Zenith Tropospheric Delay (ZTD) is a significant source of atmospheric error in the Global Navigation Satellite System (GNSS). Developing a high-accuracy ZTD prediction model is essential for both GNSS positioning and GNSS meteorology. To address the challenges of incomplete information extraction and gradient explosion present in current single and combined neural network models that utilize serial ensemble learning, this study proposes a VMD-Informer-BiLSTM-EAA hybrid model based on a parallel ensemble learning strategy. Additionally, it takes into account the non-stationarity of the ZTD sequence. The model employs the Variational Mode Decomposition (VMD) method to address the non-stationarity of ZTD. It utilizes both the informer and Bidirectional Long Short-Term Memory (BiLSTM) architectures to learn ZTD data in parallel, effectively capturing both long-term trends and short-term dynamic changes. The features are then fused using the Efficient Additive Attention (EAA) mechanism, which assigns weights to create a more comprehensive representation of the ZTD data. This enhanced representation ultimately leads to improved predictions of ZTD values. We fill in the missing parts of the GNSS-derived ZTD using the ZTD data from ERA5, sourced from the IGS stations in the Australian region, specifically at 12 IGS stations. These interpolated data are then used to develop a VMD-Informer-BiLSTM-EAA hybrid model for ZTD predictions with a one-year forecast horizon. We applied this model to predict the ZTD for each IGS station in our study area for the year 2021. The numerical results indicate that our model outperforms several comparative models, such as VMD–Informer, Transformer, BiLSTM and GPT3, based on the following key metrics: a Root Mean Square Error (RMSE) of 1.43 cm, a Mean Absolute Error (MAE) of 1.15 cm, a Standard Deviation (STD) of 1.33 cm and a correlation coefficient (R) of 0.96. Furthermore, our model reduces the training time by 8.2% compared to the Transformer model, demonstrating superior prediction performance and robustness in long-term ZTD forecasting. This study introduces a novel approach for high-accuracy ZTD modeling, which is significantly beneficial for precise GNSS positioning and the detection of water vapor content.

Inferring geographic locations via social posts is essential for many practical location-based applications such as product marketing, point-of-interest recommendation, and infector tracking for COVID-19. Unlike image-based location retrieval or social-post text embedding-based location inference, the combined effect of multi-modal information (i.e., post images, text, and hashtags) for social post positioning receives less attention. In this work, we collect real datasets of social posts with images, texts, and hashtags from Instagram and propose a novel Multi-modal Representation Learning Framework (MRLF) capable of fusing different modalities of social posts for location inference. MRLF integrates a multi-head attention mechanism to enhance location-salient information extraction while significantly improving location inference compared with single domain-based methods. To overcome the noisy user-generated textual content, we introduce a novel attention-based character-aware module that considers the relative dependencies between characters of social post texts and hashtags for flexible multi-model information fusion. The experimental results show that MRLF can make accurate location predictions and open a new door to understanding the multi-modal data of social posts for online inference tasks.