由 张 良承 A new tropospheric delay combination prediction model based on time series decomposition and deep learning
基于时间序列分解与深度学习的新型对流层延迟组合预测模型
引文格式 | Citation:
Yue Y C, Wang Y X, Shangguan M, et al. A new tropospheric delay combination prediction model based on time series decomposition and deep learning[J]. Advances in Space Research, 2025, 76(4): 1970-1983. DOI: 10.1016/j.asr.2025.05.082.
Advances in Space Research（中科院3区，IF：2.8）
Tropospheric delay modeling
Time-series decomposition
Deep learning
Combined prediction models
Precise point positioning
Time-series decomposition
Deep learning
Combined prediction models
Precise point positioning
Abstract | 摘要
Zenith tropospheric delay (ZTD) prediction is crucial for high-precision navigation. However, accurately modeling ZTD remains challenging due to its combination of linear and nonlinear characteristics. In this paper, we propose a hybrid ZTD prediction model that separately addresses the trend and seasonal variations. The model decomposes ZTD time series using seasonal-trend decomposition based on loess (STL), and then predicts nonlinear components with a long short-term memory network (LSTM) and linear components with an autoregressive integrated moving average model (ARIMA). The individual predictions are recombined to produce a final forecast, which we call the STL-LSTM-ARIMA model. To assess its effectiveness, we compare it to LSTM, ARIMA, and extreme learning machine (ELM) model. Our results show that the STL-LSTM-ARIMA model consistently outperforms these models across all evaluation metrics, including a root mean square error (RMSE, 1.32 cm), an average normalized root mean square error (NRMSE, 0.56 %), a mean absolute error (MAE, 0.98 cm) and a coefficient of determination (R2, 0.83). Further analysis reveals that the model maintains robust predictive performance across different months, with the highest accuracy observesd in January and lower performance in July. The model sustains exceptional forecasting accuracy for lead times of up to 12 hours, maintaining RMSE < 1.60 cm, NRMSE < 0.7 %, MAE < 1.25 cm, and R2 ≥ 0.75. These results conclusively validate the STL-LSTM-ARIMA model’s superior capability and reliability for short-term ZTD prediction. We apply the tropospheric delay parameters predicted by the SLA model to the static precise point positioning (PPP), and the results show that the SLA model-assisted PPP scheme (PPP-SLA) improves the positioning convergence time and accuracy to a certain extent compared to the parameter estimation scheme (PPP-EST) and the parameter estimation scheme for estimating the horizontal gradient (PPP-ESTG). Especially in the U direction, the positioning convergence time is increased by 48.6 % and 47.0 %, and the positioning accuracy is increased by 12.0 % and 7.3 %, respectively.
天顶对流层延迟（ZTD）是高精度导航定位的关键误差之一。由于ZTD时间序列中复杂的线性和非线性特性，其精确建模仍然具有挑战性。在本研究中，我们提出了一种组合预测模型） ，分别预测趋势项和季节变化再进行组合。 首先，该模型采用局部多项式合回归的季节性趋势分解算法（STL）对 ZTD 时间序列进行分解 ，并分别利用长短期记忆神经网络（LSTM）和自回归综合移动平均模型（ARIMA）预测非线性分量和线性分量，然后预测分量被重构组合以产生最终预测，我们称之为 STL-LSTM-ARIMA 模型。为了评估模型性能，将 STL-LSTM-ARIMA 模型与 LSTM，ARIMA 和极限学习机模型（ELM）进行比较。 实验结果表明，新模型在所有评估指标上均表现出显著优势：均方根误差（RMSE）为1.32 cm，归一化均方根误差（NRMSE）为0.56%，平均绝对误差（MAE）为0.98 cm，决定系数（R²）达到0.83。同时，该模型展现出较优的月份适应性，其中1月份预测精度最高，7月份相对最低。在12小时预测时长内，模型始终保持优良性能（RMSE<1.60 cm，NRMSE<0.7%，MAE<1.25 cm，R²≥0.75）。将SLA模型预测的对流层延迟参数应用于静态精密单点定位（Precise Point Positioning，PPP）并与传统参数估计方案（PPP-EST）和水平梯度参数估计方案（PPP-ESTG）进行比较，基于SLA 模型辅助的 PPP 方案（PPP-SLA） 在一定程度上提高了定位收敛时间和精度 。特别是在高程方向（U 方向）上，收敛时间分别缩短了 48.6%和 47.0%，定位精度分别提高了 12.0%和 7.3%。