顾及有色噪声的GNSS时间序列时域信号提取

随着大型地震的发生,GNSS时间序列中除线性趋势和周期信号外,还存在大量震后瞬态,准确地提取各项时域信号是运用GNSS时间序列进行地学研究的关键.为此,本文提出了顾及有色噪声的GNSS时间序列时域信号提取法.该方法首先基于白噪声（White Noise,WN）+闪烁噪声（Flicker Noise,FN）模型,使用最大似然估计（Maximum Likelihood Estimation,MLE）对震前GNSS时间序列进行参数估计,并根据参数估值来去除震后时间序列中的震前信号,以此获取残差序列;然后将残差序列作为求解特征时间尺度的观测量,WN+FN模型作为观测量的随机模型,并采取非线性最小二乘法（Non-linear Least Squares,NLS）法估计特征时间尺度;最后利用估计的特征时间尺度构建GNSS时间序列函数模型,并采用MLE估计其未知参数,进而实现时域信号的提取.经模拟数据分析,考虑有色噪声时,特征时间尺度估计算法的收敛性提高了25%,各项未知参数的标准差（Standard Deviation,STD）显著下降.最后,将该算法应用于日本区域实测数据,并与传统方法进行了对比分析.

Time domain signal extraction from GNSS time series with colored noise

With the occurrence of large earthquakes, in addition to linear trend and periodic signals, there are also a large number of post-seismic transients in GNSS time series. Accurately extracting all kinds of time domain signals is the key for various investigations using GNSS time series. Therefore, the time domain signal extraction in GNSS time series with colored noise is proposed in this paper. Firstly, the maximum likelihood estimation (MLE) with white noise (WN)+flicker noise (FN) model is used to estimate parameters from pre-seismic GNSS time series, and the pre-seismic signals are removed using parameter estimation to obtain the post-seismic residual sequence; Then, the residual sequence is used as the observation to solve the characteristic time scale, the WN+FN model is used as the stochastic model for the observation, and the non-linear least squares (NLS) method is used to estimate the characteristic time scale; Finally, the estimated characteristic time scale is used to construct functional model of GNSS time series, and MLE is used to estimate its unknown parameters, so as to extract the time domain signal. Through the analysis of simulation data, when considering colored noise, the convergence of characteristic time scale estimation algorithm is improved by 25%, and the standard deviation (STD) of unknown parameters is significantly reduced. Finally, the algorithm is applied to the measured data in Japan, and compared with the traditional method.