含缺值GNSS基准站坐标序列的非插值小波分析与信号提取

受多种因素影响,GNSS基准站坐标序列通常都含有缺值,传统小波分析需要对缺值数据进行内插或补零处理。本文基于小波系数与时间序列观测数据的重构关系,提出了一种非插值的二进小波变换的最小范数解法,导出了相应的计算式,并严格证明了传统的补零处理算法与本文的最小范数解法等价。最后利用中国地壳运动观测网络一期27个基准站实测数据以及模拟数据进行了验证分析。结果表明,本文的非插值算法与插值算法提取的信号差异较小,27个基准站坐标序列的平均残差中误差仅相差2.01%(North),0.54%(East)和1.26%(Up),两种算法提取的信号之差与信号平均方差比仅相差1.16%(North),0.54%(East)和1.62%(Up)。

Dyadic wavelet transform and signal extraction of GNSS coordinate time series with missing data

The GNSS position time series are often analyzed by using traditional dyadic wavelet transform, which requires that the time series must be complete. However, missing data inevitably occur in the GNSS position time series due to a variety of causes. In order to extract signals from the incomplete position time series, a modified dyadic wavelet transform algorithm is developed and the corresponding formulas are derived in this paper based on the principle that missing data can be reproduced by its wavelet coefficients. The equivalence between new algorithm and zero-padding algorithm is proved, which indicates that the zero-padding algorithm is essentially a least squares minimum norm solution. Finally, the real position time series of 27 based stations from Crustal Movement Observation Network of China (CMONOC) and simulated data are adopted to verify the validation of the new algorithm, the results show that the difference between the signals extracted by new algorithm and interpolation algorithm is small, with the differences of mean medium errors of 27 base stations are only 2.01%(North), 0.54%(East), 1.26%(Up) and the mean ratios of variance for difference of two signals to the variance for two signals are only 1.16%(North), 0.54%(East), 1.62%(Up).