The ULR-repro3 GPS data reanalysis solution (aka ULR7a)
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The ULR analysis center has participated in the third reprocessing campaign (repro3) of the International GNSS Service (IGS). Its ULR-repro3 solution (aka ULR7) included 601 stations for which the GNSS data available between 2000.0 and 2021.0 was reprocessed using the models and corrections adopted by the IGS for repro3. The main steps and features of ULR-repro3 reanalysis are as follows. First, daily GNSS solutions were computed using a free-network weighted least squares adjustment strategy. That is, station positions, Earth Orientation parameters, satellite orbits and zenith tropospheric delays were adjusted simultaneously using GAMIT Software version 10.71. The station networks were regional, but one global. This step yielded a number of daily solutions (subnets) of less than 50 stations each that were expressed in their own (daily) terrestrial frame. Secondly, the regional and global subnets were combined into daily global solutions (all stations included and expressed in the same but undetermined frame). These daily global solutions were then aligned to the ITRF2014 frame using a time-dependent functional model that included station positions at a reference epoch, velocities, seasonal signals (annual and semi-annual) and transformation parameters (translation, rotation, scale) between the daily undetermined frames and the ITRF2014 for a subset of IGS core stations. Station position offset discontinuities (mostly due to equipment changes or earthquakes), velocity changes and post-seismic displacement signals were added, as appropriate (based on metadata information and visual inspection of the series). This step included manual editing to identify (and remove) outliers as well as additional non-documented position offset discontinuities. It was iterated until convergence (analyst subjective criteria). From this step, daily position time series in the ITRF2014 frame for all (601) stations were retained. A minimum of three continuous years without an offset in the time series was required for the next step to estimate vertical velocities. This selection criteria yielded 554 daily station position time series, among which 457 are nearby a tide gauge (less than 15 km). The last step was concerned with the estimation of the parameters of interest and their uncertainties, in which both a functional and a stochastic model were adjusted to each of the station position time series from the previous step. To limit biases in the parameter estimation, non-tidal atmospheric loading displacements were subtracted from the position time series prior to this adjustment using the products provided by the Earth System Modelling team of the German research center for geosciences. The stochastic model accounted for a linear combination of white noise and power law process, whose parameters were estimated using the Restricted Maximum Likelihood Estimation method. The functional model included long-term linear trends, position offset discontinuities, and periodic signals (annual, semiannual, and terannual signals, GPS draconitics of 1.04 year up to the 8th harmonics and three fortnightly signals). The parameters of this functional model and their uncertainties were estimated using the weighted least squares estimator and taking the inverse of the estimated observation covariance matrix as weight matrix. Further details in the companion paper submitted to ESSD.
ULR分析中心参与了国际GNSS服务（International GNSS Service, IGS）的第三次再处理任务（repro3）。其ULR-repro3解（又称ULR7）涵盖601个测站，这些测站在2000.0至2021.0年间的GNSS数据，采用IGS针对repro3确定的模型与改正项完成了再处理。ULR-repro3再分析的主要步骤与特征如下： 1. 采用自由网加权最小二乘平差策略解算每日GNSS解。即借助GAMIT软件（GAMIT Software）10.71版本，同时解算测站坐标、地球定向参数（Earth Orientation Parameters, EOP）、卫星轨道与天顶对流层延迟。测站网络以区域子网为单元，但整体构成全球网络；该步骤得到多个每日解（子网），每个子网包含少于50个测站，采用各自的每日地面参考框架。 2. 将各区域与全球子网合并为每日全球解（纳入所有测站，采用统一但未确定的参考框架）。随后，利用时变函数模型将这些每日全球解对齐至ITRF2014参考框架，该模型包含参考历元处的测站坐标、运动速度、季节性信号（年周期与半年度周期），以及IGS核心测站子集的每日未确定参考框架与ITRF2014之间的转换参数（平移、旋转、尺度因子）。此外，基于元数据信息与序列目视检查结果，视情况加入测站坐标偏移间断（多由设备更换或地震引发）、速度变化与震后位移信号。该步骤包含人工编辑环节，用于识别并剔除粗差，以及补充未被记录的额外坐标偏移间断，迭代直至收敛（由分析人员依据主观标准判断）。经此步骤，可得到全部601个测站在ITRF2014参考框架下的每日位置时间序列。 若要开展下一步的垂直速度估计，需保证测站位置时间序列至少具备连续三年无偏移的时段。按此筛选标准共得到554条每日测站位置时间序列，其中457条邻近验潮站（距离小于15 km）。 最后一步为估计目标参数及其不确定度：针对上一步得到的每条测站位置时间序列，分别构建并平差函数模型与随机模型。为抑制参数估计中的偏差，在平差前先利用德国地球科学研究中心地球系统建模团队提供的产品，从位置时间序列中扣除非潮汐大气负荷位移。随机模型采用白噪声与幂律过程的线性组合，其参数通过受限极大似然估计（Restricted Maximum Likelihood Estimation）方法求解。函数模型包含长期线性趋势、坐标偏移间断、周期信号（年周期、半年度、季年度信号，1.04年的GPS食年周期（draconitics）谐波至8次，以及三个半月周期信号）。采用加权最小二乘估计器，并以估计得到的观测协方差矩阵的逆作为权矩阵，求解该函数模型的参数及其不确定度。更多细节详见提交至ESSD的配套论文。
