# Deep Learning CNN-GRU Method for GNSS Deformation Monitoring Prediction
## 3 Experiment  
The experiment was conducted at Sanhe Sluice of Hongze Lake, Jiangsu, China, for which the configure parameters are as shown in Table 1. The monitoring site and the refer-ence site are shown in Figure 2.  
This study validates the effectiveness of the proposed method using a North (N)-direction time series as an example. We use 80% of the time series as the training set and the remaining 20% as the validation set. A 24 h extrapolation is provided at the end for prediction. The partition of the GNSS time series is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Configure** & **Parameter** \\ \hline The experiment period & 10 September 2023–29 March 2024 \\ GNSS systems & BDS(B1I, B2I), Galileo(E1B/C, E5b),GPS(L1C/A, L2C) \\ Sampling frequency & 1 Hz \\ Ambiguity resolution method & MLAMBDA \\ Multipath error model & Stellar day filter in observational domain \\ Tropsphere method & Saastamoinen Model + Random Walk \\ Ionosphere method & Broadcast model \\ Intervals of outputs & 1 h \\ Smoothing filter method & Rauch–Tung–Striebel Smoother Filtering Method \\ \hline \hline \end{tabular}
\end{table}
Table 1: The configure parameters of the feasibility experiment.  
Figure 3 illustrates the displacement in the North direction over time, comprising a total of about 4700 h. The training dataset exhibits noise and displacement over approximately 3700 h, whereas the test dataset displays fewer outliers over about 930 h. This partitioning strategy aims to assess the prediction accuracy of the proposed CNN-GRU method in the presence of noise and displacement. This figure serves as a visual representation of the dataset's temporal characteristics and the delineation of training and validation subsets, essential for robust model development and evaluation in time series analysis tasks.  
In Figure 4, the change in the loss function during the training of the CNN-GRU model before and after data normalization is illustrated. Mean Squared Error (MSE) is  
Figure 3: Test dataset and training dataset of GNSS time series.  
Figure 2: **(a)** The monitoring station installed on the dam; **(b)** The base station installed on the roof of a building.  
selected as the loss function, which is the most commonly used evaluation metric for neural networks in regression problems. As depicted in the figure, before data normalization, both the training and testing sets exhibit large loss function values, slow convergence, and post-convergence oscillations. However, after data normalization, the loss function values for both sets decrease by two orders of magnitude, with faster convergence and no post-convergence oscillations observed. Additionally, the consistency between the training and testing sets is improved after convergence. In summary, data normalization plays a crucial role in enhancing the performance of the CNN-GRU neural network.  
To validate the performance of the proposed CNN-GRU method, the experimental section of this paper is divided into three parts. The first part consists of experiments on individual CNN and GRU models, aimed at analyzing the shortcomings of individual models. The second part is the experimental verification of the CNN-GRU model proposed in this paper, highlighting the advantages of the proposed model. The third part involves parameter-tuning experiments for the CNN-GRU model.