Predicting elevation values using Gated Recurrent Unit (GRU) neural networks

Abstract

This paper focuses on the development and evaluation of a GNSS height point prediction model based on the Gated Recurrent Unit (GRU), an advanced variant of recurrent neural networks designed for time series data. The input data consistsof height coordinate sequences (h) extracted from GNSS data processed at the CPHU station using the specialized Gamit/Globk software, achieving millimeter-level accuracy. Unlike many previous studies, the GRU model in this research was trained on the entire continuous data sequence without splitting it into separate training and testing sets. The prediction performance was assessed over the period from March 9th, 2022, to March 17th, 2022. The model was tested using two optimization algorithms, Adam and SGD, in combination with two commonly used loss functions, MSE and Huber. The performance of each configuration was evaluated using metrics including MSE, RMSE, MAE, and the coefficient of determination (R²). The results indicate that the GRU model combined with the Adam optimizer and MSE loss function yielded the best prediction performance, with an R² value of approximately 0.54 and an MAE of 4.24 mm. In contrast, using SGD and Huber led to a significant decrease in performance, with R² values ranging from only 0.33÷0.42. Additionally, the size of the sliding window (lag) also influenced the model's predictive capability: a smaller window size (lag = 10) allowed the model to better adapt to noisy dat