles. Singular spectrum analysis，a statistical technique with reconstruction and empirical orthogonal function, can effectively extract trends and cycles from the limited scale of the time series with noise. Hence, SSA has been applied to various time series analysis. It took advantages of the singular spectrum analysis and applied SSA to the process of GPS time series. Coordinate time series from Crustal Movement Observation Network of China GPS data services was used by SSA for treatment of missing values (MSE of interpolation at every direction are in millimeter degree), reconstruction and extraction of trend (N:-11.688mm/a,E:29.585mm/a,U:2.557mm/a) and cycle components (N:0.5a、1a, E:1a, U:0.25a、0.5a、1a、1.5a). The results showed that obvious trend, significant cycles and noise do exist in each direction of BJFS.